{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solutions for Radial Schrodinger Equation for the Neutron-Proton System\n",
    "### Gabe Schumm\n",
    "### Due October 26th, 2023"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerov's Algorithm\n",
    "$U ''(x) = f(x)\\Psi (x) \\longrightarrow U ''_k = f_kU_k$\n",
    "\n",
    "\n",
    "$\\phi_k = U_k\\left(1 - \\frac{\\left(\\Delta r\\right)^2 f_k}{12}\\right)$\n",
    "\n",
    "$\\phi_{k+1} = 2\\phi_k - \\phi_{k-1} + \\left(\\Delta r\\right)^2f_kU_k$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Main.Program.System"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#module containg struct for this program\n",
    "module Program \n",
    "    mutable struct System\n",
    "        β::Float64 #energy parameter in fm^-2\n",
    "        E::Float64 #energy value in MeV\n",
    "\n",
    "        r_0::Float64 #minimum radial distance, U(r_0) = 0 in fm\n",
    "        a::Float64 #range parameters of Yukawa potential in fm\n",
    "        V_0::Float64 #streng of Yukawa potential in units of E\n",
    "\n",
    "        r_max::Float64 #maximum radial distance for integration\n",
    "        ∆r::Float64 #radial distance step\n",
    "       \n",
    "        n_total::Int64 #total number of integrations steps, determined by r_max - r_0 and ∆r\n",
    "        \n",
    "        r::Float64 #current position\n",
    "        #current values of phi_n\n",
    "        phi_0::Float64 #\n",
    "        phi_1::Float64\n",
    "        phi_2::Float64\n",
    "        \n",
    "        U::Vector{Float64} #U(r) wavefunction\n",
    "\n",
    "    end\n",
    "\n",
    "    function System(r_0, a, V_0, r_max, ∆r)\n",
    "        β = -0.053667\n",
    "        E = -2.226 \n",
    "        n_total = round(Int64, (r_max - r_0) / ∆r) + 1 #n_total must be odd for Simpsons rule integration\n",
    "        U = zeros(n_total)\n",
    "        System(β, E, r_0, a, V_0, r_max, ∆r, n_total, r_max, 0,0,0, U)\n",
    "    end\n",
    "\n",
    "end\n",
    "\n",
    "System = Program.System\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Yukawa Potential\n",
    "function V_Y(self, r)\n",
    "    return -self.V_0*abs(self.E) * exp(-r/self.a) * (self.a/r)\n",
    "end\n",
    "\n",
    "#Asumptotic form of U\n",
    "function U_asymp(self, r)\n",
    "    return exp(-sqrt(-self.β)*r)\n",
    "end\n",
    "\n",
    "#f function in second order diff. eq. for U(r)\n",
    "function f(self, r)\n",
    "    return self.β * ((V_Y(self, r)/self.E) - 1)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "initialize (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function initialize(self)\n",
    "    \n",
    "    #reset U, phi_2\n",
    "    self.U = zeros(self.n_total)\n",
    "    self.phi_2 = 0\n",
    "    \n",
    "    #set value of U at r = r_max first\n",
    "    self.U[self.n_total] = U_asymp(self, self.r_max)\n",
    "    #set corresponding vaue of phi_0\n",
    "    self.phi_0 = self.U[self.n_total] * (1-((self.∆r^2) * f(self, self.r_max) / 12))\n",
    "    \n",
    "    #set value of U at r = r_max - ∆r next\n",
    "    self.U[self.n_total-1] = U_asymp(self, self.r_max - self.∆r)\n",
    "    #set corresponding vaue of phi_1\n",
    "    self.phi_1 = self.U[self.n_total-1] * (1-((self.∆r^2) * f(self, self.r_max - self.∆r) / 12))\n",
    "    \n",
    "    #set radius for third integration step \n",
    "    self.r = self.r_max - self.∆r\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "U_integration (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#integrate U(r) from r_max to r_0\n",
    "function U_integration(self)\n",
    "    #initial f(r) value\n",
    "    f1 = f(self, self.r)\n",
    "    for n=1:self.n_total-2\n",
    "        \n",
    "        #calculate phi_2 using phi_1, phi_0, U_1\n",
    "        self.phi_2 = 2*self.phi_1 - self.phi_0 + ((self.∆r)^2 * f1 * self.U[self.n_total-n])\n",
    "        self.phi_0 = self.phi_1; self.phi_1 = self.phi_2\n",
    "        \n",
    "        #progress radial position\n",
    "        self.r -= self.∆r\n",
    "        \n",
    "        #calculate f for next integration step\n",
    "        f1 = f(self, self.r)\n",
    "        #store value of U(r) using recently updated phi_1 and position \n",
    "        \n",
    "        self.U[self.n_total-n-1] = self.phi_1/(1-((self.∆r)^2 * f1 / 12))\n",
    "        \n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "find_V0 (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#locate V_0 that satisfies boundary condition for given value of a\n",
    "function find_V0(self, ∆V, ϵ)\n",
    "    \n",
    "    #start with integration using initial V_0 and save U(r_0) as prev_U0\n",
    "    initialize(self)\n",
    "    U_integration(self)\n",
    "    prev_U0 = self.U[1]\n",
    "    \n",
    "    #changes to true when U(r_0) changes from positive/negative to negative/positive after changing V_0\n",
    "    pass_zero = false\n",
    "    \n",
    "    #increment V_0 by ∆V\n",
    "    self.V_0 += ∆V\n",
    "    \n",
    "    println(\"Locating Initial V_0.\")\n",
    "    flush(stdout)\n",
    "    println()\n",
    "    \n",
    "    while !pass_zero #increase V_0 until pass_zero condition satisfied\n",
    "        \n",
    "        initialize(self)\n",
    "        U_integration(self)\n",
    "        \n",
    "        #pass through zero condition for previous integration and current integration\n",
    "        if self.U[1]*prev_U0 < 0\n",
    "            #if true, exit while loop\n",
    "            pass_zero = true\n",
    "        else\n",
    "            #if not true, store U(r_0) and increment V_0\n",
    "            prev_U0 = self.U[1]\n",
    "            self.V_0 += ∆V\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    println(\"Initial V_0/|E| = \", self.V_0)\n",
    "    flush(stdout)\n",
    "    \n",
    "   \n",
    "    \n",
    "    #once pass through zero V_0 is found, start bisection routine\n",
    "    V_1 = self.V_0 - ∆V\n",
    "    V_2 = self.V_0\n",
    "    self.V_0 = (V_1 + V_2)/2\n",
    "    \n",
    "    println(\"Starting Bisection.\")\n",
    "    println()\n",
    "    \n",
    "    #track how many bisection steps taken\n",
    "    count = 0\n",
    "    \n",
    "    #run bisection rountine until change in U(r_0) is below given threshold ϵ\n",
    "    while abs(prev_U0-self.U[1]) > ϵ\n",
    "    #while abs(V_1-V_2) > ϵ\n",
    "\n",
    "        #store current U(r_0)\n",
    "        prev_U0 = self.U[1]\n",
    "        \n",
    "        #print count, V_0 bracket, and U(r_0)\n",
    "        println(count,\". \",V_1, \" \",V_2,\" \",self.V_0, \" \",prev_U0)\n",
    "        flush(stdout)\n",
    "        count+=1\n",
    "        \n",
    "        initialize(self)\n",
    "        U_integration(self)\n",
    "        \n",
    "        #if U(r_0) passes through zero, update lower V_0 bracket \n",
    "        if self.U[1]*prev_U0 < 0\n",
    "            V_1 = self.V_0\n",
    "            self.V_0 = (V_1 + V_2)/2\n",
    "        \n",
    "        #otherwise update upper V_0 bracket\n",
    "        else\n",
    "            V_2 = self.V_0\n",
    "            self.V_0 = (V_1 + V_2)/2\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    println()\n",
    "    println(\"After \", count, \" steps, convergent value found.\")\n",
    "    println(\"U(r_0) = \", self.U[1], \" for V_0/|E| = \", self.V_0)\n",
    "    flush(stdout)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "calculate_r (generic function with 1 method)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#calculate norm of R(r)^2 = U(r)/r by integrating from r_0 to r_max using Simpsons rule\n",
    "#note: this is integration in spherical coordinates so factor of r^2 must be included from the in Jacobian\n",
    "#|R(r)|^2 * (r^2 dr) =  |U(r)|^2 dr\n",
    "function calculate_norm(self)\n",
    "    #first term has weight of 1\n",
    "    I = (self.U[1])^2\n",
    "    power = 2\n",
    "    for n=2:self.n_total-1\n",
    "        #second term has weight of 4 = 2^2 and third term has weight of 2 = 2^1\n",
    "        I += 2^power * (self.U[n])^2\n",
    "        #recursive relation for p in 2^p gives 4, 2, 4, 2... pattern\n",
    "        power = 3 - power\n",
    "    end\n",
    "    #last term has weight of 1\n",
    "    I += (self.U[end])^2\n",
    "    \n",
    "    #multiply by intgration step divided by 3\n",
    "    return (self.∆r/3) * I\n",
    "end\n",
    "\n",
    "\n",
    "#calculate sqrt(1/4<r^2>) using Simpsons rule\n",
    "#r^2 * |R(r)|^2 * (r^2 dr) = r^2 * |U(r)|^2 dr\n",
    "function calculate_r(self)\n",
    "    norm = calculate_norm(self)\n",
    "    \n",
    "    I = (self.U[1] * self.r_0)^2 \n",
    "    power = 2\n",
    "    for n=2:self.n_total-1\n",
    "        #multiply by current r value\n",
    "        I += 2^power * (self.U[n]*(self.r_0 + (n-1)*self.∆r))^2\n",
    "        power = 3 - power\n",
    "    end\n",
    "    #println(power)\n",
    "    I += (self.U[end] * self.r_max)^2\n",
    "    I *= (self.∆r/3) / norm #divide by norm of R(r)\n",
    "    return sqrt(I/4)\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "export_r_V0 (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#routine to locate optimal V_0 for a given value of a\n",
    "#export a, V_0, √<r^2> to outfile f\n",
    "function export_r_V0(a, ∆r, r_max, file)\n",
    "    #start with \"quick and dirty\" run starting at V_0 = 0\n",
    "    \n",
    "    self = System(.1, a, 0, r_max, ∆r)\n",
    "    initialize(self)\n",
    "    find_V0(self, 1, .0001) #use larger ∆V and large cutoff ϵto get in the neighborhood of the true V_0\n",
    "    \n",
    "    println()\n",
    "    \n",
    "    #repeat with initial V_0 guess near the V_0 found above\n",
    "    V_0 = self.V_0-1 #ensure initial V_0 is less than optimal V_0\n",
    "    \n",
    "    self = System(.1, a, V_0, r_max, ∆r)\n",
    "    initialize(self)\n",
    "    find_V0(self, .001, .00000001) #use smaller ∆V and smaller cutoff ϵ \n",
    "    \n",
    "    #calculate mean value of \n",
    "    mean_r = calculate_r(self)\n",
    "    \n",
    "    println(file, a, \" \", round(mean_r, digits=5), \" \", round(self.V_0, digits=5))\n",
    "    return\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find $(a, V_0)$ pairs for given values of $a$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 237.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.0 237.0 236.5 -0.0012389610737520112\n",
      "1. 236.0 236.5 236.25 -0.00015402960848935756\n",
      "2. 236.25 236.5 236.375 0.00038963094477489186\n",
      "3. 236.25 236.375 236.3125 0.0001177010312898666\n",
      "4. 236.25 236.3125 236.28125 0.0002536410736933635\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.0003216297799901303 for V_0/|E| = 236.265625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 236.42962500000556\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.42862500000555 236.42962500000556 236.42912500000557 -1.0697671886619866e-6\n",
      "1. 236.42912500000557 236.42962500000556 236.42937500000556 1.720712739994327e-8\n",
      "2. 236.42937500000556 236.42962500000556 236.42950000000556 -5.262804529479043e-7\n",
      "3. 236.42937500000556 236.42950000000556 236.42943750000558 -7.980239680902179e-7\n",
      "4. 236.42937500000556 236.42943750000558 236.42940625000557 -6.621522003102255e-7\n",
      "5. 236.42937500000556 236.42940625000557 236.42939062500557 -5.94216320247077e-7\n",
      "6. 236.42937500000556 236.42939062500557 236.42938281250557 -5.602484108930523e-7\n",
      "7. 236.42937500000556 236.42938281250557 236.42937890625558 -5.43264431116794e-7\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -5.347723998248756e-7 for V_0/|E| = 236.42937695313057\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 158.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.0 158.0 157.5 -0.0007345920461599431\n",
      "1. 157.5 158.0 157.75 0.0008603892223421105\n",
      "2. 157.5 157.75 157.625 6.199179828757216e-5\n",
      "3. 157.5 157.625 157.5625 0.0004609636675281821\n",
      "4. 157.5 157.5625 157.53125 0.000660619716054514\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.000760490284699348 for V_0/|E| = 157.515625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 157.769625000006\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.76862500000598 157.769625000006 157.769125000006 -6.05598397132104e-7\n",
      "1. 157.769125000006 157.769625000006 157.769375000006 9.89101019882629e-7\n",
      "2. 157.769125000006 157.769375000006 157.769250000006 1.917504130434414e-7\n",
      "3. 157.769125000006 157.769250000006 157.769187500006 5.904254838865973e-7\n",
      "4. 157.769125000006 157.769187500006 157.769156250006 7.897632150766136e-7\n",
      "5. 157.769125000006 157.769156250006 157.769140625006 8.89432139098803e-7\n",
      "6. 157.769125000006 157.769140625006 157.769132812506 9.392665582121229e-7\n",
      "7. 157.769125000006 157.769132812506 157.76912890625601 9.641837800392926e-7\n",
      "8. 157.769125000006 157.76912890625601 157.769126953131 9.766424046757269e-7\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 9.828717019598432e-7 for V_0/|E| = 157.7691259765685\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 114.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.0 114.0 113.5 -0.003200846185412003\n",
      "1. 113.0 113.5 113.25 -0.001036782628654238\n",
      "2. 113.25 113.5 113.375 5.057408812709543e-5\n",
      "3. 113.375 113.5 113.4375 -0.0004935486985752905\n",
      "4. 113.375 113.4375 113.40625 -0.0007652767194206759\n",
      "5. 113.375 113.40625 113.390625 -0.0006294404793055202\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0005615015323583067 for V_0/|E| = 113.3828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 113.2618125000042\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.26081250000419 113.2618125000042 113.2613125000042 -8.835671932490241e-7\n",
      "1. 113.2613125000042 113.2618125000042 113.2615625000042 1.294373615323068e-6\n",
      "2. 113.2613125000042 113.2615625000042 113.2614375000042 2.0540142193209953e-7\n",
      "3. 113.2613125000042 113.2614375000042 113.2613750000042 7.498870850240896e-7\n",
      "4. 113.2613125000042 113.2613750000042 113.26134375000419 1.0221302585248493e-6\n",
      "5. 113.2613125000042 113.26134375000419 113.26132812500418 1.158251870177106e-6\n",
      "6. 113.2613125000042 113.26132812500418 113.26132031250418 1.2263127096286546e-6\n",
      "7. 113.2613125000042 113.26132031250418 113.2613164062542 1.260343184161892e-6\n",
      "8. 113.2613125000042 113.2613164062542 113.26131445312919 1.277358396205549e-6\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 1.285866001071752e-6 for V_0/|E| = 113.2613134765667\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 86.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.0 86.0 85.5 -0.002079095456042481\n",
      "1. 85.5 86.0 85.75 0.0007426189481487338\n",
      "2. 85.75 86.0 85.875 -0.0006713776783123051\n",
      "3. 85.75 85.875 85.8125 -0.0013760204350970024\n",
      "4. 85.75 85.8125 85.78125 -0.0010238951471301465\n",
      "5. 85.75 85.78125 85.765625 -0.0008476854507492384\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0007595438259668467 for V_0/|E| = 85.7578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 85.63181250000417\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.63081250000417 85.63181250000417 85.63131250000417 -3.6942657917428365e-6\n",
      "1. 85.63081250000417 85.63131250000417 85.63106250000416 -8.66603919694582e-7\n",
      "2. 85.63106250000416 85.63131250000417 85.63118750000416 5.472364257823195e-7\n",
      "3. 85.63118750000416 85.63131250000417 85.63125000000417 -1.5968451995036103e-7\n",
      "4. 85.63118750000416 85.63125000000417 85.63121875000417 -5.131444347394597e-7\n",
      "5. 85.63118750000416 85.63121875000417 85.63120312500416 -3.364145086634441e-7\n",
      "6. 85.63118750000416 85.63120312500416 85.63119531250416 -2.4804953521628654e-7\n",
      "7. 85.63118750000416 85.63119531250416 85.63119140625416 -2.0386701135664046e-7\n",
      "8. 85.63118750000416 85.63119140625416 85.63118945312917 -1.8177575142752405e-7\n",
      "9. 85.63118750000416 85.63118945312917 85.63118847656666 -1.7073010723539124e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -1.6520736107560578e-7 for V_0/|E| = 85.6311879882854\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 68.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.0 68.0 67.5 -0.005025140180003077\n",
      "1. 67.0 67.5 67.25 -0.0015274490240774709\n",
      "2. 67.25 67.5 67.375 0.00023674091134113302\n",
      "3. 67.375 67.5 67.4375 -0.0006466362710714488\n",
      "4. 67.375 67.4375 67.40625 -0.0010873629369958478\n",
      "5. 67.375 67.40625 67.390625 -0.0008670797094104209\n",
      "6. 67.375 67.390625 67.3828125 -0.0007568780206614092\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0007017621539892122 for V_0/|E| = 67.37890625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 67.28390625000432\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.28290625000432 67.28390625000432 67.28340625000432 -3.12885002932372e-6\n",
      "1. 67.28340625000432 67.28390625000432 67.28365625000433 4.0702733252523816e-7\n",
      "2. 67.28365625000433 67.28390625000432 67.28378125000432 -1.3609165174443864e-6\n",
      "3. 67.28365625000433 67.28378125000432 67.28371875000433 -2.2448845884596004e-6\n",
      "4. 67.28365625000433 67.28371875000433 67.28368750000433 -1.802900829783559e-6\n",
      "5. 67.28365625000433 67.28368750000433 67.28367187500433 -1.5819087432854386e-6\n",
      "6. 67.28365625000433 67.28367187500433 67.28366406250433 -1.4714126638579917e-6\n",
      "7. 67.28365625000433 67.28366406250433 67.28366015625433 -1.41616453464005e-6\n",
      "8. 67.28365625000433 67.28366015625433 67.28365820312933 -1.3885405106075995e-6\n",
      "9. 67.28365625000433 67.28365820312933 67.28365722656683 -1.37472849661337e-6\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -1.3678225111877803e-6 for V_0/|E| = 67.28365673828557\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 55.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.0 55.0 54.5 -0.004591842422900399\n",
      "1. 54.0 54.5 54.25 -0.0003327800008729877\n",
      "2. 54.25 54.5 54.375 0.0018203954369883106\n",
      "3. 54.25 54.375 54.3125 0.0007418304915889683\n",
      "4. 54.25 54.3125 54.28125 0.0012806181410641758\n",
      "5. 54.25 54.28125 54.265625 0.001550383018610023\n",
      "6. 54.25 54.265625 54.2578125 0.001685358277065587\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = 0.0017528691183543465 for V_0/|E| = 54.25390625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 54.461906249997185\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.46090624999719 54.461906249997185 54.46140624999718 -5.710888336605195e-6\n",
      "1. 54.46090624999719 54.46140624999718 54.46115624999719 -1.41550070096916e-6\n",
      "2. 54.46115624999719 54.46140624999718 54.461281249997185 7.322167629367567e-7\n",
      "3. 54.461281249997185 54.46140624999718 54.461343749997184 -3.416439124318422e-7\n",
      "4. 54.461281249997185 54.461343749997184 54.461312499997184 -8.785728437530148e-7\n",
      "5. 54.461281249997185 54.461312499997184 54.46129687499719 -6.101085344898969e-7\n",
      "6. 54.461281249997185 54.46129687499719 54.46128906249719 -4.7587627156366043e-7\n",
      "7. 54.461281249997185 54.46128906249719 54.461285156247186 -4.0876011065274153e-7\n",
      "8. 54.461281249997185 54.461285156247186 54.461283203122186 -3.7520200914127e-7\n",
      "9. 54.461281249997185 54.461283203122186 54.46128222655969 -3.5842298542346934e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -3.50033455182939e-7 for V_0/|E| = 54.46128173827844\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 46.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.0 46.0 45.5 -0.00869396031123247\n",
      "1. 45.0 45.5 45.25 -0.0037072839906535024\n",
      "2. 45.0 45.25 45.125 -0.0011795361014060694\n",
      "3. 45.125 45.25 45.1875 9.299241593169655e-5\n",
      "4. 45.1875 45.25 45.21875 -0.0005439946136648989\n",
      "5. 45.1875 45.21875 45.203125 -0.0008619459333814993\n",
      "6. 45.1875 45.203125 45.1953125 -0.0007030154320812497\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0006235163143091384 for V_0/|E| = 45.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 45.1344062499978\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.133406249997805 45.1344062499978 45.13390624999781 -2.9666118362325968e-6\n",
      "1. 45.13390624999781 45.1344062499978 45.1341562499978 2.1333754183607612e-6\n",
      "2. 45.1341562499978 45.1344062499978 45.1342812499978 -4.166297551129807e-7\n",
      "3. 45.1341562499978 45.1342812499978 45.1342187499978 -1.6916236912181793e-6\n",
      "4. 45.1341562499978 45.1342187499978 45.1341874999978 -1.054127469426855e-6\n",
      "5. 45.1341562499978 45.1341874999978 45.134171874997804 -7.353787729376352e-7\n",
      "6. 45.1341562499978 45.134171874997804 45.1341640624978 -5.760042986164928e-7\n",
      "7. 45.1341562499978 45.1341640624978 45.1341601562478 -4.963170483579457e-7\n",
      "8. 45.1341562499978 45.1341601562478 45.1341582031228 -4.564734181328211e-7\n",
      "9. 45.1341562499978 45.1341582031228 45.134157226560305 -4.365515891750728e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -4.2659064770544247e-7 for V_0/|E| = 45.13415673827905\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 39.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.0 39.0 38.5 -0.010180677026497924\n",
      "1. 38.0 38.5 38.25 -0.004398107569039491\n",
      "2. 38.0 38.25 38.125 -0.0014584135105923607\n",
      "3. 38.125 38.25 38.1875 2.3624838794390976e-5\n",
      "4. 38.1875 38.25 38.21875 -0.000718412937461726\n",
      "5. 38.1875 38.21875 38.203125 -0.0010886676747575107\n",
      "6. 38.1875 38.203125 38.1953125 -0.0009036039436896676\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0008110243530770242 for V_0/|E| = 38.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 38.12740624999782\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.12640624999782 38.12740624999782 38.126906249997816 -4.981360562725997e-6\n",
      "1. 38.126906249997816 38.12740624999782 38.12715624999782 9.625358557601962e-7\n",
      "2. 38.12715624999782 38.12740624999782 38.12728124999782 -2.0094286861625916e-6\n",
      "3. 38.12715624999782 38.12728124999782 38.12721874999782 -3.495398680663531e-6\n",
      "4. 38.12715624999782 38.12721874999782 38.12718749999782 -2.7524146391996613e-6\n",
      "5. 38.12715624999782 38.12718749999782 38.12717187499781 -2.380921963665686e-6\n",
      "6. 38.12715624999782 38.12717187499781 38.12716406249781 -2.195175376282608e-6\n",
      "7. 38.12715624999782 38.12716406249781 38.12716015624781 -2.1023020636436084e-6\n",
      "8. 38.12715624999782 38.12716015624781 38.12715820312282 -2.0558653820093166e-6\n",
      "9. 38.12715624999782 38.12715820312282 38.127157226560314 -2.032647052622366e-6\n",
      "10. 38.12715624999782 38.127157226560314 38.12715673827907 -2.0210378918007436e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -2.0152332440954984e-6 for V_0/|E| = 38.12715649413845\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 33.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.0 33.0 32.5 -0.003774088703140587\n",
      "1. 32.5 33.0 32.75 0.0030381084108908416\n",
      "2. 32.75 33.0 32.875 -0.00039025328969084555\n",
      "3. 32.75 32.875 32.8125 -0.0020877160032085006\n",
      "4. 32.75 32.8125 32.78125 -0.0012403734912012293\n",
      "5. 32.75 32.78125 32.765625 -0.0008156609261146925\n",
      "6. 32.75 32.765625 32.7578125 -0.0006030440323447052\n",
      "7. 32.75 32.7578125 32.75390625 -0.000496670397265541\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.0004434672780981286 for V_0/|E| = 32.751953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 32.72195312499862\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.72095312499862 32.72195312499862 32.72145312499862 -7.857546267006128e-6\n",
      "1. 32.72095312499862 32.72145312499862 32.721203124998624 -1.035376217402747e-6\n",
      "2. 32.721203124998624 32.72145312499862 32.72132812499862 2.37577573604287e-6\n",
      "3. 32.721203124998624 32.72132812499862 32.72126562499862 6.701941823355936e-7\n",
      "4. 32.721203124998624 32.72126562499862 32.72123437499862 1.522983547979194e-6\n",
      "5. 32.721203124998624 32.72123437499862 32.72121874999863 1.9493792912624014e-6\n",
      "6. 32.721203124998624 32.72121874999863 32.721210937498626 2.1625774472010783e-6\n",
      "7. 32.721203124998624 32.721210937498626 32.721207031248625 2.269176582120733e-6\n",
      "8. 32.721203124998624 32.721207031248625 32.721205078123624 2.3224761337187718e-6\n",
      "9. 32.721203124998624 32.721205078123624 32.72120410156113 2.3491259263743516e-6\n",
      "10. 32.721203124998624 32.72120410156113 32.721203613279876 2.3624508295041863e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.3691132829448204e-6 for V_0/|E| = 32.721203369139246\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 29.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.0 29.0 28.5 -0.008244760499647714\n",
      "1. 28.0 28.5 28.25 -0.0006516980933440038\n",
      "2. 28.25 28.5 28.375 0.003233256111964255\n",
      "3. 28.25 28.375 28.3125 0.0012833564125154739\n",
      "4. 28.25 28.3125 28.28125 0.002256446544409814\n",
      "5. 28.25 28.28125 28.265625 0.0027443858894529573\n",
      "6. 28.25 28.265625 28.2578125 0.0029887045773068547\n",
      "7. 28.25 28.2578125 28.25390625 0.003110951230865429\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00317209639193716 for V_0/|E| = 28.251953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 28.457953125001474\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.456953125001473 28.457953125001474 28.45745312500147 -2.4470313612695413e-6\n",
      "1. 28.45745312500147 28.457953125001474 28.457703125001473 5.283602807608351e-6\n",
      "2. 28.45745312500147 28.457703125001473 28.457578125001472 1.4182561041964683e-6\n",
      "3. 28.45745312500147 28.457578125001472 28.45751562500147 3.350922021632319e-6\n",
      "4. 28.45745312500147 28.45751562500147 28.45748437500147 4.317260573555831e-6\n",
      "5. 28.45745312500147 28.45748437500147 28.45746875000147 4.800431243115312e-6\n",
      "6. 28.45745312500147 28.45746875000147 28.457460937501473 5.042016869951334e-6\n",
      "7. 28.45745312500147 28.457460937501473 28.457457031251472 5.1628097745734125e-6\n",
      "8. 28.45745312500147 28.457457031251472 28.457455078126472 5.223206287816351e-6\n",
      "9. 28.45745312500147 28.457455078126472 28.45745410156397 5.253404536321518e-6\n",
      "10. 28.45745312500147 28.45745410156397 28.457453613282723 5.268503622112115e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 5.276053251599215e-6 for V_0/|E| = 28.457453369142097\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 26.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.0 26.0 25.5 -0.016220192320681524\n",
      "1. 25.0 25.5 25.25 -0.00799067342006825\n",
      "2. 25.0 25.25 25.125 -0.003763179898307725\n",
      "3. 25.0 25.125 25.0625 -0.001620911636531088\n",
      "4. 25.0 25.0625 25.03125 -0.0005426045902775437\n",
      "5. 25.0 25.03125 25.015625 -1.6525025192625165e-6\n",
      "6. 25.015625 25.03125 25.0234375 0.0002692738506806764\n",
      "7. 25.015625 25.0234375 25.01953125 0.000133773128437341\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00020151410163550803 for V_0/|E| = 25.017578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 25.03157812500124\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.030578125001238 25.03157812500124 25.031078125001237 -7.3387362764759855e-6\n",
      "1. 25.031078125001237 25.03157812500124 25.031328125001238 1.3260536601306558e-6\n",
      "2. 25.031328125001238 25.03157812500124 25.03145312500124 -3.006379715324381e-6\n",
      "3. 25.031328125001238 25.03145312500124 25.031390625001237 -5.172567605286206e-6\n",
      "4. 25.031328125001238 25.031390625001237 25.031359375001237 -4.089476071860413e-6\n",
      "5. 25.031328125001238 25.031359375001237 25.031343750001238 -3.5479285129774905e-6\n",
      "6. 25.031328125001238 25.031343750001238 25.03133593750124 -3.2771542789559166e-6\n",
      "7. 25.031328125001238 25.03133593750124 25.03133203125124 -3.141767035059967e-6\n",
      "8. 25.031328125001238 25.03133203125124 25.03133007812624 -3.07407335821088e-6\n",
      "9. 25.031328125001238 25.03133007812624 25.03132910156374 -3.04022654879775e-6\n",
      "10. 25.031328125001238 25.03132910156374 25.03132861328249 -3.0233031307067893e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -3.0148414389302523e-6 for V_0/|E| = 25.031328369141864\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 23.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.0 23.0 22.5 -0.014316319961286602\n",
      "1. 22.0 22.5 22.25 -0.005094542493988693\n",
      "2. 22.0 22.25 22.125 -0.0003392945688678908\n",
      "3. 22.125 22.25 22.1875 0.0020749154578611263\n",
      "4. 22.125 22.1875 22.15625 0.0008647467343511911\n",
      "5. 22.125 22.15625 22.140625 0.001469064049969934\n",
      "6. 22.125 22.140625 22.1328125 0.0017717978524519366\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7. 22.125 22.1328125 22.12890625 0.0019233086622469403\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0019991000596601563 for V_0/|E| = 22.126953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 22.23295312500135\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.23195312500135 22.23295312500135 22.23245312500135 -1.1498991744821913e-5\n",
      "1. 22.23195312500135 22.23245312500135 22.232203125001348 -1.8775913415364495e-6\n",
      "2. 22.232203125001348 22.23245312500135 22.23232812500135 2.9332556126365743e-6\n",
      "3. 22.232203125001348 22.23232812500135 22.232265625001347 5.278198850157063e-7\n",
      "4. 22.232203125001348 22.232265625001347 22.232234375001347 1.7305347187026093e-6\n",
      "5. 22.232203125001348 22.232234375001347 22.232218750001348 2.3318943470836335e-6\n",
      "6. 22.232203125001348 22.232218750001348 22.23221093750135 2.632574855986222e-6\n",
      "7. 22.232203125001348 22.23221093750135 22.23220703125135 2.782915131785639e-6\n",
      "8. 22.232203125001348 22.23220703125135 22.23220507812635 2.8580854034316347e-6\n",
      "9. 22.232203125001348 22.23220507812635 22.23220410156385 2.8956704685025443e-6\n",
      "10. 22.232203125001348 22.23220410156385 22.2322036132826 2.9144630854759707e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.9238593591820665e-6 for V_0/|E| = 22.232203369141974\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 20.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.0 20.0 19.5 -0.0018129506234044362\n",
      "1. 19.5 20.0 19.75 0.008946746032758036\n",
      "2. 19.5 19.75 19.625 0.003505171244120964\n",
      "3. 19.5 19.625 19.5625 0.006210424570330557\n",
      "4. 19.5 19.5625 19.53125 0.007574688924084649\n",
      "5. 19.5 19.53125 19.515625 0.008259741773086913\n",
      "6. 19.5 19.515625 19.5078125 0.008602999775035106\n",
      "7. 19.5 19.5078125 19.50390625 0.008774811846707623\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00886076367227075 for V_0/|E| = 19.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 19.914953125001727\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.913953125001726 19.914953125001727 19.914453125001728 -1.7545655907418293e-5\n",
      "1. 19.913953125001726 19.914453125001728 19.914203125001727 -6.948458790109698e-6\n",
      "2. 19.913953125001726 19.914203125001727 19.914078125001726 -1.649676682088154e-6\n",
      "3. 19.914078125001726 19.914203125001727 19.91414062500173 9.99760296757199e-7\n",
      "4. 19.91414062500173 19.914203125001727 19.914171875001728 -3.249619946192738e-7\n",
      "5. 19.91414062500173 19.914171875001728 19.914156250001728 -9.873203328405992e-7\n",
      "6. 19.91414062500173 19.914156250001728 19.91414843750173 -6.561414422182764e-7\n",
      "7. 19.91414062500173 19.91414843750173 19.91414453125173 -4.905517600048026e-7\n",
      "8. 19.91414062500173 19.91414453125173 19.91414257812673 -4.0775692966598455e-7\n",
      "9. 19.91414062500173 19.91414257812673 19.91414160156423 -3.663594469444599e-7\n",
      "10. 19.91414062500173 19.91414160156423 19.91414111328298 -3.456607732759449e-7\n",
      "11. 19.91414062500173 19.91414111328298 19.914140869142354 -3.3531138043914146e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.301366900156567e-7 for V_0/|E| = 19.91414074707204\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 18.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.0 18.0 17.5 -0.0006883619857411831\n",
      "1. 17.5 18.0 17.75 0.011170192393956639\n",
      "2. 17.5 17.75 17.625 0.005164522201486649\n",
      "3. 17.5 17.625 17.5625 0.008148116132828996\n",
      "4. 17.5 17.5625 17.53125 0.009654326023176198\n",
      "5. 17.5 17.53125 17.515625 0.010411049899538316\n",
      "6. 17.5 17.515625 17.5078125 0.010790318538035049\n",
      "7. 17.5 17.5078125 17.50390625 0.010980179778602736\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.011075167160061907 for V_0/|E| = 17.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.970953125001795\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.969953125001794 17.970953125001795 17.970453125001796 -1.610119932798524e-5\n",
      "1. 17.969953125001794 17.970453125001796 17.970203125001795 -4.511391258420149e-6\n",
      "2. 17.970203125001795 17.970453125001796 17.970328125001796 1.2837389796855507e-6\n",
      "3. 17.970328125001796 17.970453125001796 17.970390625001798 -1.6138449580371948e-6\n",
      "4. 17.970328125001796 17.970390625001798 17.9703593750018 -3.0626227986954056e-6\n",
      "5. 17.970328125001796 17.9703593750018 17.970343750001796 -2.3382350776161898e-6\n",
      "6. 17.970328125001796 17.970343750001796 17.970335937501794 -1.976040307750193e-6\n",
      "7. 17.970328125001796 17.970335937501794 17.970332031251793 -1.7949427105883248e-6\n",
      "8. 17.970328125001796 17.970332031251793 17.970330078126793 -1.7043938933503287e-6\n",
      "9. 17.970328125001796 17.970330078126793 17.970329101564296 -1.6591194312288941e-6\n",
      "10. 17.970328125001796 17.970329101564296 17.970328613283044 -1.6364822100166304e-6\n",
      "11. 17.970328125001796 17.970328613283044 17.970328369142422 -1.6251635940774955e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.6195042868115692e-6 for V_0/|E| = 17.97032824707211\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.0 17.0 16.5 -0.016404328052216772\n",
      "1. 16.0 16.5 16.25 -0.004424289462044077\n",
      "2. 16.25 16.5 16.375 0.0018359041876054225\n",
      "3. 16.375 16.5 16.4375 -0.001317024782977257\n",
      "4. 16.375 16.4375 16.40625 -0.0028763411741483066\n",
      "5. 16.375 16.40625 16.390625 -0.0020981069839088634\n",
      "6. 16.375 16.390625 16.3828125 -0.001707922259311673\n",
      "7. 16.375 16.3828125 16.37890625 -0.0015125626619597282\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.0014148160135595245 for V_0/|E| = 16.376953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 16.322953125000048\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.321953125000046 16.322953125000048 16.322453125000045 -9.79439575258013e-6\n",
      "1. 16.322453125000045 16.322953125000048 16.322703125000046 2.802288923602939e-6\n",
      "2. 16.322703125000046 16.322953125000048 16.322828125000047 -3.4961451258115677e-6\n",
      "3. 16.322703125000046 16.322828125000047 16.322765625000045 -6.645293338677517e-6\n",
      "4. 16.322703125000046 16.322765625000045 16.322734375000046 -5.070724955754077e-6\n",
      "5. 16.322703125000046 16.322734375000046 16.322718750000046 -4.283436381485552e-6\n",
      "6. 16.322703125000046 16.322718750000046 16.322710937500048 -3.88979110652493e-6\n",
      "7. 16.322703125000046 16.322710937500048 16.322707031250047 -3.692968179710623e-6\n",
      "8. 16.322703125000046 16.322707031250047 16.322705078125047 -3.5945566483683866e-6\n",
      "9. 16.322703125000046 16.322705078125047 16.322704101562547 -3.545350916652541e-6\n",
      "10. 16.322703125000046 16.322704101562547 16.3227036132813 -3.5207480106411204e-6\n",
      "11. 16.322703125000046 16.3227036132813 16.322703369140672 -3.508446530542654e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.5022958014133773e-6 for V_0/|E| = 16.322703247070358\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 15.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.0 15.0 14.5 -0.0023714526703757354\n",
      "1. 14.5 15.0 14.75 0.011532907286490686\n",
      "2. 14.5 14.75 14.625 0.004469283832968778\n",
      "3. 14.5 14.625 14.5625 0.007972974558632101\n",
      "4. 14.5 14.5625 14.53125 0.009745877962932595\n",
      "5. 14.5 14.53125 14.515625 0.010637622783993963\n",
      "6. 14.5 14.515625 14.5078125 0.01108482206176084\n",
      "7. 14.5 14.5078125 14.50390625 0.011308753866509131\n",
      "8. 14.5 14.50390625 14.501953125 0.01142080286655202\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.011476848148072672 for V_0/|E| = 14.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.912976562499217\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.911976562499218 14.912976562499217 14.912476562499219 -1.5265279927147885e-5\n",
      "1. 14.911976562499218 14.912476562499219 14.912226562499217 -1.6507007138778964e-6\n",
      "2. 14.912226562499217 14.912476562499219 14.912351562499218 5.156919274512e-6\n",
      "3. 14.912226562499217 14.912351562499218 14.912289062499218 1.7530816959309123e-6\n",
      "4. 14.912226562499217 14.912289062499218 14.912257812499217 3.454993589339781e-6\n",
      "5. 14.912226562499217 14.912257812499217 14.912242187499217 4.305954712186267e-6\n",
      "6. 14.912226562499217 14.912242187499217 14.912234374999217 4.731436504831184e-6\n",
      "7. 14.912226562499217 14.912234374999217 14.912230468749218 4.944177781902103e-6\n",
      "8. 14.912226562499217 14.912230468749218 14.912228515624218 5.050548450007989e-6\n",
      "9. 14.912226562499217 14.912228515624218 14.912227539061718 5.103733870781666e-6\n",
      "10. 14.912226562499217 14.912227539061718 14.912227050780468 5.13032657887366e-6\n",
      "11. 14.912226562499217 14.912227050780468 14.912226806639843 5.143622908732691e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 5.1502710770870755e-6 for V_0/|E| = 14.91222668456953\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.0 14.0 13.5 -0.008735317960566117\n",
      "1. 13.5 14.0 13.75 0.0057948989553777\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2. 13.75 14.0 13.875 -0.0016004726392254737\n",
      "3. 13.75 13.875 13.8125 -0.005200124244863601\n",
      "4. 13.75 13.8125 13.78125 -0.0034083975853466415\n",
      "5. 13.75 13.78125 13.765625 -0.0025064651537831354\n",
      "6. 13.75 13.765625 13.7578125 -0.002053977064936429\n",
      "7. 13.75 13.7578125 13.75390625 -0.001827351976518818\n",
      "8. 13.75 13.75390625 13.751953125 -0.0017139440992741102\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0016572163184180224 for V_0/|E| = 13.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.695976562499476\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.694976562499477 13.695976562499476 13.695476562499476 -2.4630813028671734e-5\n",
      "1. 13.694976562499477 13.695476562499476 13.695226562499476 -9.989026854584417e-6\n",
      "2. 13.694976562499477 13.695226562499476 13.695101562499477 -2.667741277331015e-6\n",
      "3. 13.695101562499477 13.695226562499476 13.695164062499476 9.929997057677764e-7\n",
      "4. 13.695164062499476 13.695226562499476 13.695195312499475 -8.37378940512093e-7\n",
      "5. 13.695164062499476 13.695195312499475 13.695179687499476 -1.7525621465277029e-6\n",
      "6. 13.695164062499476 13.695179687499476 13.695171874999476 -1.2949710554080497e-6\n",
      "7. 13.695164062499476 13.695171874999476 13.695167968749477 -1.0661751664304801e-6\n",
      "8. 13.695164062499476 13.695167968749477 13.695166015624476 -9.517770756516436e-7\n",
      "9. 13.695164062499476 13.695166015624476 13.695165039061976 -8.945780372239132e-7\n",
      "10. 13.695164062499476 13.695165039061976 13.695164550780726 -8.659784545427383e-7\n",
      "11. 13.695164062499476 13.695164550780726 13.695164306640102 -8.516787389226369e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -8.445288628844033e-7 for V_0/|E| = 13.695164184569789\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.0 13.0 12.5 -0.011085944162261326\n",
      "1. 12.5 13.0 12.75 0.004316054964252294\n",
      "2. 12.75 13.0 12.875 -0.003537393493586828\n",
      "3. 12.75 12.875 12.8125 -0.0073493464351087985\n",
      "4. 12.75 12.8125 12.78125 -0.005452843411645729\n",
      "5. 12.75 12.78125 12.765625 -0.004497493594670509\n",
      "6. 12.75 12.765625 12.7578125 -0.004018038178703832\n",
      "7. 12.75 12.7578125 12.75390625 -0.0037778646011125488\n",
      "8. 12.75 12.75390625 12.751953125 -0.0036576662518746843\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0035975391754816044 for V_0/|E| = 12.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.636976562499509\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.63597656249951 12.636976562499509 12.63647656249951 -2.5079404163490468e-5\n",
      "1. 12.63597656249951 12.63647656249951 12.636226562499509 -9.402007897082415e-6\n",
      "2. 12.63597656249951 12.636226562499509 12.636101562499508 -1.5628476461053408e-6\n",
      "3. 12.636101562499508 12.636226562499509 12.636164062499509 2.356848032007752e-6\n",
      "4. 12.636101562499508 12.636164062499509 12.636132812499508 3.969905673931512e-7\n",
      "5. 12.636101562499508 12.636132812499508 12.636117187499508 1.3769168747839664e-6\n",
      "6. 12.636101562499508 12.636117187499508 12.636109374999508 1.866881852700025e-6\n",
      "7. 12.636101562499508 12.636109374999508 12.63610546874951 2.1118648171831487e-6\n",
      "8. 12.636101562499508 12.63610546874951 12.636103515624509 2.2343563641792993e-6\n",
      "9. 12.636101562499508 12.636103515624509 12.636102539062009 2.2956022031985133e-6\n",
      "10. 12.636101562499508 12.636102539062009 12.636102050780758 2.326225056917792e-6\n",
      "11. 12.636101562499508 12.636102050780758 12.636101806640134 2.3415365455849676e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 2.3491922718680774e-6 for V_0/|E| = 12.636101684569821\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.0 12.0 11.5 -0.00950688925736767\n",
      "1. 11.5 12.0 11.75 0.007097577450331145\n",
      "2. 11.75 12.0 11.875 -0.0013836781869773025\n",
      "3. 11.75 11.875 11.8125 -0.005489481100561716\n",
      "4. 11.75 11.8125 11.78125 -0.0034476983661856906\n",
      "5. 11.75 11.78125 11.765625 -0.0024184766639452292\n",
      "6. 11.75 11.765625 11.7578125 -0.001901775612840585\n",
      "7. 11.75 11.7578125 11.75390625 -0.0016429015831631534\n",
      "8. 11.75 11.75390625 11.751953125 -0.0015133335729765598\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.001448516804048013 for V_0/|E| = 11.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.708976562499469\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.70797656249947 11.708976562499469 11.70847656249947 -1.6751489395583296e-5\n",
      "1. 11.70797656249947 11.70847656249947 11.708226562499469 -3.154488055483494e-8\n",
      "2. 11.708226562499469 11.70847656249947 11.70835156249947 8.328966597022136e-6\n",
      "3. 11.708226562499469 11.70835156249947 11.70828906249947 4.148665926242919e-6\n",
      "4. 11.708226562499469 11.70828906249947 11.708257812499468 6.238805036721588e-6\n",
      "5. 11.708226562499469 11.708257812499468 11.708242187499469 7.283883028651243e-6\n",
      "6. 11.708226562499469 11.708242187499469 11.708234374999469 7.806424072616866e-6\n",
      "7. 11.708226562499469 11.708234374999469 11.70823046874947 8.067695199863416e-6\n",
      "8. 11.708226562499469 11.70823046874947 11.70822851562447 8.198330854395044e-6\n",
      "9. 11.708226562499469 11.70822851562447 11.70822753906197 8.263648726259789e-6\n",
      "10. 11.708226562499469 11.70822753906197 11.70822705078072 8.296307671961343e-6\n",
      "11. 11.708226562499469 11.70822705078072 11.708226806640095 8.312637148607946e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 8.320801895493785e-6 for V_0/|E| = 11.708226684569782\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.0038485832240026828\n",
      "1. 10.5 11.0 10.75 0.014394268462318935\n",
      "2. 10.5 10.75 10.625 0.0050614937986439455\n",
      "3. 10.5 10.625 10.5625 0.009674325294426554\n",
      "4. 10.5 10.5625 10.53125 0.012020817311683505\n",
      "5. 10.5 10.53125 10.515625 0.013204161620427967\n",
      "6. 10.5 10.515625 10.5078125 0.01379836829979438\n",
      "7. 10.5 10.5078125 10.50390625 0.01409610651739011\n",
      "8. 10.5 10.50390625 10.501953125 0.014245134501601805\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.014319688232150784 for V_0/|E| = 10.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.89097656249923\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.88997656249923 10.89097656249923 10.89047656249923 -1.4195237688931465e-5\n",
      "1. 10.89047656249923 10.89097656249923 10.89072656249923 3.5715545780120287e-6\n",
      "2. 10.89072656249923 10.89097656249923 10.890851562499229 -5.312049746295982e-6\n",
      "3. 10.89072656249923 10.890851562499229 10.89078906249923 -9.753695805876071e-6\n",
      "4. 10.89072656249923 10.89078906249923 10.890757812499231 -7.532885747032147e-6\n",
      "5. 10.89072656249923 10.890757812499231 10.890742187499232 -6.42247102728325e-6\n",
      "6. 10.89072656249923 10.890742187499232 10.89073437499923 -5.867261145537353e-6\n",
      "7. 10.89072656249923 10.89073437499923 10.89073046874923 -5.589655643744818e-6\n",
      "8. 10.89072656249923 10.89073046874923 10.890728515624229 -5.450852724493855e-6\n",
      "9. 10.89072656249923 10.890728515624229 10.890727539061729 -5.381451261909152e-6\n",
      "10. 10.89072656249923 10.890727539061729 10.89072705078048 -5.346750512366837e-6\n",
      "11. 10.89072656249923 10.89072705078048 10.890726806639854 -5.329400125792208e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -5.3207249230931055e-6 for V_0/|E| = 10.890726684569543\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.028833152766864788\n",
      "1. 10.0 10.5 10.25 -0.012173490004784033\n",
      "2. 10.0 10.25 10.125 -0.003160708534957201\n",
      "3. 10.125 10.25 10.1875 0.0015224591796706482\n",
      "4. 10.1875 10.25 10.21875 -0.0008340390183809928\n",
      "5. 10.1875 10.21875 10.203125 -0.0020010885589814443\n",
      "6. 10.1875 10.203125 10.1953125 -0.0014184942067532744\n",
      "7. 10.1875 10.1953125 10.19140625 -0.0011264994326035428\n",
      "8. 10.1875 10.19140625 10.189453125 -0.0009803274575316972\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0009071977993408525 for V_0/|E| = 10.1884765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.165476562499459\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.164476562499459 10.165476562499459 10.164976562499458 -7.082893360069511e-6\n",
      "1. 10.164976562499458 10.165476562499459 10.165226562499459 1.1734636405628765e-5\n",
      "2. 10.164976562499458 10.165226562499459 10.165101562499459 2.3256322728910147e-6\n",
      "3. 10.164976562499458 10.165101562499459 10.165039062499458 7.030074494370143e-6\n",
      "4. 10.164976562499458 10.165039062499458 10.165007812499457 9.382340503189258e-6\n",
      "5. 10.164976562499458 10.165007812499457 10.164992187499458 1.0558484686203292e-5\n",
      "6. 10.164976562499458 10.164992187499458 10.164984374999458 1.1146559678371681e-5\n",
      "7. 10.164976562499458 10.164984374999458 10.164980468749459 1.1440597807983079e-5\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8. 10.164976562499458 10.164980468749459 10.164978515624458 1.1587617092505792e-5\n",
      "9. 10.164976562499458 10.164978515624458 10.164977539061958 1.1661126707577997e-5\n",
      "10. 10.164976562499458 10.164977539061958 10.164977050780708 1.1697881570853774e-5\n",
      "11. 10.164976562499458 10.164977050780708 10.164976806640084 1.171625900208613e-5\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 1.17254477273131e-5 for V_0/|E| = 10.16497668456977\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.0 10.0 9.5 -0.018134393155727763\n",
      "1. 9.5 10.0 9.75 0.0007444962428795427\n",
      "2. 9.75 10.0 9.875 -0.008960179065520792\n",
      "3. 9.75 9.875 9.8125 -0.01361252504895846\n",
      "4. 9.75 9.8125 9.78125 -0.011302794400382564\n",
      "5. 9.75 9.78125 9.765625 -0.010135613980328256\n",
      "6. 9.75 9.765625 9.7578125 -0.009548930422751432\n",
      "7. 9.75 9.7578125 9.75390625 -0.009254813480445915\n",
      "8. 9.75 9.75390625 9.751953125 -0.009107560989735421\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.00903388621094351 for V_0/|E| = 9.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.518976562499574\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.517976562499575 9.518976562499574 9.518476562499576 -1.114160040545235e-5\n",
      "1. 9.518476562499576 9.518976562499574 9.518726562499575 8.727746184038547e-6\n",
      "2. 9.518726562499575 9.518976562499574 9.518851562499574 -1.207200360531626e-6\n",
      "3. 9.518726562499575 9.518851562499574 9.518789062499575 -6.174468675360936e-6\n",
      "4. 9.518726562499575 9.518789062499575 9.518757812499576 -3.690851559276301e-6\n",
      "5. 9.518726562499575 9.518757812499576 9.518742187499576 -2.4490302526486945e-6\n",
      "6. 9.518726562499575 9.518742187499576 9.518734374999575 -1.8281164231013266e-6\n",
      "7. 9.518726562499575 9.518734374999575 9.518730468749574 -1.5176586627282333e-6\n",
      "8. 9.518726562499575 9.518730468749574 9.518728515624574 -1.362429580679424e-6\n",
      "9. 9.518726562499575 9.518728515624574 9.518727539062073 -1.284814943365087e-6\n",
      "10. 9.518726562499575 9.518727539062073 9.518727050780825 -1.2460076726101224e-6\n",
      "11. 9.518726562499575 9.518727050780825 9.518726806640199 -1.2266040187429919e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.2169021764343714e-6 for V_0/|E| = 9.518726684569888\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.0025160507024429694\n",
      "1. 8.5 9.0 8.75 0.019366515298550862\n",
      "2. 8.5 8.75 8.625 0.008106840063572459\n",
      "3. 8.5 8.625 8.5625 0.01365570740250968\n",
      "4. 8.5 8.5625 8.53125 0.016490695361633775\n",
      "5. 8.5 8.53125 8.515625 0.017923479536327322\n",
      "6. 8.5 8.515625 8.5078125 0.018643713236980428\n",
      "7. 8.5 8.5078125 8.50390625 0.01900479288066906\n",
      "8. 8.5 8.50390625 8.501953125 0.019185573700121736\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.019276024396652137 for V_0/|E| = 8.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.939976562499647\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.938976562499647 8.939976562499647 8.939476562499646 -2.2485598894329317e-5\n",
      "1. 8.938976562499647 8.939476562499646 8.939226562499647 -1.5642530979184812e-6\n",
      "2. 8.939226562499647 8.939476562499646 8.939351562499645 8.897350230487186e-6\n",
      "3. 8.939226562499647 8.939351562499645 8.939289062499647 3.666470996853399e-6\n",
      "4. 8.939226562499647 8.939289062499647 8.939257812499648 6.28189119183578e-6\n",
      "5. 8.939226562499647 8.939257812499648 8.939242187499648 7.589615880295302e-6\n",
      "6. 8.939226562499647 8.939242187499648 8.939234374999646 8.243481798314829e-6\n",
      "7. 8.939226562499647 8.939234374999646 8.939230468749646 8.57041574250207e-6\n",
      "8. 8.939226562499647 8.939230468749646 8.939228515624645 8.733882877223692e-6\n",
      "9. 8.939226562499647 8.939228515624645 8.939227539062145 8.815616515746084e-6\n",
      "10. 8.939226562499647 8.939227539062145 8.939227050780897 8.85648336119025e-6\n",
      "11. 8.939226562499647 8.939227050780897 8.93922680664027 8.876916829216868e-6\n",
      "12. 8.939226562499647 8.93922680664027 8.93922668456996 8.887133514647141e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 8.892241873942459e-6 for V_0/|E| = 8.939226623534804\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.02373068738070887\n",
      "1. 8.0 8.5 8.25 -0.003559586928037163\n",
      "2. 8.25 8.5 8.375 0.007550889616967234\n",
      "3. 8.25 8.375 8.3125 0.0019075570826918805\n",
      "4. 8.25 8.3125 8.28125 0.004706994716079075\n",
      "5. 8.25 8.28125 8.265625 0.006123359221954606\n",
      "6. 8.25 8.265625 8.2578125 0.006835725450493902\n",
      "7. 8.25 8.2578125 8.25390625 0.007192957386773207\n",
      "8. 8.25 8.25390625 8.251953125 0.007371835914535538\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.007461340862510628 for V_0/|E| = 8.2509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.418976562500019\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.41797656250002 8.418976562500019 8.418476562500018 -3.5773487126604006e-5\n",
      "1. 8.41797656250002 8.418476562500018 8.418226562500019 -1.3800443903760756e-5\n",
      "2. 8.41797656250002 8.418226562500019 8.41810156250002 -2.812872091743959e-6\n",
      "3. 8.41810156250002 8.418226562500019 8.418164062500018 2.6811764379112052e-6\n",
      "4. 8.418164062500018 8.418226562500019 8.418195312500018 -6.586971267134227e-8\n",
      "5. 8.418164062500018 8.418195312500018 8.418179687500018 -1.439376416895915e-6\n",
      "6. 8.418164062500018 8.418179687500018 8.418171875000018 -7.526243858650717e-7\n",
      "7. 8.418164062500018 8.418171875000018 8.41816796875002 -4.0924741077557446e-7\n",
      "8. 8.418164062500018 8.41816796875002 8.418166015625019 -2.375586599727412e-7\n",
      "9. 8.418164062500018 8.418166015625019 8.418165039062519 -1.517142559038923e-7\n",
      "10. 8.418164062500018 8.418165039062519 8.418164550781269 -1.087919675538932e-7\n",
      "11. 8.418164062500018 8.418164550781269 8.418164306640644 -8.733086589326041e-8\n",
      "12. 8.418164062500018 8.418164306640644 8.418164184570331 -7.660031369323214e-8\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -7.123495043646458e-8 for V_0/|E| = 8.418164123535174\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.002418695911512759\n",
      "1. 7.5 8.0 7.75 0.021880604521835018\n",
      "2. 7.5 7.75 7.625 0.009325192172094697\n",
      "3. 7.5 7.625 7.5625 0.015499440483839402\n",
      "4. 7.5 7.5625 7.53125 0.018663902655826806\n",
      "5. 7.5 7.53125 7.515625 0.02026569150174342\n",
      "6. 7.5 7.515625 7.5078125 0.021071503461692998\n",
      "7. 7.5 7.5078125 7.50390625 0.021475642349894727\n",
      "8. 7.5 7.50390625 7.501953125 0.021678020462277722\n",
      "9. 7.5 7.501953125 7.5009765625 0.021779286740792228\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = 0.02182993919246541 for V_0/|E| = 7.50048828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.947488281250483\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.946488281250483 7.947488281250483 7.9469882812504835 -1.767306080581602e-5\n",
      "1. 7.9469882812504835 7.947488281250483 7.947238281250483 5.354998250184006e-6\n",
      "2. 7.947238281250483 7.947488281250483 7.9473632812504835 -6.1594244678255825e-6\n",
      "3. 7.947238281250483 7.9473632812504835 7.947300781250483 -1.191634093289196e-5\n",
      "4. 7.947238281250483 7.947300781250483 7.947269531250483 -9.037907271108708e-6\n",
      "5. 7.947238281250483 7.947269531250483 7.947253906250483 -7.598672044487275e-6\n",
      "6. 7.947238281250483 7.947253906250483 7.947246093750483 -6.879049757118318e-6\n",
      "7. 7.947238281250483 7.947246093750483 7.947242187500483 -6.519237448790677e-6\n",
      "8. 7.947238281250483 7.947242187500483 7.947240234375483 -6.339331071877349e-6\n",
      "9. 7.947238281250483 7.947240234375483 7.947239257812983 -6.249377772190365e-6\n",
      "10. 7.947238281250483 7.947239257812983 7.947238769531733 -6.204401134324987e-6\n",
      "11. 7.947238281250483 7.947238769531733 7.947238525391108 -6.181912768918863e-6\n",
      "12. 7.947238281250483 7.947238525391108 7.947238403320796 -6.170668636257256e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -6.165046586026463e-6 for V_0/|E| = 7.947238342285639\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.02154970954105787\n",
      "1. 7.5 8.0 7.75 0.0009553263377593351\n",
      "2. 7.75 8.0 7.875 -0.010719646439300777\n",
      "3. 7.75 7.875 7.8125 -0.016238017950871875\n",
      "4. 7.75 7.8125 7.78125 -0.013504948607936983\n",
      "5. 7.75 7.78125 7.765625 -0.012118862048003028\n",
      "6. 7.75 7.765625 7.7578125 -0.011420899817664915\n",
      "7. 7.75 7.7578125 7.75390625 -0.01107068507835919\n",
      "8. 7.75 7.75390625 7.751953125 -0.010895268815874463\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.010807483400581287 for V_0/|E| = 7.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.519976562500257\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.5189765625002565 7.519976562500257 7.519476562500257 -9.501928103180688e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. 7.519476562500257 7.519976562500257 7.5197265625002565 1.4578525855968806e-5\n",
      "2. 7.519476562500257 7.5197265625002565 7.519601562500257 2.5378593551019653e-6\n",
      "3. 7.519476562500257 7.519601562500257 7.519539062500257 8.558082730201755e-6\n",
      "4. 7.519476562500257 7.519539062500257 7.519507812500257 1.156827682372279e-5\n",
      "5. 7.519476562500257 7.519507812500257 7.519492187500257 1.3073394432935547e-5\n",
      "6. 7.519476562500257 7.519492187500257 7.519484375000257 1.3825958416506791e-5\n",
      "7. 7.519476562500257 7.519484375000257 7.519480468750257 1.4202241651826584e-5\n",
      "8. 7.519476562500257 7.519480468750257 7.5194785156252575 1.4390383609074901e-5\n",
      "9. 7.519476562500257 7.5194785156252575 7.519477539062757 1.4484454737646153e-5\n",
      "10. 7.519476562500257 7.519477539062757 7.519477050781507 1.4531490256516988e-5\n",
      "11. 7.519476562500257 7.519477050781507 7.519476806640882 1.4555008044977826e-5\n",
      "12. 7.519476562500257 7.519476806640882 7.51947668457057 1.4566766897104532e-5\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 1.4572646303829127e-5 for V_0/|E| = 7.519476623535414\n"
     ]
    }
   ],
   "source": [
    "a_values = .5:.1:3\n",
    "\n",
    "open(\"vr.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .001, 30, file)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing $\\Delta_r$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing $V_0$ vs. $a$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_values = .5:.1:3\n",
    "\n",
    "open(\"vr_.0001.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .0001, 30, file)\n",
    "    end\n",
    "end\n",
    "\n",
    "open(\"vr_.001.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .001, 30, file)\n",
    "    end\n",
    "end\n",
    "\n",
    "open(\"vr_.01.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .01, 30, file)\n",
    "    end\n",
    "end\n",
    "\n",
    "open(\"vr_.1.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .1, 30, file)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing $U(r)$ vs. $r$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0001\n",
      "0.001\n",
      "0.01\n"
     ]
    }
   ],
   "source": [
    "a = 1.3\n",
    "V_0 = 32.7212\n",
    "\n",
    "self_10_4 = System(.1, a, V_0, 30, .0001)#System(r_0, a, V_0, r_max, ∆r, ∆V)\n",
    "initialize(self_10_4)\n",
    "U_integration(self_10_4)\n",
    "\n",
    "r_10_4 = collect(self_10_4.r_0:self_10_4.∆r:self_10_4.r_max)\n",
    "\n",
    "open(\"U_deltar_.0001.dat\", \"w\") do file\n",
    "    for i=1:length(r_10_4)\n",
    "        println(file, r_10_4[i], \" \", self_10_4.U[i])\n",
    "    end\n",
    "end\n",
    "\n",
    "self_10_3 = System(.1, a, V_0, 30, .001)#System(r_0, a, V_0, r_max, ∆r, ∆V)\n",
    "initialize(self_10_3)\n",
    "U_integration(self_10_3)\n",
    "\n",
    "r_10_3 = collect(self_10_3.r_0:self_10_3.∆r:self_10_3.r_max)\n",
    "\n",
    "open(\"U_deltar_.001.dat\", \"w\") do file\n",
    "    for i=1:length(r_10_3)\n",
    "        println(file, r_10_3[i], \" \", self_10_3.U[i])\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "self_10_2 = System(.1, a, V_0, 30, .01)#System(r_0, a, V_0, r_max, ∆r, ∆V)\n",
    "initialize(self_10_2)\n",
    "U_integration(self_10_2)\n",
    "\n",
    "r_10_2 = collect(self_10_2.r_0:self_10_2.∆r:self_10_2.r_max)\n",
    "\n",
    "open(\"U_deltar_.01.dat\", \"w\") do file\n",
    "    for i=1:length(r_10_2)\n",
    "        println(file, r_10_2[i], \" \", self_10_2.U[i])\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing $r_{max}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing $V_0$ vs. $a$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 237.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.0 237.0 236.5 -0.001239066171607346\n",
      "1. 236.0 236.5 236.25 -0.0001541341813195194\n",
      "2. 236.25 236.5 236.375 0.0003895266352555894\n",
      "3. 236.25 236.375 236.3125 0.00011759659039392205\n",
      "4. 236.25 236.3125 236.28125 0.0002535366982126211\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.00032152543673105786 for V_0/|E| = 236.265625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 236.42962500000556\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.42862500000555 236.42962500000556 236.42912500000557 -1.1742649582963352e-6\n",
      "1. 236.42862500000555 236.42912500000557 236.42887500000558 -8.729101753827695e-8\n",
      "2. 236.42887500000558 236.42912500000557 236.42900000000557 4.5619847410678215e-7\n",
      "3. 236.42887500000558 236.42900000000557 236.4289375000056 1.8445228417704231e-7\n",
      "4. 236.42887500000558 236.4289375000056 236.42890625000558 3.20324837695221e-7\n",
      "5. 236.42887500000558 236.42890625000558 236.42889062500558 3.882621658309898e-7\n",
      "6. 236.42887500000558 236.42889062500558 236.42888281250558 4.2222925147508593e-7\n",
      "7. 236.42887500000558 236.42888281250558 236.4288789062556 4.392141532381755e-7\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 4.4770573766073363e-7 for V_0/|E| = 236.42887695313058\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 158.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.0 158.0 157.5 -0.0007346644604416547\n",
      "1. 157.5 158.0 157.75 0.0008603174245528197\n",
      "2. 157.5 157.75 157.625 6.191969163802589e-5\n",
      "3. 157.5 157.625 157.5625 0.00046089171652955124\n",
      "4. 157.5 157.5625 157.53125 0.0006605478419734582\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.0007604184482476496 for V_0/|E| = 157.515625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 157.769625000006\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.76862500000598 157.769625000006 157.769125000006 -6.777286125543649e-7\n",
      "1. 157.769125000006 157.769625000006 157.769375000006 9.169715646865678e-7\n",
      "2. 157.769125000006 157.769375000006 157.769250000006 1.196199273556512e-7\n",
      "3. 157.769125000006 157.769250000006 157.769187500006 5.182961812200209e-7\n",
      "4. 157.769125000006 157.769187500006 157.769156250006 7.176340449078416e-7\n",
      "5. 157.769125000006 157.769156250006 157.769140625006 8.173020682836442e-7\n",
      "6. 157.769125000006 157.769140625006 157.769132812506 8.67136602077964e-7\n",
      "7. 157.769125000006 157.769132812506 157.76912890625601 8.920539809491999e-7\n",
      "8. 157.769125000006 157.76912890625601 157.769126953131 9.045124442276521e-7\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 9.107421263559277e-7 for V_0/|E| = 157.7691259765685\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 114.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.0 114.0 113.5 -0.0032009003765620095\n",
      "1. 113.0 113.5 113.25 -0.0010368361189212528\n",
      "2. 113.25 113.5 113.375 5.052095072374574e-5\n",
      "3. 113.375 113.5 113.4375 -0.0004936020120726431\n",
      "4. 113.375 113.4375 113.40625 -0.000765330121129028\n",
      "5. 113.375 113.40625 113.390625 -0.0006294938385121749\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.000561554868198843 for V_0/|E| = 113.3828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 113.2618125000042\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.26081250000419 113.2618125000042 113.2613125000042 -9.367212725264573e-7\n",
      "1. 113.2613125000042 113.2618125000042 113.2615625000042 1.2412195833217961e-6\n",
      "2. 113.2613125000042 113.2615625000042 113.2614375000042 1.5224692249745764e-7\n",
      "3. 113.2613125000042 113.2614375000042 113.2613750000042 6.967329355342984e-7\n",
      "4. 113.2613125000042 113.2613750000042 113.26134375000419 9.68976703283273e-7\n",
      "5. 113.2613125000042 113.26134375000419 113.26132812500418 1.1050973520471505e-6\n",
      "6. 113.2613125000042 113.26132812500418 113.26132031250418 1.173157312299262e-6\n",
      "7. 113.2613125000042 113.26132031250418 113.2613164062542 1.207188710751157e-6\n",
      "8. 113.2613125000042 113.2613164062542 113.26131445312919 1.2242037597984974e-6\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 1.2327123651338923e-6 for V_0/|E| = 113.2613134765667\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 86.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.0 86.0 85.5 -0.0020791370789010246\n",
      "1. 85.5 86.0 85.75 0.0007425781127559805\n",
      "2. 85.75 86.0 85.875 -0.0006714189086239535\n",
      "3. 85.75 85.875 85.8125 -0.0013760618614019609\n",
      "4. 85.75 85.8125 85.78125 -0.0010239364750102562\n",
      "5. 85.75 85.78125 85.765625 -0.0008477267309059132\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0007595850815987512 for V_0/|E| = 85.7578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 85.63181250000417\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.63081250000417 85.63181250000417 85.63131250000417 -3.7353089694924966e-6\n",
      "1. 85.63081250000417 85.63131250000417 85.63106250000416 -9.076482577013485e-7\n",
      "2. 85.63106250000416 85.63131250000417 85.63118750000416 5.061937712150545e-7\n",
      "3. 85.63118750000416 85.63131250000417 85.63125000000417 -2.0072752757466802e-7\n",
      "4. 85.63118750000416 85.63125000000417 85.63121875000417 -5.541877791888062e-7\n",
      "5. 85.63118750000416 85.63121875000417 85.63120312500416 -3.774578915965258e-7\n",
      "6. 85.63118750000416 85.63120312500416 85.63119531250416 -2.8909137730992244e-7\n",
      "7. 85.63118750000416 85.63119531250416 85.63119140625416 -2.449117285377317e-7\n",
      "8. 85.63118750000416 85.63119140625416 85.63118945312917 -2.2281859061900514e-7\n",
      "9. 85.63118750000416 85.63118945312917 85.63118847656666 -2.1177240682611845e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -2.0624969084119022e-7 for V_0/|E| = 85.6311879882854\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 68.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.0 68.0 67.5 -0.00502517423510451\n",
      "1. 67.0 67.5 67.25 -0.0015274822178607363\n",
      "2. 67.25 67.5 67.375 0.00023670815273393273\n",
      "3. 67.375 67.5 67.4375 -0.0006466692478720556\n",
      "4. 67.375 67.4375 67.40625 -0.0010873960213748748\n",
      "5. 67.375 67.40625 67.390625 -0.0008671127382468328\n",
      "6. 67.375 67.390625 67.3828125 -0.0007569110232385351\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0007017951440865548 for V_0/|E| = 67.37890625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 67.28390625000432\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.28290625000432 67.28390625000432 67.28340625000432 -3.161668444562902e-6\n",
      "1. 67.28340625000432 67.28390625000432 67.28365625000433 3.7420993875440105e-7\n",
      "2. 67.28365625000433 67.28390625000432 67.28378125000432 -1.3937345221698244e-6\n",
      "3. 67.28365625000433 67.28378125000432 67.28371875000433 -2.277702687004581e-6\n",
      "4. 67.28365625000433 67.28371875000433 67.28368750000433 -1.835719426642713e-6\n",
      "5. 67.28365625000433 67.28368750000433 67.28367187500433 -1.6147268342497116e-6\n",
      "6. 67.28365625000433 67.28367187500433 67.28366406250433 -1.5042301748307423e-6\n",
      "7. 67.28365625000433 67.28366406250433 67.28366015625433 -1.4489834886212502e-6\n",
      "8. 67.28365625000433 67.28366015625433 67.28365820312933 -1.4213578802735319e-6\n",
      "9. 67.28365625000433 67.28365820312933 67.28365722656683 -1.4075471064638618e-6\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -1.4006395842042427e-6 for V_0/|E| = 67.28365673828557\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 55.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.0 55.0 54.5 -0.004591870397951977\n",
      "1. 54.0 54.5 54.25 -0.00033280703368896786\n",
      "2. 54.25 54.5 54.375 0.0018203688789377541\n",
      "3. 54.25 54.375 54.3125 0.000741803695830267\n",
      "4. 54.25 54.3125 54.28125 0.001280591462740804\n",
      "5. 54.25 54.28125 54.265625 0.0015503564003434068\n",
      "6. 54.25 54.265625 54.2578125 0.0016853316877338271\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = 0.0017528425452950664 for V_0/|E| = 54.25390625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 54.461906249997185\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.46090624999719 54.461906249997185 54.46140624999718 -5.7378494507149805e-6\n",
      "1. 54.46090624999719 54.46140624999718 54.46115624999719 -1.4424608465999873e-6\n",
      "2. 54.46115624999719 54.46140624999718 54.461281249997185 7.052568460621759e-7\n",
      "3. 54.461281249997185 54.46140624999718 54.461343749997184 -3.6860273817784276e-7\n",
      "4. 54.461281249997185 54.461343749997184 54.461312499997184 -9.055318273376383e-7\n",
      "5. 54.461281249997185 54.461312499997184 54.46129687499719 -6.37067428174773e-7\n",
      "6. 54.461281249997185 54.46129687499719 54.46128906249719 -5.028356833062243e-7\n",
      "7. 54.461281249997185 54.46128906249719 54.461285156247186 -4.3572068367062984e-7\n",
      "8. 54.461281249997185 54.461285156247186 54.461283203122186 -4.021617098315117e-7\n",
      "9. 54.461281249997185 54.461283203122186 54.46128222655969 -3.8538177395941934e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -3.7699256026884806e-7 for V_0/|E| = 54.46128173827844\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 46.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.0 46.0 45.5 -0.008693984695477861\n",
      "1. 45.0 45.5 45.25 -0.00370730736507077\n",
      "2. 45.0 45.25 45.125 -0.0011795589675635\n",
      "3. 45.125 45.25 45.1875 9.296980478361523e-5\n",
      "4. 45.1875 45.25 45.21875 -0.0005440173526399188\n",
      "5. 45.1875 45.21875 45.203125 -0.000861968735520371\n",
      "6. 45.1875 45.203125 45.1953125 -0.0007030382016190136\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0006235390679645697 for V_0/|E| = 45.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 45.1344062499978\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.133406249997805 45.1344062499978 45.13390624999781 -2.9892413379223334e-6\n",
      "1. 45.13390624999781 45.1344062499978 45.1341562499978 2.1107456864989785e-6\n",
      "2. 45.1341562499978 45.1344062499978 45.1342812499978 -4.392596510584749e-7\n",
      "3. 45.1341562499978 45.1342812499978 45.1342187499978 -1.7142536919430825e-6\n",
      "4. 45.1341562499978 45.1342187499978 45.1341874999978 -1.076756753729395e-6\n",
      "5. 45.1341562499978 45.1341874999978 45.134171874997804 -7.580075558586826e-7\n",
      "6. 45.1341562499978 45.134171874997804 45.1341640624978 -5.986329400446218e-7\n",
      "7. 45.1341562499978 45.1341640624978 45.1341601562478 -5.189467493301117e-7\n",
      "8. 45.1341562499978 45.1341601562478 45.1341582031228 -4.791028481514264e-7\n",
      "9. 45.1341562499978 45.1341582031228 45.134157226560305 -4.591806099646763e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -4.4922058548717836e-7 for V_0/|E| = 45.13415673827905\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 39.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.0 39.0 38.5 -0.010180698251304122\n",
      "1. 38.0 38.5 38.25 -0.004398127714799595\n",
      "2. 38.0 38.25 38.125 -0.001458433110167687\n",
      "3. 38.125 38.25 38.1875 2.3605511760144307e-5\n",
      "4. 38.1875 38.25 38.21875 -0.0007184324004948712\n",
      "5. 38.1875 38.21875 38.203125 -0.0010886872079035395\n",
      "6. 38.1875 38.203125 38.1953125 -0.0009036234410489536\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0008110438331929535 for V_0/|E| = 38.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 38.12740624999782\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.12640624999782 38.12740624999782 38.126906249997816 -5.000689721302952e-6\n",
      "1. 38.126906249997816 38.12740624999782 38.12715624999782 9.432063406080443e-7\n",
      "2. 38.12715624999782 38.12740624999782 38.12728124999782 -2.028758005789713e-6\n",
      "3. 38.12715624999782 38.12728124999782 38.12721874999782 -3.514729844260145e-6\n",
      "4. 38.12715624999782 38.12721874999782 38.12718749999782 -2.771744910077438e-6\n",
      "5. 38.12715624999782 38.12718749999782 38.12717187499781 -2.4002527437334813e-6\n",
      "6. 38.12715624999782 38.12717187499781 38.12716406249781 -2.2145069512122627e-6\n",
      "7. 38.12715624999782 38.12716406249781 38.12716015624781 -2.1216319567590877e-6\n",
      "8. 38.12715624999782 38.12716015624781 38.12715820312282 -2.0751943043466505e-6\n",
      "9. 38.12715624999782 38.12715820312282 38.127157226560314 -2.0519777238017122e-6\n",
      "10. 38.12715624999782 38.127157226560314 38.12715673827907 -2.0403668467009204e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -2.0345632594665303e-6 for V_0/|E| = 38.12715649413845\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 33.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.0 33.0 32.5 -0.0037741061045654164\n",
      "1. 32.5 33.0 32.75 0.0030380921743777293\n",
      "2. 32.75 33.0 32.875 -0.0003902701108890359\n",
      "3. 32.75 32.875 32.8125 -0.002087733115168764\n",
      "4. 32.75 32.8125 32.78125 -0.00124039045731393\n",
      "5. 32.75 32.78125 32.765625 -0.0008156778204897484\n",
      "6. 32.75 32.765625 32.7578125 -0.0006030608891101491\n",
      "7. 32.75 32.7578125 32.75390625 -0.0004966872350604412\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.0004434841086728764 for V_0/|E| = 32.751953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 32.72195312499862\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.72095312499862 32.72195312499862 32.72145312499862 -7.874300549871745e-6\n",
      "1. 32.72095312499862 32.72145312499862 32.721203124998624 -1.0521308039855992e-6\n",
      "2. 32.721203124998624 32.72145312499862 32.72132812499862 2.35902078847137e-6\n",
      "3. 32.721203124998624 32.72132812499862 32.72126562499862 6.534391039862089e-7\n",
      "4. 32.721203124998624 32.72126562499862 32.72123437499862 1.506230844592675e-6\n",
      "5. 32.721203124998624 32.72123437499862 32.72121874999863 1.9326259119261937e-6\n",
      "6. 32.721203124998624 32.72121874999863 32.721210937498626 2.145821818657127e-6\n",
      "7. 32.721203124998624 32.721210937498626 32.721207031248625 2.2524213667544387e-6\n",
      "8. 32.721203124998624 32.721207031248625 32.721205078123624 2.305721855097125e-6\n",
      "9. 32.721203124998624 32.721205078123624 32.72120410156113 2.3323716121951808e-6\n",
      "10. 32.721203124998624 32.72120410156113 32.721203613279876 2.3456971468038807e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.352359518718019e-6 for V_0/|E| = 32.721203369139246\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 29.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.0 29.0 28.5 -0.008244776529704297\n",
      "1. 28.0 28.5 28.25 -0.0006517128979049019\n",
      "2. 28.25 28.5 28.375 0.003233241928510905\n",
      "3. 28.25 28.375 28.3125 0.001283341917623985\n",
      "4. 28.25 28.3125 28.28125 0.002256432205772726\n",
      "5. 28.25 28.28125 28.265625 0.002744371625667118\n",
      "6. 28.25 28.265625 28.2578125 0.002988690352612621\n",
      "7. 28.25 28.2578125 28.25390625 0.003110937027013128\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.003172082196651908 for V_0/|E| = 28.251953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 28.457953125001474\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.456953125001473 28.457953125001474 28.45745312500147 -2.4617328835546575e-6\n",
      "1. 28.45745312500147 28.457953125001474 28.457703125001473 5.268903270577225e-6\n",
      "2. 28.45745312500147 28.457703125001473 28.457578125001472 1.4035573296405163e-6\n",
      "3. 28.45745312500147 28.457578125001472 28.45751562500147 3.3362231532541755e-6\n",
      "4. 28.45745312500147 28.45751562500147 28.45748437500147 4.302562037792111e-6\n",
      "5. 28.45745312500147 28.45748437500147 28.45746875000147 4.78573089600909e-6\n",
      "6. 28.45745312500147 28.45746875000147 28.457460937501473 5.027317332196326e-6\n",
      "7. 28.45745312500147 28.457460937501473 28.457457031251472 5.14810961003018e-6\n",
      "8. 28.45745312500147 28.457457031251472 28.457455078126472 5.20850761520464e-6\n",
      "9. 28.45745312500147 28.457455078126472 28.45745410156397 5.238704908064457e-6\n",
      "10. 28.45745312500147 28.45745410156397 28.457453613282723 5.253804785916323e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 5.261354806271113e-6 for V_0/|E| = 28.457453369142097\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 26.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.0 26.0 25.5 -0.01622020783145422\n",
      "1. 25.0 25.5 25.25 -0.00799068766237216\n",
      "2. 25.0 25.25 25.125 -0.0037631934988698874\n",
      "3. 25.0 25.125 25.0625 -0.001620924912701446\n",
      "4. 25.0 25.0625 25.03125 -0.0005426177046481965\n",
      "5. 25.0 25.03125 25.015625 -1.6655358913973826e-6\n",
      "6. 25.015625 25.03125 25.0234375 0.00026926085744885195\n",
      "7. 25.015625 25.0234375 25.01953125 0.0001337601169680536\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00020150109876461444 for V_0/|E| = 25.017578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 25.03157812500124\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.030578125001238 25.03157812500124 25.031078125001237 -7.3517697204212845e-6\n",
      "1. 25.031078125001237 25.03157812500124 25.031328125001238 1.3130212008842052e-6\n",
      "2. 25.031328125001238 25.03157812500124 25.03145312500124 -3.019413698193451e-6\n",
      "3. 25.031328125001238 25.03145312500124 25.031390625001237 -5.1856013309522864e-6\n",
      "4. 25.031328125001238 25.031390625001237 25.031359375001237 -4.102508491315543e-6\n",
      "5. 25.031328125001238 25.031359375001237 25.031343750001238 -3.5609625194532833e-6\n",
      "6. 25.031328125001238 25.031343750001238 25.03133593750124 -3.2901892086842956e-6\n",
      "7. 25.031328125001238 25.03133593750124 25.03133203125124 -3.154800137580771e-6\n",
      "8. 25.031328125001238 25.03133203125124 25.03133007812624 -3.087106831182853e-6\n",
      "9. 25.031328125001238 25.03133007812624 25.03132910156374 -3.053260120979566e-6\n",
      "10. 25.031328125001238 25.03132910156374 25.03132861328249 -3.0363364844247703e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -3.027874542476985e-6 for V_0/|E| = 25.031328369141864\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 23.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.0 23.0 22.5 -0.014316333670953047\n",
      "1. 22.0 22.5 22.25 -0.0050945548757473326\n",
      "2. 22.0 22.25 22.125 -0.00033930627542912774\n",
      "3. 22.125 22.25 22.1875 0.002074904089430453\n",
      "4. 22.125 22.1875 22.15625 0.0008647351968267734\n",
      "5. 22.125 22.15625 22.140625 0.0014690525980099274\n",
      "6. 22.125 22.140625 22.1328125 0.0017717864426223715\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7. 22.125 22.1328125 22.12890625 0.001923297274676015\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0019990886817764695 for V_0/|E| = 22.126953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 22.23295312500135\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.23195312500135 22.23295312500135 22.23245312500135 -1.151065217664422e-5\n",
      "1. 22.23195312500135 22.23245312500135 22.232203125001348 -1.8892497601914624e-6\n",
      "2. 22.232203125001348 22.23245312500135 22.23232812500135 2.921597063429388e-6\n",
      "3. 22.232203125001348 22.23232812500135 22.232265625001347 5.161608662528406e-7\n",
      "4. 22.232203125001348 22.232265625001347 22.232234375001347 1.7188749296915765e-6\n",
      "5. 22.232203125001348 22.232234375001347 22.232218750001348 2.3202358905690496e-6\n",
      "6. 22.232203125001348 22.232218750001348 22.23221093750135 2.620916545466308e-6\n",
      "7. 22.232203125001348 22.23221093750135 22.23220703125135 2.7712573627348004e-6\n",
      "8. 22.232203125001348 22.23220703125135 22.23220507812635 2.8464279555997525e-6\n",
      "9. 22.232203125001348 22.23220507812635 22.23220410156385 2.884011947855377e-6\n",
      "10. 22.232203125001348 22.23220410156385 22.2322036132826 2.902805099969834e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.9122009455332616e-6 for V_0/|E| = 22.232203369141974\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 20.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.0 20.0 19.5 -0.0018129613721425421\n",
      "1. 19.5 20.0 19.75 0.008946736677090159\n",
      "2. 19.5 19.75 19.625 0.0035051611888318227\n",
      "3. 19.5 19.625 19.5625 0.006210414864845436\n",
      "4. 19.5 19.5625 19.53125 0.007574679392257963\n",
      "5. 19.5 19.53125 19.515625 0.008259732329630357\n",
      "6. 19.5 19.515625 19.5078125 0.008602990378048306\n",
      "7. 19.5 19.5078125 19.50390625 0.008774802469663657\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.008860754306522502 for V_0/|E| = 19.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 19.914953125001727\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.913953125001726 19.914953125001727 19.914453125001728 -1.755617015998076e-5\n",
      "1. 19.913953125001726 19.914453125001728 19.914203125001727 -6.958972558876604e-6\n",
      "2. 19.913953125001726 19.914203125001727 19.914078125001726 -1.6601882023733058e-6\n",
      "3. 19.914078125001726 19.914203125001727 19.91414062500173 9.89248861005078e-7\n",
      "4. 19.91414062500173 19.914203125001727 19.914171875001728 -3.354747745257595e-7\n",
      "5. 19.91414062500173 19.914171875001728 19.914156250001728 -9.978328191413445e-7\n",
      "6. 19.91414062500173 19.914156250001728 19.91414843750173 -6.666523961330065e-7\n",
      "7. 19.91414062500173 19.91414843750173 19.91414453125173 -5.010632365022212e-7\n",
      "8. 19.91414062500173 19.91414453125173 19.91414257812673 -4.182692376477707e-7\n",
      "9. 19.91414062500173 19.91414257812673 19.91414160156423 -3.7687175232179196e-7\n",
      "10. 19.91414062500173 19.91414160156423 19.91414111328298 -3.561730834384051e-7\n",
      "11. 19.91414062500173 19.91414111328298 19.914140869142354 -3.4582324789711603e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.4064998363933376e-7 for V_0/|E| = 19.91414074707204\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 18.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.0 18.0 17.5 -0.0006883716089958467\n",
      "1. 17.5 18.0 17.75 0.011170184138903742\n",
      "2. 17.5 17.75 17.625 0.005164513257216539\n",
      "3. 17.5 17.625 17.5625 0.008148107532366571\n",
      "4. 17.5 17.5625 17.53125 0.009654317595422027\n",
      "5. 17.5 17.53125 17.515625 0.01041104155891802\n",
      "6. 17.5 17.515625 17.5078125 0.01079031024001517\n",
      "7. 17.5 17.5078125 17.50390625 0.010980171501502082\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.011075158894262149 for V_0/|E| = 17.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.970953125001795\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.969953125001794 17.970953125001795 17.970453125001796 -1.6110744068700835e-5\n",
      "1. 17.969953125001794 17.970453125001796 17.970203125001795 -4.520936266266922e-6\n",
      "2. 17.970203125001795 17.970453125001796 17.970328125001796 1.2741958824748036e-6\n",
      "3. 17.970328125001796 17.970453125001796 17.970390625001798 -1.6233874452281859e-6\n",
      "4. 17.970328125001796 17.970390625001798 17.9703593750018 -3.0721649920316414e-6\n",
      "5. 17.970328125001796 17.9703593750018 17.970343750001796 -2.34777794437978e-6\n",
      "6. 17.970328125001796 17.970343750001796 17.970335937501794 -1.9855823570824323e-6\n",
      "7. 17.970328125001796 17.970335937501794 17.970332031251793 -1.804486262319223e-6\n",
      "8. 17.970328125001796 17.970332031251793 17.970330078126793 -1.713937007897641e-6\n",
      "9. 17.970328125001796 17.970330078126793 17.970329101564296 -1.6686633814064367e-6\n",
      "10. 17.970328125001796 17.970329101564296 17.970328613283044 -1.6460262689457248e-6\n",
      "11. 17.970328125001796 17.970328613283044 17.970328369142422 -1.6347073897240378e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.6290479634891226e-6 for V_0/|E| = 17.97032824707211\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.0 17.0 16.5 -0.016404338328013673\n",
      "1. 16.0 16.5 16.25 -0.00442429859436212\n",
      "2. 16.25 16.5 16.375 0.001835895642506397\n",
      "3. 16.375 16.5 16.4375 -0.0013170336224617482\n",
      "4. 16.375 16.4375 16.40625 -0.002876350160631104\n",
      "5. 16.375 16.40625 16.390625 -0.0020981158975908747\n",
      "6. 16.375 16.390625 16.3828125 -0.0017079311350429623\n",
      "7. 16.375 16.3828125 16.37890625 -0.0015125715209359475\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.0014148248625884862 for V_0/|E| = 16.376953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 16.322953125000048\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.321953125000046 16.322953125000048 16.322453125000045 -9.803113946930617e-6\n",
      "1. 16.322453125000045 16.322953125000048 16.322703125000046 2.793573502396901e-6\n",
      "2. 16.322703125000046 16.322953125000048 16.322828125000047 -3.5048619255015125e-6\n",
      "3. 16.322703125000046 16.322828125000047 16.322765625000045 -6.654011069899804e-6\n",
      "4. 16.322703125000046 16.322765625000045 16.322734375000046 -5.079441211522917e-6\n",
      "5. 16.322703125000046 16.322734375000046 16.322718750000046 -4.292153891038869e-6\n",
      "6. 16.322703125000046 16.322718750000046 16.322710937500048 -3.8985070174740364e-6\n",
      "7. 16.322703125000046 16.322710937500048 16.322707031250047 -3.7016835330006445e-6\n",
      "8. 16.322703125000046 16.322707031250047 16.322705078125047 -3.6032737849569055e-6\n",
      "9. 16.322703125000046 16.322705078125047 16.322704101562547 -3.554067473215981e-6\n",
      "10. 16.322703125000046 16.322704101562547 16.3227036132813 -3.5294650566327956e-6\n",
      "11. 16.322703125000046 16.3227036132813 16.322703369140672 -3.5171628219825524e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.511012116337293e-6 for V_0/|E| = 16.322703247070358\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 15.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.0 15.0 14.5 -0.0023714607983908224\n",
      "1. 14.5 15.0 14.75 0.011532899887681037\n",
      "2. 14.5 14.75 14.625 0.004469276063280897\n",
      "3. 14.5 14.625 14.5625 0.007972966972457755\n",
      "4. 14.5 14.5625 14.53125 0.009745870468963242\n",
      "5. 14.5 14.53125 14.515625 0.010637615334549098\n",
      "6. 14.5 14.515625 14.5078125 0.011084814638571801\n",
      "7. 14.5 14.5078125 14.50390625 0.011308746453354983\n",
      "8. 14.5 14.50390625 14.501953125 0.011420795459681601\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.011476840742613244 for V_0/|E| = 14.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.912976562499217\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.911976562499218 14.912976562499217 14.912476562499219 -1.5273285422437324e-5\n",
      "1. 14.911976562499218 14.912476562499219 14.912226562499217 -1.6587050135648003e-6\n",
      "2. 14.912226562499217 14.912476562499219 14.912351562499218 5.148914983362604e-6\n",
      "3. 14.912226562499217 14.912351562499218 14.912289062499218 1.7450770033738212e-6\n",
      "4. 14.912226562499217 14.912289062499218 14.912257812499217 3.4469906180563987e-6\n",
      "5. 14.912226562499217 14.912257812499217 14.912242187499217 4.297950943198905e-6\n",
      "6. 14.912226562499217 14.912242187499217 14.912234374999217 4.723431987117012e-6\n",
      "7. 14.912226562499217 14.912234374999217 14.912230468749218 4.936173305637954e-6\n",
      "8. 14.912226562499217 14.912230468749218 14.912228515624218 5.042545297545201e-6\n",
      "9. 14.912226562499217 14.912228515624218 14.912227539061718 5.095729234115417e-6\n",
      "10. 14.912226562499217 14.912227539061718 14.912227050780468 5.122322984674961e-6\n",
      "11. 14.912226562499217 14.912227050780468 14.912226806639843 5.1356191063985985e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 5.142267393711833e-6 for V_0/|E| = 14.91222668456953\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.0 14.0 13.5 -0.008735325133243911\n",
      "1. 13.5 14.0 13.75 0.005794891445213837\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2. 13.75 14.0 13.875 -0.001600479987725138\n",
      "3. 13.75 13.875 13.8125 -0.005200131508124951\n",
      "4. 13.75 13.8125 13.78125 -0.003408404890536142\n",
      "5. 13.75 13.78125 13.765625 -0.0025064724816807934\n",
      "6. 13.75 13.765625 13.7578125 -0.0020539844029373844\n",
      "7. 13.75 13.7578125 13.75390625 -0.0018273593201994923\n",
      "8. 13.75 13.75390625 13.751953125 -0.0017139514474902742\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.001657223666427299 for V_0/|E| = 13.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.695976562499476\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.694976562499477 13.695976562499476 13.695476562499476 -2.4638197133918703e-5\n",
      "1. 13.694976562499477 13.695476562499476 13.695226562499476 -9.996411954846734e-6\n",
      "2. 13.694976562499477 13.695226562499476 13.695101562499477 -2.6751255435139237e-6\n",
      "3. 13.695101562499477 13.695226562499476 13.695164062499476 9.856135872704877e-7\n",
      "4. 13.695164062499476 13.695226562499476 13.695195312499475 -8.447628284629432e-7\n",
      "5. 13.695164062499476 13.695195312499475 13.695179687499476 -1.7599471017256681e-6\n",
      "6. 13.695164062499476 13.695179687499476 13.695171874999476 -1.3023564382705865e-6\n",
      "7. 13.695164062499476 13.695171874999476 13.695167968749477 -1.073560819232755e-6\n",
      "8. 13.695164062499476 13.695167968749477 13.695166015624476 -9.591628827297236e-7\n",
      "9. 13.695164062499476 13.695166015624476 13.695165039061976 -9.019652395563076e-7\n",
      "10. 13.695164062499476 13.695165039061976 13.695164550780726 -8.733629867419673e-7\n",
      "11. 13.695164062499476 13.695164550780726 13.695164306640102 -8.590646508361286e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -8.519131386957328e-7 for V_0/|E| = 13.695164184569789\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.0 13.0 12.5 -0.011085949228820717\n",
      "1. 12.5 13.0 12.75 0.004316047460344532\n",
      "2. 12.75 13.0 12.875 -0.003537399785463936\n",
      "3. 12.75 12.875 12.8125 -0.007349352115969839\n",
      "4. 12.75 12.8125 12.78125 -0.005452849397705831\n",
      "5. 12.75 12.78125 12.765625 -0.004497499733049815\n",
      "6. 12.75 12.765625 12.7578125 -0.004018044394152708\n",
      "7. 12.75 12.7578125 12.75390625 -0.003777870855736451\n",
      "8. 12.75 12.75390625 12.751953125 -0.0036576725259404343\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0035975454592344657 for V_0/|E| = 12.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.636976562499509\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.63597656249951 12.636976562499509 12.63647656249951 -2.508624511922678e-5\n",
      "1. 12.63597656249951 12.63647656249951 12.636226562499509 -9.408851873541468e-6\n",
      "2. 12.63597656249951 12.636226562499509 12.636101562499508 -1.5696917631038004e-6\n",
      "3. 12.636101562499508 12.636226562499509 12.636164062499509 2.3500032048424053e-6\n",
      "4. 12.636101562499508 12.636164062499509 12.636132812499508 3.901456807903544e-7\n",
      "5. 12.636101562499508 12.636132812499508 12.636117187499508 1.370071947402965e-6\n",
      "6. 12.636101562499508 12.636117187499508 12.636109374999508 1.8600372475478583e-6\n",
      "7. 12.636101562499508 12.636109374999508 12.63610546874951 2.1050191222153872e-6\n",
      "8. 12.636101562499508 12.63610546874951 12.636103515624509 2.2275110935145926e-6\n",
      "9. 12.636101562499508 12.636103515624509 12.636102539062009 2.2887570209670545e-6\n",
      "10. 12.636101562499508 12.636102539062009 12.636102050780758 2.3193792897838014e-6\n",
      "11. 12.636101562499508 12.636102050780758 12.636101806640134 2.334692060715177e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 2.342346686090751e-6 for V_0/|E| = 12.636101684569821\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.0 12.0 11.5 -0.00950689194063101\n",
      "1. 11.5 12.0 11.75 0.007097568457520806\n",
      "2. 11.75 12.0 11.875 -0.0013836840306020565\n",
      "3. 11.75 11.875 11.8125 -0.005489485364863974\n",
      "4. 11.75 11.8125 11.78125 -0.003447703423732556\n",
      "5. 11.75 11.78125 11.765625 -0.0024184821140916164\n",
      "6. 11.75 11.765625 11.7578125 -0.001901781260738134\n",
      "7. 11.75 11.7578125 11.75390625 -0.001642907330674204\n",
      "8. 11.75 11.75390625 11.751953125 -0.0015133393696119511\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0014485226244713547 for V_0/|E| = 11.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.708976562499469\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.70797656249947 11.708976562499469 11.70847656249947 -1.675785070068058e-5\n",
      "1. 11.70797656249947 11.70847656249947 11.708226562499469 -3.7911861458609374e-8\n",
      "2. 11.708226562499469 11.70847656249947 11.70835156249947 8.322595006499196e-6\n",
      "3. 11.708226562499469 11.70835156249947 11.70828906249947 4.142294136179394e-6\n",
      "4. 11.708226562499469 11.70828906249947 11.708257812499468 6.232435127048401e-6\n",
      "5. 11.708226562499469 11.708257812499468 11.708242187499469 7.2775119859534245e-6\n",
      "6. 11.708226562499469 11.708242187499469 11.708234374999469 7.800050625563125e-6\n",
      "7. 11.708226562499469 11.708234374999469 11.70823046874947 8.061322634686792e-6\n",
      "8. 11.708226562499469 11.70823046874947 11.70822851562447 8.191959695147023e-6\n",
      "9. 11.708226562499469 11.70822851562447 11.70822753906197 8.257275866725721e-6\n",
      "10. 11.708226562499469 11.70822753906197 11.70822705078072 8.289935880728032e-6\n",
      "11. 11.708226562499469 11.70822705078072 11.708226806640095 8.306266086526773e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 8.314430402795585e-6 for V_0/|E| = 11.708226684569782\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.003848586300374907\n",
      "1. 10.5 11.0 10.75 0.014394252294615054\n",
      "2. 10.5 10.75 10.625 0.005061484167454802\n",
      "3. 10.5 10.625 10.5625 0.00967431239292324\n",
      "4. 10.5 10.5625 10.53125 0.012020802777769136\n",
      "5. 10.5 10.53125 10.515625 0.013204146269826418\n",
      "6. 10.5 10.515625 10.5078125 0.013798352538781415\n",
      "7. 10.5 10.5078125 10.50390625 0.014096090555272231\n",
      "8. 10.5 10.50390625 10.501953125 0.014245118437847063\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.014319672116839623 for V_0/|E| = 10.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.89097656249923\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.88997656249923 10.89097656249923 10.89047656249923 -1.4201174608384793e-5\n",
      "1. 10.89047656249923 10.89097656249923 10.89072656249923 3.5656061023450623e-6\n",
      "2. 10.89072656249923 10.89097656249923 10.890851562499229 -5.317994111162198e-6\n",
      "3. 10.89072656249923 10.890851562499229 10.89078906249923 -9.759636171069197e-6\n",
      "4. 10.89072656249923 10.89078906249923 10.890757812499231 -7.5388266545205e-6\n",
      "5. 10.89072656249923 10.890757812499231 10.890742187499232 -6.428413033394417e-6\n",
      "6. 10.89072656249923 10.890742187499232 10.89073437499923 -5.8732046522876535e-6\n",
      "7. 10.89072656249923 10.89073437499923 10.89073046874923 -5.595598131474172e-6\n",
      "8. 10.89072656249923 10.89073046874923 10.890728515624229 -5.456796017169134e-6\n",
      "9. 10.89072656249923 10.890728515624229 10.890727539061729 -5.387393769671233e-6\n",
      "10. 10.89072656249923 10.890727539061729 10.89072705078048 -5.352693696394709e-6\n",
      "11. 10.89072656249923 10.89072705078048 10.890726806639854 -5.335342031327729e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -5.326668546617176e-6 for V_0/|E| = 10.890726684569543\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.028833117649994588\n",
      "1. 10.0 10.5 10.25 -0.012173479205015584\n",
      "2. 10.0 10.25 10.125 -0.00316070996007309\n",
      "3. 10.125 10.25 10.1875 0.0015224516350567424\n",
      "4. 10.1875 10.25 10.21875 -0.0008340435031747611\n",
      "5. 10.1875 10.21875 10.203125 -0.002001091513815694\n",
      "6. 10.1875 10.203125 10.1953125 -0.001418497923782245\n",
      "7. 10.1875 10.1953125 10.19140625 -0.0011265035350819588\n",
      "8. 10.1875 10.19140625 10.189453125 -0.0009803317495742613\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0009072021893294994 for V_0/|E| = 10.1884765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.165476562499459\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.164476562499459 10.165476562499459 10.164976562499458 -7.088455657882508e-6\n",
      "1. 10.164976562499458 10.165476562499459 10.165226562499459 1.1729049088431905e-5\n",
      "2. 10.164976562499458 10.165226562499459 10.165101562499459 2.320058068728205e-6\n",
      "3. 10.164976562499458 10.165101562499459 10.165039062499458 7.024493805509551e-6\n",
      "4. 10.164976562499458 10.165039062499458 10.165007812499457 9.376756839121742e-6\n",
      "5. 10.164976562499458 10.165007812499457 10.164992187499458 1.055289900016383e-5\n",
      "6. 10.164976562499458 10.164992187499458 10.164984374999458 1.114097438625336e-5\n",
      "7. 10.164976562499458 10.164984374999458 10.164980468749459 1.1435009564888584e-5\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8. 10.164976562499458 10.164980468749459 10.164978515624458 1.1582030828898305e-5\n",
      "9. 10.164976562499458 10.164978515624458 10.164977539061958 1.1655539514870878e-5\n",
      "10. 10.164976562499458 10.164977539061958 10.164977050780708 1.1692295604243846e-5\n",
      "11. 10.164976562499458 10.164977050780708 10.164976806640084 1.1710670056174008e-5\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 1.1719859848169686e-5 for V_0/|E| = 10.16497668456977\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.0 10.0 9.5 -0.018134357442420777\n",
      "1. 9.5 10.0 9.75 0.0007444894108901215\n",
      "2. 9.75 10.0 9.875 -0.008960164584936646\n",
      "3. 9.75 9.875 9.8125 -0.013612499938411751\n",
      "4. 9.75 9.8125 9.78125 -0.011302774601519384\n",
      "5. 9.75 9.78125 9.765625 -0.010135596839921164\n",
      "6. 9.75 9.765625 9.7578125 -0.009548914610497266\n",
      "7. 9.75 9.7578125 9.75390625 -0.009254798335110918\n",
      "8. 9.75 9.75390625 9.751953125 -0.009107546175559408\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.00903387156326568 for V_0/|E| = 9.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.518976562499574\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.517976562499575 9.518976562499574 9.518476562499576 -1.1146812449946193e-5\n",
      "1. 9.518476562499576 9.518976562499574 9.518726562499575 8.72249225425814e-6\n",
      "2. 9.518726562499575 9.518976562499574 9.518851562499574 -1.212433277678986e-6\n",
      "3. 9.518726562499575 9.518851562499574 9.518789062499575 -6.1796898009738555e-6\n",
      "4. 9.518726562499575 9.518789062499575 9.518757812499576 -3.6960791020148945e-6\n",
      "5. 9.518726562499575 9.518757812499576 9.518742187499576 -2.4542602988827817e-6\n",
      "6. 9.518726562499575 9.518742187499576 9.518734374999575 -1.833348590714514e-6\n",
      "7. 9.518726562499575 9.518734374999575 9.518730468749574 -1.5228915493812394e-6\n",
      "8. 9.518726562499575 9.518730468749574 9.518728515624574 -1.3676624639075127e-6\n",
      "9. 9.518726562499575 9.518728515624574 9.518727539062073 -1.2900486112736124e-6\n",
      "10. 9.518726562499575 9.518727539062073 9.518727050780825 -1.2512406168979667e-6\n",
      "11. 9.518726562499575 9.518727050780825 9.518726806640199 -1.2318364682573654e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.2221357833685536e-6 for V_0/|E| = 9.518726684569888\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.0025160470713672073\n",
      "1. 8.5 9.0 8.75 0.0193664481412427\n",
      "2. 8.5 8.75 8.625 0.008106808307957611\n",
      "3. 8.5 8.625 8.5625 0.01365565794228881\n",
      "4. 8.5 8.5625 8.53125 0.0164906370504042\n",
      "5. 8.5 8.53125 8.515625 0.017923416802895418\n",
      "6. 8.5 8.515625 8.5078125 0.018643648290867273\n",
      "7. 8.5 8.5078125 8.50390625 0.01900472682958106\n",
      "8. 8.5 8.50390625 8.501953125 0.019185507097837375\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.01927595751720114 for V_0/|E| = 8.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.939976562499647\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.938976562499647 8.939976562499647 8.939476562499646 -2.2490456895274547e-5\n",
      "1. 8.938976562499647 8.939476562499646 8.939226562499647 -1.5691817426730926e-6\n",
      "2. 8.939226562499647 8.939476562499646 8.939351562499645 8.892386887260044e-6\n",
      "3. 8.939226562499647 8.939351562499645 8.939289062499647 3.6615250660783655e-6\n",
      "4. 8.939226562499647 8.939289062499647 8.939257812499648 6.276935640500659e-6\n",
      "5. 8.939226562499647 8.939257812499648 8.939242187499648 7.584655995750661e-6\n",
      "6. 8.939226562499647 8.939242187499648 8.939234374999646 8.238521724213244e-6\n",
      "7. 8.939226562499647 8.939234374999646 8.939230468749646 8.565453111313607e-6\n",
      "8. 8.939226562499647 8.939230468749646 8.939228515624645 8.72891986445565e-6\n",
      "9. 8.939226562499647 8.939228515624645 8.939227539062145 8.810651171261908e-6\n",
      "10. 8.939226562499647 8.939227539062145 8.939227050780897 8.851521372988093e-6\n",
      "11. 8.939226562499647 8.939227050780897 8.93922680664027 8.87195399052293e-6\n",
      "12. 8.939226562499647 8.93922680664027 8.93922668456996 8.882170926423777e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 8.887277758597562e-6 for V_0/|E| = 8.939226623534804\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.023730561882404036\n",
      "1. 8.0 8.5 8.25 -0.0035595731578591805\n",
      "2. 8.25 8.5 8.375 0.007550847015656345\n",
      "3. 8.25 8.375 8.3125 0.0019075426915518496\n",
      "4. 8.25 8.3125 8.28125 0.004706966224539456\n",
      "5. 8.25 8.28125 8.265625 0.006123323676402732\n",
      "6. 8.25 8.265625 8.2578125 0.006835686376819297\n",
      "7. 8.25 8.2578125 8.25390625 0.007192916551055107\n",
      "8. 8.25 8.25390625 8.251953125 0.007371794196243024\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.007461298704977892 for V_0/|E| = 8.2509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.418976562500019\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.41797656250002 8.418976562500019 8.418476562500018 -3.577796499496844e-5\n",
      "1. 8.41797656250002 8.418476562500018 8.418226562500019 -1.3805032682985147e-5\n",
      "2. 8.41797656250002 8.418226562500019 8.41810156250002 -2.8175178792590543e-6\n",
      "3. 8.41810156250002 8.418226562500019 8.418164062500018 2.67650244604016e-6\n",
      "4. 8.418164062500018 8.418226562500019 8.418195312500018 -7.052945569234609e-8\n",
      "5. 8.418164062500018 8.418195312500018 8.418179687500018 -1.4440300904098491e-6\n",
      "6. 8.418164062500018 8.418179687500018 8.418171875000018 -7.572810352485765e-7\n",
      "7. 8.418164062500018 8.418171875000018 8.41816796875002 -4.1390629058560424e-7\n",
      "8. 8.418164062500018 8.41816796875002 8.418166015625019 -2.4221814829797286e-7\n",
      "9. 8.418164062500018 8.418166015625019 8.418165039062519 -1.5637566354579348e-7\n",
      "10. 8.418164062500018 8.418165039062519 8.418164550781269 -1.1345318594179051e-7\n",
      "11. 8.418164062500018 8.418164550781269 8.418164306640644 -9.198939975282427e-8\n",
      "12. 8.418164062500018 8.418164306640644 8.418164184570331 -8.126074452736359e-8\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -7.589383729005483e-8 for V_0/|E| = 8.418164123535174\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.002418681973327005\n",
      "1. 7.5 8.0 7.75 0.02188044451201813\n",
      "2. 7.5 7.75 7.625 0.009325119222886811\n",
      "3. 7.5 7.625 7.5625 0.015499324005963792\n",
      "4. 7.5 7.5625 7.53125 0.018663764408505097\n",
      "5. 7.5 7.53125 7.515625 0.020265542370950258\n",
      "6. 7.5 7.515625 7.5078125 0.02107134888844057\n",
      "7. 7.5 7.5078125 7.50390625 0.02147548505701582\n",
      "8. 7.5 7.50390625 7.501953125 0.021677861810037287\n",
      "9. 7.5 7.501953125 7.5009765625 0.021779127411127693\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = 0.0218297795192516 for V_0/|E| = 7.50048828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.947488281250483\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.946488281250483 7.947488281250483 7.9469882812504835 -1.767734160679937e-5\n",
      "1. 7.9469882812504835 7.947488281250483 7.947238281250483 5.350543651374698e-6\n",
      "2. 7.947238281250483 7.947488281250483 7.9473632812504835 -6.163792616799907e-6\n",
      "3. 7.947238281250483 7.9473632812504835 7.947300781250483 -1.1920665951583927e-5\n",
      "4. 7.947238281250483 7.947300781250483 7.947269531250483 -9.042253566992857e-6\n",
      "5. 7.947238281250483 7.947269531250483 7.947253906250483 -7.603029741356147e-6\n",
      "6. 7.947238281250483 7.947253906250483 7.947246093750483 -6.8834126009730105e-6\n",
      "7. 7.947238281250483 7.947246093750483 7.947242187500483 -6.523601898922189e-6\n",
      "8. 7.947238281250483 7.947242187500483 7.947240234375483 -6.343697665880264e-6\n",
      "9. 7.947238281250483 7.947240234375483 7.947239257812983 -6.253745025404396e-6\n",
      "10. 7.947238281250483 7.947239257812983 7.947238769531733 -6.208768569650668e-6\n",
      "11. 7.947238281250483 7.947238769531733 7.947238525391108 -6.186280258290574e-6\n",
      "12. 7.947238281250483 7.947238525391108 7.947238403320796 -6.1750361630458865e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -6.169414358110633e-6 for V_0/|E| = 7.947238342285639\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.021549466426926747\n",
      "1. 7.5 8.0 7.75 0.0009553118721673529\n",
      "2. 7.75 8.0 7.875 -0.010719531468420382\n",
      "3. 7.75 7.875 7.8125 -0.01623783871619307\n",
      "4. 7.75 7.8125 7.78125 -0.013504801460586482\n",
      "5. 7.75 7.78125 7.765625 -0.012118730978137864\n",
      "6. 7.75 7.765625 7.7578125 -0.011420776794198787\n",
      "7. 7.75 7.7578125 7.75390625 -0.01107056607912212\n",
      "8. 7.75 7.75390625 7.751953125 -0.01089515183056509\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.010807367421752973 for V_0/|E| = 7.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.519976562500257\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.5189765625002565 7.519976562500257 7.519476562500257 -9.506015713343958e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. 7.519476562500257 7.519976562500257 7.5197265625002565 1.457417641530531e-5\n",
      "2. 7.519476562500257 7.5197265625002565 7.519601562500257 2.533640843115205e-6\n",
      "3. 7.519476562500257 7.519601562500257 7.519539062500257 8.55380255617066e-6\n",
      "4. 7.519476562500257 7.519539062500257 7.519507812500257 1.1563962716069035e-5\n",
      "5. 7.519476562500257 7.519507812500257 7.519492187500257 1.3069063097547001e-5\n",
      "6. 7.519476562500257 7.519492187500257 7.519484375000257 1.382161871992575e-5\n",
      "7. 7.519476562500257 7.519484375000257 7.519480468750257 1.4197898380834102e-5\n",
      "8. 7.519476562500257 7.519480468750257 7.5194785156252575 1.4386037744637152e-5\n",
      "9. 7.519476562500257 7.5194785156252575 7.519477539062757 1.4480108173728428e-5\n",
      "10. 7.519476562500257 7.519477539062757 7.519477050781507 1.4527142729285003e-5\n",
      "11. 7.519476562500257 7.519477050781507 7.519476806640882 1.4550659689209807e-5\n",
      "12. 7.519476562500257 7.519476806640882 7.51947668457057 1.4562419886546758e-5\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 1.4568300183500776e-5 for V_0/|E| = 7.519476623535414\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 237.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.0 237.0 236.5 -0.0012390662204849806\n",
      "1. 236.0 236.5 236.25 -0.00015413423060129443\n",
      "2. 236.25 236.5 236.375 0.0003895265848741852\n",
      "3. 236.25 236.375 236.3125 0.00011759654060634675\n",
      "4. 236.25 236.3125 236.28125 0.0002535366491774347\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.00032152538742556485 for V_0/|E| = 236.265625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 236.42962500000556\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.42862500000555 236.42962500000556 236.42912500000557 -1.1743148858024132e-6\n",
      "1. 236.42862500000555 236.42912500000557 236.42887500000558 -8.734081349618041e-8\n",
      "2. 236.42887500000558 236.42912500000557 236.42900000000557 4.561487069070272e-7\n",
      "3. 236.42887500000558 236.42900000000557 236.4289375000056 1.844025869376025e-7\n",
      "4. 236.42887500000558 236.4289375000056 236.42890625000558 3.2027593788677233e-7\n",
      "5. 236.42887500000558 236.42890625000558 236.42889062500558 3.8821247188976467e-7\n",
      "6. 236.42887500000558 236.42889062500558 236.42888281250558 4.2217929425309823e-7\n",
      "7. 236.42887500000558 236.42888281250558 236.4288789062556 4.391641233691977e-7\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 4.476559061619446e-7 for V_0/|E| = 236.42887695313058\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 158.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.0 158.0 157.5 -0.0007346645030896164\n",
      "1. 157.5 158.0 157.75 0.0008603173825042042\n",
      "2. 157.5 157.75 157.625 6.19196490345392e-5\n",
      "3. 157.5 157.625 157.5625 0.00046089167369744224\n",
      "4. 157.5 157.5625 157.53125 0.0006605477993289971\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.0007604184054106902 for V_0/|E| = 157.515625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 157.769625000006\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.76862500000598 157.769625000006 157.769125000006 -6.777704610889433e-7\n",
      "1. 157.769125000006 157.769625000006 157.769375000006 9.169289744535503e-7\n",
      "2. 157.769125000006 157.769375000006 157.769250000006 1.1957840957794195e-7\n",
      "3. 157.769125000006 157.769250000006 157.769187500006 5.182539012068225e-7\n",
      "4. 157.769125000006 157.769187500006 157.769156250006 7.175919243795289e-7\n",
      "5. 157.769125000006 157.769156250006 157.769140625006 8.172607873820284e-7\n",
      "6. 157.769125000006 157.769140625006 157.769132812506 8.670953661234664e-7\n",
      "7. 157.769125000006 157.769132812506 157.76912890625601 8.920110763597637e-7\n",
      "8. 157.769125000006 157.76912890625601 157.769126953131 9.04470193390812e-7\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 9.106996526225187e-7 for V_0/|E| = 157.7691259765685\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 114.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.0 114.0 113.5 -0.0032009004133131927\n",
      "1. 113.0 113.5 113.25 -0.0010368361547451461\n",
      "2. 113.25 113.5 113.375 5.0520913747236754e-5\n",
      "3. 113.375 113.5 113.4375 -0.000493602049442111\n",
      "4. 113.375 113.4375 113.40625 -0.000765330158208392\n",
      "5. 113.375 113.40625 113.390625 -0.000629493874972823\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0005615549055443792 for V_0/|E| = 113.3828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 113.2618125000042\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.26081250000419 113.2618125000042 113.2613125000042 -9.36759363750394e-7\n",
      "1. 113.2613125000042 113.2618125000042 113.2615625000042 1.2411824482812094e-6\n",
      "2. 113.2613125000042 113.2615625000042 113.2614375000042 1.5220938403033328e-7\n",
      "3. 113.2613125000042 113.2614375000042 113.2613750000042 6.966962364297098e-7\n",
      "4. 113.2613125000042 113.2613750000042 113.26134375000419 9.689400392648278e-7\n",
      "5. 113.2613125000042 113.26134375000419 113.26132812500418 1.1050609253215676e-6\n",
      "6. 113.2613125000042 113.26132812500418 113.26132031250418 1.173121554269105e-6\n",
      "7. 113.2613125000042 113.26132031250418 113.2613164062542 1.207152717041397e-6\n",
      "8. 113.2613125000042 113.2613164062542 113.26131445312919 1.2241669941834197e-6\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 1.2326751207076762e-6 for V_0/|E| = 113.2613134765667\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 86.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.0 86.0 85.5 -0.0020791371123892025\n",
      "1. 85.5 86.0 85.75 0.0007425780795235066\n",
      "2. 85.75 86.0 85.875 -0.0006714189417607154\n",
      "3. 85.75 85.875 85.8125 -0.0013760618934272812\n",
      "4. 85.75 85.8125 85.78125 -0.001023936508530656\n",
      "5. 85.75 85.78125 85.765625 -0.0008477267642792661\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0007595851138280597 for V_0/|E| = 85.7578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 85.63181250000417\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.63081250000417 85.63181250000417 85.63131250000417 -3.735342382726045e-6\n",
      "1. 85.63081250000417 85.63131250000417 85.63106250000416 -9.076801508276215e-7\n",
      "2. 85.63106250000416 85.63131250000417 85.63118750000416 5.061609070013886e-7\n",
      "3. 85.63118750000416 85.63131250000417 85.63125000000417 -2.0076023570720653e-7\n",
      "4. 85.63118750000416 85.63125000000417 85.63121875000417 -5.542208962946832e-7\n",
      "5. 85.63118750000416 85.63121875000417 85.63120312500416 -3.774909717271965e-7\n",
      "6. 85.63118750000416 85.63120312500416 85.63119531250416 -2.89124867910663e-7\n",
      "7. 85.63118750000416 85.63119531250416 85.63119140625416 -2.4494485513352797e-7\n",
      "8. 85.63118750000416 85.63119140625416 85.63118945312917 -2.2285160080327628e-7\n",
      "9. 85.63118750000416 85.63118945312917 85.63118847656666 -2.11807336989e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -2.0628353259625044e-7 for V_0/|E| = 85.6311879882854\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 68.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.0 68.0 67.5 -0.0050251742645519735\n",
      "1. 67.0 67.5 67.25 -0.0015274822459802181\n",
      "2. 67.25 67.5 67.375 0.00023670812256982768\n",
      "3. 67.375 67.5 67.4375 -0.0006466692775540738\n",
      "4. 67.375 67.4375 67.40625 -0.0010873960509726708\n",
      "5. 67.375 67.40625 67.390625 -0.0008671127690830855\n",
      "6. 67.375 67.390625 67.3828125 -0.0007569110547817234\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0007017951725847434 for V_0/|E| = 67.37890625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 67.28390625000432\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.28290625000432 67.28390625000432 67.28340625000432 -3.1616976132577647e-6\n",
      "1. 67.28340625000432 67.28390625000432 67.28365625000433 3.7418037812490816e-7\n",
      "2. 67.28365625000433 67.28390625000432 67.28378125000432 -1.3937624355642935e-6\n",
      "3. 67.28365625000433 67.28378125000432 67.28371875000433 -2.2777319899463557e-6\n",
      "4. 67.28365625000433 67.28371875000433 67.28368750000433 -1.835747298289772e-6\n",
      "5. 67.28365625000433 67.28368750000433 67.28367187500433 -1.6147568985590736e-6\n",
      "6. 67.28365625000433 67.28367187500433 67.28366406250433 -1.5042595192124352e-6\n",
      "7. 67.28365625000433 67.28366406250433 67.28366015625433 -1.4490121194974341e-6\n",
      "8. 67.28365625000433 67.28366015625433 67.28365820312933 -1.4213879291187267e-6\n",
      "9. 67.28365625000433 67.28365820312933 67.28365722656683 -1.407575504196323e-6\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -1.4006695166475007e-6 for V_0/|E| = 67.28365673828557\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 55.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.0 55.0 54.5 -0.004591870424894438\n",
      "1. 54.0 54.5 54.25 -0.00033280706030709755\n",
      "2. 54.25 54.5 54.375 0.0018203688515433542\n",
      "3. 54.25 54.375 54.3125 0.0007418036696098898\n",
      "4. 54.25 54.3125 54.28125 0.0012805914361574092\n",
      "5. 54.25 54.28125 54.265625 0.0015503563742112795\n",
      "6. 54.25 54.265625 54.2578125 0.0016853316618917614\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = 0.0017528425183193648 for V_0/|E| = 54.25390625\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 54.461906249997185\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.46090624999719 54.461906249997185 54.46140624999718 -5.737876679033821e-6\n",
      "1. 54.46090624999719 54.46140624999718 54.46115624999719 -1.4424867860532495e-6\n",
      "2. 54.46115624999719 54.46140624999718 54.461281249997185 7.052301905791828e-7\n",
      "3. 54.461281249997185 54.46140624999718 54.461343749997184 -3.686298867758057e-7\n",
      "4. 54.461281249997185 54.461343749997184 54.461312499997184 -9.055589243620186e-7\n",
      "5. 54.461281249997185 54.461312499997184 54.46129687499719 -6.370944569839386e-7\n",
      "6. 54.461281249997185 54.46129687499719 54.46128906249719 -5.028628945879652e-7\n",
      "7. 54.461281249997185 54.46128906249719 54.461285156247186 -4.3574794902504204e-7\n",
      "8. 54.461281249997185 54.461285156247186 54.461283203122186 -4.0218798442765685e-7\n",
      "9. 54.461281249997185 54.461283203122186 54.46128222655969 -3.8540905546164854e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -3.770190581432396e-7 for V_0/|E| = 54.46128173827844\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 46.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.0 46.0 45.5 -0.008693984719614323\n",
      "1. 45.0 45.5 45.25 -0.0037073073896452084\n",
      "2. 45.0 45.25 45.125 -0.0011795589920624633\n",
      "3. 45.125 45.25 45.1875 9.2969779322107e-5\n",
      "4. 45.1875 45.25 45.21875 -0.0005440173774477054\n",
      "5. 45.1875 45.21875 45.203125 -0.0008619687599187398\n",
      "6. 45.1875 45.203125 45.1953125 -0.0007030382268388328\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0006235390925499445 for V_0/|E| = 45.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 45.1344062499978\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.133406249997805 45.1344062499978 45.13390624999781 -2.9892664650866554e-6\n",
      "1. 45.13390624999781 45.1344062499978 45.1341562499978 2.110720500589785e-6\n",
      "2. 45.1341562499978 45.1344062499978 45.1342812499978 -4.392836807825655e-7\n",
      "3. 45.1341562499978 45.1342812499978 45.1342187499978 -1.7142779548126903e-6\n",
      "4. 45.1341562499978 45.1342187499978 45.1341874999978 -1.0767811477983655e-6\n",
      "5. 45.1341562499978 45.1341874999978 45.134171874997804 -7.580328066366905e-7\n",
      "6. 45.1341562499978 45.134171874997804 45.1341640624978 -5.986571858914025e-7\n",
      "7. 45.1341562499978 45.1341640624978 45.1341601562478 -5.189714899344749e-7\n",
      "8. 45.1341562499978 45.1341601562478 45.1341582031228 -4.79127113891023e-7\n",
      "9. 45.1341562499978 45.1341582031228 45.134157226560305 -4.592045643343352e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -4.49244802236072e-7 for V_0/|E| = 45.13415673827905\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 39.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.0 39.0 38.5 -0.010180698274335155\n",
      "1. 38.0 38.5 38.25 -0.0043981277366229215\n",
      "2. 38.0 38.25 38.125 -0.001458433132392269\n",
      "3. 38.125 38.25 38.1875 2.3605488548295096e-5\n",
      "4. 38.1875 38.25 38.21875 -0.0007184324234608319\n",
      "5. 38.1875 38.21875 38.203125 -0.0010886872300070235\n",
      "6. 38.1875 38.203125 38.1953125 -0.0009036234640363763\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0008110438554790648 for V_0/|E| = 38.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 38.12740624999782\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.12640624999782 38.12740624999782 38.126906249997816 -5.0007127332780705e-6\n",
      "1. 38.126906249997816 38.12740624999782 38.12715624999782 9.43182713655472e-7\n",
      "2. 38.12715624999782 38.12740624999782 38.12728124999782 -2.028781751450416e-6\n",
      "3. 38.12715624999782 38.12728124999782 38.12721874999782 -3.514751992782337e-6\n",
      "4. 38.12715624999782 38.12721874999782 38.12718749999782 -2.7717667707627517e-6\n",
      "5. 38.12715624999782 38.12718749999782 38.12717187499781 -2.40027575226872e-6\n",
      "6. 38.12715624999782 38.12717187499781 38.12716406249781 -2.214529960306835e-6\n",
      "7. 38.12715624999782 38.12716406249781 38.12716015624781 -2.121654453845084e-6\n",
      "8. 38.12715624999782 38.12716015624781 38.12715820312282 -2.0752175553859945e-6\n",
      "9. 38.12715624999782 38.12715820312282 38.127157226560314 -2.0520006040594093e-6\n",
      "10. 38.12715624999782 38.127157226560314 38.12715673827907 -2.040390266500454e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -2.0345864462033744e-6 for V_0/|E| = 38.12715649413845\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 33.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.0 33.0 32.5 -0.0037741061255663145\n",
      "1. 32.5 33.0 32.75 0.0030380921528178613\n",
      "2. 32.75 33.0 32.875 -0.00039027013156969575\n",
      "3. 32.75 32.875 32.8125 -0.0020877331367528014\n",
      "4. 32.75 32.8125 32.78125 -0.0012403904790124663\n",
      "5. 32.75 32.78125 32.765625 -0.0008156778417164179\n",
      "6. 32.75 32.765625 32.7578125 -0.0006030609103631671\n",
      "7. 32.75 32.7578125 32.75390625 -0.0004966872566234965\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.0004434841307927343 for V_0/|E| = 32.751953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 32.72195312499862\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.72095312499862 32.72195312499862 32.72145312499862 -7.874321803265199e-6\n",
      "1. 32.72095312499862 32.72145312499862 32.721203124998624 -1.052151946867807e-6\n",
      "2. 32.721203124998624 32.72145312499862 32.72132812499862 2.358999597581909e-6\n",
      "3. 32.721203124998624 32.72132812499862 32.72126562499862 6.534187668851273e-7\n",
      "4. 32.721203124998624 32.72126562499862 32.72123437499862 1.506208987592258e-6\n",
      "5. 32.721203124998624 32.72123437499862 32.72121874999863 1.932604008096367e-6\n",
      "6. 32.721203124998624 32.72121874999863 32.721210937498626 2.1458023299828544e-6\n",
      "7. 32.721203124998624 32.721210937498626 32.721207031248625 2.2524004998297637e-6\n",
      "8. 32.721203124998624 32.721207031248625 32.721205078123624 2.3057009875967822e-6\n",
      "9. 32.721203124998624 32.721205078123624 32.72120410156113 2.332349561882305e-6\n",
      "10. 32.721203124998624 32.72120410156113 32.721203613279876 2.3456757660886126e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.35233734531786e-6 for V_0/|E| = 32.721203369139246\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 29.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.0 29.0 28.5 -0.008244776549303032\n",
      "1. 28.0 28.5 28.25 -0.0006517129177203254\n",
      "2. 28.25 28.5 28.375 0.0032332419073263494\n",
      "3. 28.25 28.375 28.3125 0.001283341897451615\n",
      "4. 28.25 28.3125 28.28125 0.0022564321845893543\n",
      "5. 28.25 28.28125 28.265625 0.0027443716052413347\n",
      "6. 28.25 28.265625 28.2578125 0.0029886903324990786\n",
      "7. 28.25 28.2578125 28.25390625 0.003110937007433357\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.003172082177548366 for V_0/|E| = 28.251953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 28.457953125001474\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.456953125001473 28.457953125001474 28.45745312500147 -2.4617513745936793e-6\n",
      "1. 28.45745312500147 28.457953125001474 28.457703125001473 5.268882991937034e-6\n",
      "2. 28.45745312500147 28.457703125001473 28.457578125001472 1.4035379428997694e-6\n",
      "3. 28.45745312500147 28.457578125001472 28.45751562500147 3.336202941564433e-6\n",
      "4. 28.45745312500147 28.45751562500147 28.45748437500147 4.3025426671719746e-6\n",
      "5. 28.45745312500147 28.45748437500147 28.45746875000147 4.78571243338958e-6\n",
      "6. 28.45745312500147 28.45746875000147 28.457460937501473 5.0272975758816405e-6\n",
      "7. 28.45745312500147 28.457460937501473 28.457457031251472 5.148088908738388e-6\n",
      "8. 28.45745312500147 28.457457031251472 28.457455078126472 5.208487508534339e-6\n",
      "9. 28.45745312500147 28.457455078126472 28.45745410156397 5.238685270107077e-6\n",
      "10. 28.45745312500147 28.45745410156397 28.457453613282723 5.253784581004684e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 5.261335461959933e-6 for V_0/|E| = 28.457453369142097\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 26.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.0 26.0 25.5 -0.016220207849241268\n",
      "1. 25.0 25.5 25.25 -0.00799068768056505\n",
      "2. 25.0 25.25 25.125 -0.003763193516881599\n",
      "3. 25.0 25.125 25.0625 -0.0016209249313668915\n",
      "4. 25.0 25.0625 25.03125 -0.0005426177240334725\n",
      "5. 25.0 25.03125 25.015625 -1.665555504365234e-6\n",
      "6. 25.015625 25.03125 25.0234375 0.00026926083816632265\n",
      "7. 25.015625 25.0234375 25.01953125 0.0001337600986854838\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00020150107883445495 for V_0/|E| = 25.017578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 25.03157812500124\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.030578125001238 25.03157812500124 25.031078125001237 -7.351788217899058e-6\n",
      "1. 25.031078125001237 25.03157812500124 25.031328125001238 1.3130019308295101e-6\n",
      "2. 25.031328125001238 25.03157812500124 25.03145312500124 -3.019432831869518e-6\n",
      "3. 25.031328125001238 25.03145312500124 25.031390625001237 -5.185620180476165e-6\n",
      "4. 25.031328125001238 25.031390625001237 25.031359375001237 -4.102527431162262e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5. 25.031328125001238 25.031359375001237 25.031343750001238 -3.560982049375527e-6\n",
      "6. 25.031328125001238 25.031343750001238 25.03133593750124 -3.2902073981767773e-6\n",
      "7. 25.031328125001238 25.03133593750124 25.03133203125124 -3.154819030257631e-6\n",
      "8. 25.031328125001238 25.03133203125124 25.03133007812624 -3.087126061826422e-6\n",
      "9. 25.031328125001238 25.03133007812624 25.03132910156374 -3.053278956443396e-6\n",
      "10. 25.031328125001238 25.03132910156374 25.03132861328249 -3.0363551596259064e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -3.0278932467418307e-6 for V_0/|E| = 25.031328369141864\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 23.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.0 23.0 22.5 -0.014316333687464138\n",
      "1. 22.0 22.5 22.25 -0.005094554892754677\n",
      "2. 22.0 22.25 22.125 -0.00033930629374947304\n",
      "3. 22.125 22.25 22.1875 0.0020749040722727115\n",
      "4. 22.125 22.1875 22.15625 0.0008647351791455276\n",
      "5. 22.125 22.15625 22.140625 0.0014690525796943893\n",
      "6. 22.125 22.140625 22.1328125 0.0017717864247858935\n",
      "7. 22.125 22.1328125 22.12890625 0.001923297256404785\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0019990886635584647 for V_0/|E| = 22.126953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 22.23295312500135\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.23195312500135 22.23295312500135 22.23245312500135 -1.1510670376524791e-5\n",
      "1. 22.23195312500135 22.23245312500135 22.232203125001348 -1.8892672259637637e-6\n",
      "2. 22.232203125001348 22.23245312500135 22.23232812500135 2.9215794898859327e-6\n",
      "3. 22.232203125001348 22.23232812500135 22.232265625001347 5.161429735025566e-7\n",
      "4. 22.232203125001348 22.232265625001347 22.232234375001347 1.7188562932833968e-6\n",
      "5. 22.232203125001348 22.232234375001347 22.232218750001348 2.320218249245007e-6\n",
      "6. 22.232203125001348 22.232218750001348 22.23221093750135 2.6208985822171677e-6\n",
      "7. 22.232203125001348 22.23221093750135 22.23220703125135 2.7712405385996296e-6\n",
      "8. 22.232203125001348 22.23220703125135 22.23220507812635 2.846409520609239e-6\n",
      "9. 22.232203125001348 22.23220507812635 22.23220410156385 2.8839941880042978e-6\n",
      "10. 22.232203125001348 22.23220410156385 22.2322036132826 2.902788067977571e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.912182986941969e-6 for V_0/|E| = 22.232203369141974\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 20.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.0 20.0 19.5 -0.0018129613891725387\n",
      "1. 19.5 20.0 19.75 0.00894673666122503\n",
      "2. 19.5 19.75 19.625 0.0035051611713357604\n",
      "3. 19.5 19.625 19.5625 0.0062104148464879085\n",
      "4. 19.5 19.5625 19.53125 0.007574679375266196\n",
      "5. 19.5 19.53125 19.515625 0.00825973231298758\n",
      "6. 19.5 19.515625 19.5078125 0.008602990360320077\n",
      "7. 19.5 19.5078125 19.50390625 0.008774802452930802\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.008860754290377163 for V_0/|E| = 19.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 19.914953125001727\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.913953125001726 19.914953125001727 19.914453125001728 -1.7556187129863304e-5\n",
      "1. 19.913953125001726 19.914453125001728 19.914203125001727 -6.95898897252929e-6\n",
      "2. 19.913953125001726 19.914203125001727 19.914078125001726 -1.6602049253387566e-6\n",
      "3. 19.914078125001726 19.914203125001727 19.91414062500173 9.892325986597977e-7\n",
      "4. 19.91414062500173 19.914203125001727 19.914171875001728 -3.354907351179953e-7\n",
      "5. 19.91414062500173 19.914171875001728 19.914156250001728 -9.97850255939608e-7\n",
      "6. 19.91414062500173 19.914156250001728 19.91414843750173 -6.666703428551582e-7\n",
      "7. 19.91414062500173 19.91414843750173 19.91414453125173 -5.010812305443382e-7\n",
      "8. 19.91414062500173 19.91414453125173 19.91414257812673 -4.1828610194966725e-7\n",
      "9. 19.91414062500173 19.91414257812673 19.91414160156423 -3.7688840174832116e-7\n",
      "10. 19.91414062500173 19.91414160156423 19.91414111328298 -3.561902562181936e-7\n",
      "11. 19.91414062500173 19.91414111328298 19.914140869142354 -3.458399010742976e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.4066627654876473e-7 for V_0/|E| = 19.91414074707204\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 18.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.0 18.0 17.5 -0.0006883716241914501\n",
      "1. 17.5 18.0 17.75 0.011170184123257668\n",
      "2. 17.5 17.75 17.625 0.005164513241270017\n",
      "3. 17.5 17.625 17.5625 0.008148107517032111\n",
      "4. 17.5 17.5625 17.53125 0.0096543175799252\n",
      "5. 17.5 17.53125 17.515625 0.010411041542873827\n",
      "6. 17.5 17.515625 17.5078125 0.010790310223140673\n",
      "7. 17.5 17.5078125 17.50390625 0.010980171485471816\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.011075158878792115 for V_0/|E| = 17.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.970953125001795\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.969953125001794 17.970953125001795 17.970453125001796 -1.6110759119366664e-5\n",
      "1. 17.969953125001794 17.970453125001796 17.970203125001795 -4.520951377568561e-6\n",
      "2. 17.970203125001795 17.970453125001796 17.970328125001796 1.2741795622951022e-6\n",
      "3. 17.970328125001796 17.970453125001796 17.970390625001798 -1.623403756704918e-6\n",
      "4. 17.970328125001796 17.970390625001798 17.9703593750018 -3.072181678310353e-6\n",
      "5. 17.970328125001796 17.9703593750018 17.970343750001796 -2.3477944859910006e-6\n",
      "6. 17.970328125001796 17.970343750001796 17.970335937501794 -1.985599359448701e-6\n",
      "7. 17.970328125001796 17.970335937501794 17.970332031251793 -1.804502357970878e-6\n",
      "8. 17.970328125001796 17.970332031251793 17.970330078126793 -1.713953126223444e-6\n",
      "9. 17.970328125001796 17.970330078126793 17.970329101564296 -1.6686787843060683e-6\n",
      "10. 17.970328125001796 17.970329101564296 17.970328613283044 -1.6460415777808237e-6\n",
      "11. 17.970328125001796 17.970328613283044 17.970328369142422 -1.634724002745037e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.6290627861532927e-6 for V_0/|E| = 17.97032824707211\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.0 17.0 16.5 -0.016404338344723816\n",
      "1. 16.0 16.5 16.25 -0.004424298610313909\n",
      "2. 16.25 16.5 16.375 0.0018358956281028108\n",
      "3. 16.375 16.5 16.4375 -0.0013170336372154488\n",
      "4. 16.375 16.4375 16.40625 -0.00287635017360294\n",
      "5. 16.375 16.40625 16.390625 -0.0020981159124556273\n",
      "6. 16.375 16.390625 16.3828125 -0.0017079311500355332\n",
      "7. 16.375 16.3828125 16.37890625 -0.0015125715351793597\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.001414824877745656 for V_0/|E| = 16.376953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 16.322953125000048\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.321953125000046 16.322953125000048 16.322453125000045 -9.803129097298924e-6\n",
      "1. 16.322453125000045 16.322953125000048 16.322703125000046 2.793557182791023e-6\n",
      "2. 16.322703125000046 16.322953125000048 16.322828125000047 -3.50487626992187e-6\n",
      "3. 16.322703125000046 16.322828125000047 16.322765625000045 -6.654026251531276e-6\n",
      "4. 16.322703125000046 16.322765625000045 16.322734375000046 -5.079456804444187e-6\n",
      "5. 16.322703125000046 16.322734375000046 16.322718750000046 -4.292168297871971e-6\n",
      "6. 16.322703125000046 16.322718750000046 16.322710937500048 -3.89852244719536e-6\n",
      "7. 16.322703125000046 16.322710937500048 16.322707031250047 -3.7016997175381063e-6\n",
      "8. 16.322703125000046 16.322707031250047 16.322705078125047 -3.6032878575368954e-6\n",
      "9. 16.322703125000046 16.322705078125047 16.322704101562547 -3.5540826975315096e-6\n",
      "10. 16.322703125000046 16.322704101562547 16.3227036132813 -3.5294797583011468e-6\n",
      "11. 16.322703125000046 16.3227036132813 16.322703369140672 -3.5171782705121603e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.5110273489157803e-6 for V_0/|E| = 16.322703247070358\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 15.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.0 15.0 14.5 -0.0023714608127726106\n",
      "1. 14.5 15.0 14.75 0.011532899875722867\n",
      "2. 14.5 14.75 14.625 0.004469276050511915\n",
      "3. 14.5 14.625 14.5625 0.007972966959655006\n",
      "4. 14.5 14.5625 14.53125 0.009745870455994872\n",
      "5. 14.5 14.53125 14.515625 0.010637615325353445\n",
      "6. 14.5 14.515625 14.5078125 0.01108481462557911\n",
      "7. 14.5 14.5078125 14.50390625 0.011308746442854869\n",
      "8. 14.5 14.50390625 14.501953125 0.011420795448103139\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.011476840731263191 for V_0/|E| = 14.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.912976562499217\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.911976562499218 14.912976562499217 14.912476562499219 -1.5273299417410693e-5\n",
      "1. 14.911976562499218 14.912476562499219 14.912226562499217 -1.6587193855501543e-6\n",
      "2. 14.912226562499217 14.912476562499219 14.912351562499218 5.148899843287486e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3. 14.912226562499217 14.912351562499218 14.912289062499218 1.7450631948634717e-6\n",
      "4. 14.912226562499217 14.912289062499218 14.912257812499217 3.446975754724534e-6\n",
      "5. 14.912226562499217 14.912257812499217 14.912242187499217 4.297937006569601e-6\n",
      "6. 14.912226562499217 14.912242187499217 14.912234374999217 4.723416755183678e-6\n",
      "7. 14.912226562499217 14.912234374999217 14.912230468749218 4.936159136638853e-6\n",
      "8. 14.912226562499217 14.912230468749218 14.912228515624218 5.042531760085615e-6\n",
      "9. 14.912226562499217 14.912228515624218 14.912227539061718 5.095715316395211e-6\n",
      "10. 14.912226562499217 14.912227539061718 14.912227050780468 5.1223097678664415e-6\n",
      "11. 14.912226562499217 14.912227050780468 14.912226806639843 5.135604590082802e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 5.142253287309174e-6 for V_0/|E| = 14.91222668456953\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.0 14.0 13.5 -0.008735325154021634\n",
      "1. 13.5 14.0 13.75 0.005794891434838685\n",
      "2. 13.75 14.0 13.875 -0.0016004800037113503\n",
      "3. 13.75 13.875 13.8125 -0.005200131526043714\n",
      "4. 13.75 13.8125 13.78125 -0.003408404907939338\n",
      "5. 13.75 13.78125 13.765625 -0.002506472497791601\n",
      "6. 13.75 13.765625 13.7578125 -0.002053984419142667\n",
      "7. 13.75 13.7578125 13.75390625 -0.0018273593350922916\n",
      "8. 13.75 13.75390625 13.751953125 -0.0017139514599434484\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.001657223680502475 for V_0/|E| = 13.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.695976562499476\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.694976562499477 13.695976562499476 13.695476562499476 -2.4638212248198607e-5\n",
      "1. 13.694976562499477 13.695476562499476 13.695226562499476 -9.99642606521562e-6\n",
      "2. 13.694976562499477 13.695226562499476 13.695101562499477 -2.6751399001176286e-6\n",
      "3. 13.695101562499477 13.695226562499476 13.695164062499476 9.85600718967225e-7\n",
      "4. 13.695164062499476 13.695226562499476 13.695195312499475 -8.447772727918254e-7\n",
      "5. 13.695164062499476 13.695195312499475 13.695179687499476 -1.7599621733194106e-6\n",
      "6. 13.695164062499476 13.695179687499476 13.695171874999476 -1.3023699425892097e-6\n",
      "7. 13.695164062499476 13.695171874999476 13.695167968749477 -1.0735753848154357e-6\n",
      "8. 13.695164062499476 13.695167968749477 13.695166015624476 -9.59176082344761e-7\n",
      "9. 13.695164062499476 13.695166015624476 13.695165039061976 -9.019775990281549e-7\n",
      "10. 13.695164062499476 13.695165039061976 13.695164550780726 -8.733793796661725e-7\n",
      "11. 13.695164062499476 13.695164550780726 13.695164306640102 -8.590776727919135e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -8.519267714401893e-7 for V_0/|E| = 13.695164184569789\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.0 13.0 12.5 -0.011085949266576274\n",
      "1. 12.5 13.0 12.75 0.004316047458149389\n",
      "2. 12.75 13.0 12.875 -0.003537399805430256\n",
      "3. 12.75 12.875 12.8125 -0.007349352145141027\n",
      "4. 12.75 12.8125 12.78125 -0.005452849423939053\n",
      "5. 12.75 12.78125 12.765625 -0.004497499756786529\n",
      "6. 12.75 12.765625 12.7578125 -0.004018044415788914\n",
      "7. 12.75 12.7578125 12.75390625 -0.0037778708764543948\n",
      "8. 12.75 12.75390625 12.751953125 -0.0036576725456812053\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0035975454796914204 for V_0/|E| = 12.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.636976562499509\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.63597656249951 12.636976562499509 12.63647656249951 -2.5086258354027987e-5\n",
      "1. 12.63597656249951 12.63647656249951 12.636226562499509 -9.40886495736522e-6\n",
      "2. 12.63597656249951 12.636226562499509 12.636101562499508 -1.5697074554736564e-6\n",
      "3. 12.636101562499508 12.636226562499509 12.636164062499509 2.3499884679230035e-6\n",
      "4. 12.636101562499508 12.636164062499509 12.636132812499508 3.901325365501343e-7\n",
      "5. 12.636101562499508 12.636132812499508 12.636117187499508 1.3700594622448844e-6\n",
      "6. 12.636101562499508 12.636117187499508 12.636109374999508 1.8600232017522118e-6\n",
      "7. 12.636101562499508 12.636109374999508 12.63610546874951 2.1050049239842514e-6\n",
      "8. 12.636101562499508 12.63610546874951 12.636103515624509 2.227497637003687e-6\n",
      "9. 12.636101562499508 12.636103515624509 12.636102539062009 2.288743192923517e-6\n",
      "10. 12.636101562499508 12.636102539062009 12.636102050780758 2.3193666283670798e-6\n",
      "11. 12.636101562499508 12.636102050780758 12.636101806640134 2.334677295260638e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 2.3423330682981917e-6 for V_0/|E| = 12.636101684569821\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.0 12.0 11.5 -0.009506891998614075\n",
      "1. 11.5 12.0 11.75 0.007097568477964881\n",
      "2. 11.75 12.0 11.875 -0.0013836840515004873\n",
      "3. 11.75 11.875 11.8125 -0.005489485404566664\n",
      "4. 11.75 11.8125 11.78125 -0.0034477034525233507\n",
      "5. 11.75 11.78125 11.765625 -0.0024184821379473562\n",
      "6. 11.75 11.765625 11.7578125 -0.0019017812828187224\n",
      "7. 11.75 11.7578125 11.75390625 -0.0016429073498725574\n",
      "8. 11.75 11.75390625 11.751953125 -0.0015133393879690428\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0014485226440579715 for V_0/|E| = 11.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.708976562499469\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.70797656249947 11.708976562499469 11.70847656249947 -1.6757865478610876e-5\n",
      "1. 11.70797656249947 11.70847656249947 11.708226562499469 -3.792703086045224e-8\n",
      "2. 11.708226562499469 11.70847656249947 11.70835156249947 8.322582441471392e-6\n",
      "3. 11.708226562499469 11.70835156249947 11.70828906249947 4.142282685622831e-6\n",
      "4. 11.708226562499469 11.70828906249947 11.708257812499468 6.232419996228919e-6\n",
      "5. 11.708226562499469 11.708257812499468 11.708242187499469 7.277498097191964e-6\n",
      "6. 11.708226562499469 11.708242187499469 11.708234374999469 7.800040063399668e-6\n",
      "7. 11.708226562499469 11.708234374999469 11.70823046874947 8.061311948157645e-6\n",
      "8. 11.708226562499469 11.70823046874947 11.70822851562447 8.19194454037202e-6\n",
      "9. 11.708226562499469 11.70822851562447 11.70822753906197 8.257264067798253e-6\n",
      "10. 11.708226562499469 11.70822753906197 11.70822705078072 8.28992334971891e-6\n",
      "11. 11.708226562499469 11.70822705078072 11.708226806640095 8.306253766036162e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 8.314417723998328e-6 for V_0/|E| = 11.708226684569782\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.0038485863535671558\n",
      "1. 10.5 11.0 10.75 0.01439425241883808\n",
      "2. 10.5 10.75 10.625 0.005061484203997694\n",
      "3. 10.5 10.625 10.5625 0.009674312471381532\n",
      "4. 10.5 10.5625 10.53125 0.012020802878394804\n",
      "5. 10.5 10.53125 10.515625 0.013204146380351594\n",
      "6. 10.5 10.515625 10.5078125 0.013798352659052228\n",
      "7. 10.5 10.5078125 10.50390625 0.01409609067494421\n",
      "8. 10.5 10.50390625 10.501953125 0.01424511855851522\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.014319672239029265 for V_0/|E| = 10.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.89097656249923\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.88997656249923 10.89097656249923 10.89047656249923 -1.4201186169344899e-5\n",
      "1. 10.89047656249923 10.89097656249923 10.89072656249923 3.5655921627496122e-6\n",
      "2. 10.89072656249923 10.89097656249923 10.890851562499229 -5.318004029641125e-6\n",
      "3. 10.89072656249923 10.890851562499229 10.89078906249923 -9.759647702299971e-6\n",
      "4. 10.89072656249923 10.89078906249923 10.890757812499231 -7.538840140611931e-6\n",
      "5. 10.89072656249923 10.890757812499231 10.890742187499232 -6.4284268315815395e-6\n",
      "6. 10.89072656249923 10.890742187499232 10.89073437499923 -5.8732165603588e-6\n",
      "7. 10.89072656249923 10.89073437499923 10.89073046874923 -5.595609492644835e-6\n",
      "8. 10.89072656249923 10.89073046874923 10.890728515624229 -5.456809316053478e-6\n",
      "9. 10.89072656249923 10.890728515624229 10.890727539061729 -5.387406517250006e-6\n",
      "10. 10.89072656249923 10.890727539061729 10.89072705078048 -5.352705673632023e-6\n",
      "11. 10.89072656249923 10.89072705078048 10.890726806639854 -5.335355264458809e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -5.326679741518341e-6 for V_0/|E| = 10.890726684569543\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.028833118260309196\n",
      "1. 10.0 10.5 10.25 -0.01217347945913894\n",
      "2. 10.0 10.25 10.125 -0.0031607100321290812\n",
      "3. 10.125 10.25 10.1875 0.0015224516550569121\n",
      "4. 10.1875 10.25 10.21875 -0.0008340435297618189\n",
      "5. 10.1875 10.21875 10.203125 -0.0020010915661859145\n",
      "6. 10.1875 10.203125 10.1953125 -0.0014184979653107618\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7. 10.1875 10.1953125 10.19140625 -0.001126503568125579\n",
      "8. 10.1875 10.19140625 10.189453125 -0.0009803317799650128\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0009072022175882101 for V_0/|E| = 10.1884765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.165476562499459\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.164476562499459 10.165476562499459 10.164976562499458 -7.088468701188727e-6\n",
      "1. 10.164976562499458 10.165476562499459 10.165226562499459 1.1729037746472012e-5\n",
      "2. 10.164976562499458 10.165226562499459 10.165101562499459 2.320045409144682e-6\n",
      "3. 10.164976562499458 10.165101562499459 10.165039062499458 7.024483179173803e-6\n",
      "4. 10.164976562499458 10.165039062499458 10.165007812499457 9.376743844639328e-6\n",
      "5. 10.164976562499458 10.165007812499457 10.164992187499458 1.0552888701204957e-5\n",
      "6. 10.164976562499458 10.164992187499458 10.164984374999458 1.114096099492873e-5\n",
      "7. 10.164976562499458 10.164984374999458 10.164980468749459 1.1435000015005825e-5\n",
      "8. 10.164976562499458 10.164980468749459 10.164978515624458 1.1582019372664235e-5\n",
      "9. 10.164976562499458 10.164978515624458 10.164977539061958 1.1655527336055432e-5\n",
      "10. 10.164976562499458 10.164977539061958 10.164977050780708 1.1692282375072302e-5\n",
      "11. 10.164976562499458 10.164977050780708 10.164976806640084 1.1710660751808778e-5\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 1.171985038258212e-5 for V_0/|E| = 10.16497668456977\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.0 10.0 9.5 -0.018134358139277888\n",
      "1. 9.5 10.0 9.75 0.0007444894281325668\n",
      "2. 9.75 10.0 9.875 -0.008960164925379583\n",
      "3. 9.75 9.875 9.8125 -0.013612500457732156\n",
      "4. 9.75 9.8125 9.78125 -0.011302775031434798\n",
      "5. 9.75 9.78125 9.765625 -0.010135597225426445\n",
      "6. 9.75 9.765625 9.7578125 -0.00954891497361213\n",
      "7. 9.75 9.7578125 9.75390625 -0.009254798686034202\n",
      "8. 9.75 9.75390625 9.751953125 -0.009107546521188403\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.00903387190710761 for V_0/|E| = 9.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.518976562499574\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.517976562499575 9.518976562499574 9.518476562499576 -1.114682586887172e-5\n",
      "1. 9.518476562499576 9.518976562499574 9.518726562499575 8.722478904547336e-6\n",
      "2. 9.518726562499575 9.518976562499574 9.518851562499574 -1.2124460293695588e-6\n",
      "3. 9.518726562499575 9.518851562499574 9.518789062499575 -6.179702748121185e-6\n",
      "4. 9.518726562499575 9.518789062499575 9.518757812499576 -3.696090869169721e-6\n",
      "5. 9.518726562499575 9.518757812499576 9.518742187499576 -2.454272565814517e-6\n",
      "6. 9.518726562499575 9.518742187499576 9.518734374999575 -1.8333598144020226e-6\n",
      "7. 9.518726562499575 9.518734374999575 9.518730468749574 -1.5229030078439714e-6\n",
      "8. 9.518726562499575 9.518730468749574 9.518728515624574 -1.367673720554085e-6\n",
      "9. 9.518726562499575 9.518728515624574 9.518727539062073 -1.2900582134163646e-6\n",
      "10. 9.518726562499575 9.518727539062073 9.518727050780825 -1.2512519334108516e-6\n",
      "11. 9.518726562499575 9.518727050780825 9.518726806640199 -1.2318491779521542e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.222146727155878e-6 for V_0/|E| = 9.518726684569888\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.002516047243036627\n",
      "1. 8.5 9.0 8.75 0.019366449307036137\n",
      "2. 8.5 8.75 8.625 0.0081068088052711\n",
      "3. 8.5 8.625 8.5625 0.01365565877337858\n",
      "4. 8.5 8.5625 8.53125 0.016490638050105876\n",
      "5. 8.5 8.53125 8.515625 0.017923417883899454\n",
      "6. 8.5 8.515625 8.5078125 0.01864364941684252\n",
      "7. 8.5 8.5078125 8.50390625 0.0190047279755404\n",
      "8. 8.5 8.50390625 8.501953125 0.019185508252875228\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.019275958677189783 for V_0/|E| = 8.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.939976562499647\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.938976562499647 8.939976562499647 8.939476562499646 -2.2490468479541276e-5\n",
      "1. 8.938976562499647 8.939476562499646 8.939226562499647 -1.5691923543398541e-6\n",
      "2. 8.939226562499647 8.939476562499646 8.939351562499645 8.892375361298295e-6\n",
      "3. 8.939226562499647 8.939351562499645 8.939289062499647 3.661513403285169e-6\n",
      "4. 8.939226562499647 8.939289062499647 8.939257812499648 6.276926576070465e-6\n",
      "5. 8.939226562499647 8.939257812499648 8.939242187499648 7.58464665591762e-6\n",
      "6. 8.939226562499647 8.939242187499648 8.939234374999646 8.238510867984883e-6\n",
      "7. 8.939226562499647 8.939234374999646 8.939230468749646 8.565443290069869e-6\n",
      "8. 8.939226562499647 8.939230468749646 8.939228515624645 8.728909439650627e-6\n",
      "9. 8.939226562499647 8.939228515624645 8.939227539062145 8.810644107545793e-6\n",
      "10. 8.939226562499647 8.939227539062145 8.939227050780897 8.851509707538382e-6\n",
      "11. 8.939226562499647 8.939227050780897 8.93922680664027 8.871943623437552e-6\n",
      "12. 8.939226562499647 8.93922680664027 8.93922668456996 8.8821588615344e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 8.887267247275599e-6 for V_0/|E| = 8.939226623534804\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.02373056467053629\n",
      "1. 8.0 8.5 8.25 -0.0035595735623665304\n",
      "2. 8.25 8.5 8.375 0.007550847817851898\n",
      "3. 8.25 8.375 8.3125 0.0019075428893812957\n",
      "4. 8.25 8.3125 8.28125 0.004706966722263958\n",
      "5. 8.25 8.28125 8.265625 0.00612332432619901\n",
      "6. 8.25 8.265625 8.2578125 0.006835687103627682\n",
      "7. 8.25 8.2578125 8.25390625 0.0071929173126047885\n",
      "8. 8.25 8.25390625 8.251953125 0.0073717949779440375\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.007461299493848462 for V_0/|E| = 8.2509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.418976562500019\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.41797656250002 8.418976562500019 8.418476562500018 -3.577797854824414e-5\n",
      "1. 8.41797656250002 8.418476562500018 8.418226562500019 -1.3805046932876226e-5\n",
      "2. 8.41797656250002 8.418226562500019 8.41810156250002 -2.817528457701286e-6\n",
      "3. 8.41810156250002 8.418226562500019 8.418164062500018 2.676491912817719e-6\n",
      "4. 8.418164062500018 8.418226562500019 8.418195312500018 -7.054118884615422e-8\n",
      "5. 8.418164062500018 8.418195312500018 8.418179687500018 -1.4440408894342014e-6\n",
      "6. 8.418164062500018 8.418179687500018 8.418171875000018 -7.572921007653268e-7\n",
      "7. 8.418164062500018 8.418171875000018 8.41816796875002 -4.1391638870066636e-7\n",
      "8. 8.418164062500018 8.41816796875002 8.418166015625019 -2.422276763582648e-7\n",
      "9. 8.418164062500018 8.418166015625019 8.418165039062519 -1.5638467500455438e-7\n",
      "10. 8.418164062500018 8.418165039062519 8.418164550781269 -1.1346257904096047e-7\n",
      "11. 8.418164062500018 8.418164550781269 8.418164306640644 -9.200208820340778e-8\n",
      "12. 8.418164062500018 8.418164306640644 8.418164184570331 -8.127210545719564e-8\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -7.590533679855241e-8 for V_0/|E| = 8.418164123535174\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.002418682422873482\n",
      "1. 7.5 8.0 7.75 0.021880448226680633\n",
      "2. 7.5 7.75 7.625 0.009325120857490092\n",
      "3. 7.5 7.625 7.5625 0.015499326679769299\n",
      "4. 7.5 7.5625 7.53125 0.018663767602644946\n",
      "5. 7.5 7.53125 7.515625 0.020265545829058183\n",
      "6. 7.5 7.515625 7.5078125 0.021071352476548077\n",
      "7. 7.5 7.5078125 7.50390625 0.02147548871168525\n",
      "8. 7.5 7.50390625 7.501953125 0.021677865496102743\n",
      "9. 7.5 7.501953125 7.5009765625 0.021779131111830215\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = 0.02182978323118894 for V_0/|E| = 7.50048828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.947488281250483\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.946488281250483 7.947488281250483 7.9469882812504835 -1.767735425509213e-5\n",
      "1. 7.9469882812504835 7.947488281250483 7.947238281250483 5.3505347926603535e-6\n",
      "2. 7.947238281250483 7.947488281250483 7.9473632812504835 -6.1638039173183e-6\n",
      "3. 7.947238281250483 7.9473632812504835 7.947300781250483 -1.1920676610137541e-5\n",
      "4. 7.947238281250483 7.947300781250483 7.947269531250483 -9.042265643963848e-6\n",
      "5. 7.947238281250483 7.947269531250483 7.947253906250483 -7.60304021397121e-6\n",
      "6. 7.947238281250483 7.947253906250483 7.947246093750483 -6.883422622385365e-6\n",
      "7. 7.947238281250483 7.947246093750483 7.947242187500483 -6.5236128125182325e-6\n",
      "8. 7.947238281250483 7.947242187500483 7.947240234375483 -6.343708720025016e-6\n",
      "9. 7.947238281250483 7.947240234375483 7.947239257812983 -6.253757473117578e-6\n",
      "10. 7.947238281250483 7.947239257812983 7.947238769531733 -6.2087820511170345e-6\n",
      "11. 7.947238281250483 7.947238769531733 7.947238525391108 -6.186290331174752e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12. 7.947238281250483 7.947238525391108 7.947238403320796 -6.175045475321588e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -6.169423887976435e-6 for V_0/|E| = 7.947238342285639\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.02154947303927156\n",
      "1. 7.5 8.0 7.75 0.000955312137492575\n",
      "2. 7.75 8.0 7.875 -0.01071953465870774\n",
      "3. 7.75 7.875 7.8125 -0.016237843623025064\n",
      "4. 7.75 7.8125 7.78125 -0.013504805510335734\n",
      "5. 7.75 7.78125 7.765625 -0.012118734599409996\n",
      "6. 7.75 7.765625 7.7578125 -0.011420780200772224\n",
      "7. 7.75 7.7578125 7.75390625 -0.011070569379137155\n",
      "8. 7.75 7.75390625 7.751953125 -0.01089515507690784\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.010807370643101343 for V_0/|E| = 7.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.519976562500257\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.5189765625002565 7.519976562500257 7.519476562500257 -9.506028687196065e-6\n",
      "1. 7.519476562500257 7.519976562500257 7.5197265625002565 1.45741733984819e-5\n",
      "2. 7.519476562500257 7.5197265625002565 7.519601562500257 2.533632195023843e-6\n",
      "3. 7.519476562500257 7.519601562500257 7.519539062500257 8.55379342157197e-6\n",
      "4. 7.519476562500257 7.519539062500257 7.519507812500257 1.1563956044179596e-5\n",
      "5. 7.519476562500257 7.519507812500257 7.519492187500257 1.3069057578272358e-5\n",
      "6. 7.519476562500257 7.519492187500257 7.519484375000257 1.3821611716061957e-5\n",
      "7. 7.519476562500257 7.519484375000257 7.519480468750257 1.4197893131963062e-5\n",
      "8. 7.519476562500257 7.519480468750257 7.5194785156252575 1.4386033393710073e-5\n",
      "9. 7.519476562500257 7.5194785156252575 7.519477539062757 1.448010369055589e-5\n",
      "10. 7.519476562500257 7.519477539062757 7.519477050781507 1.4527137969444881e-5\n",
      "11. 7.519476562500257 7.519477050781507 7.519476806640882 1.4550653747253704e-5\n",
      "12. 7.519476562500257 7.519476806640882 7.51947668457057 1.4562414453549168e-5\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 1.4568294393512508e-5 for V_0/|E| = 7.519476623535414\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 237.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.0 237.0 236.5 -0.0012390662552007037\n",
      "1. 236.0 236.5 236.25 -0.00015413426525159768\n",
      "2. 236.25 236.5 236.375 0.00038952655085469276\n",
      "3. 236.25 236.375 236.3125 0.00011759650588534637\n",
      "4. 236.25 236.3125 236.28125 0.00025353661441198104\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.00032152535302583873 for V_0/|E| = 236.265625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 236.42962500000556\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.42862500000555 236.42962500000556 236.42912500000557 -1.1743494453799746e-6\n",
      "1. 236.42862500000555 236.42912500000557 236.42887500000558 -8.737503351722307e-8\n",
      "2. 236.42887500000558 236.42912500000557 236.42900000000557 4.561141790712733e-7\n",
      "3. 236.42887500000558 236.42900000000557 236.4289375000056 1.8436862615223662e-7\n",
      "4. 236.42887500000558 236.4289375000056 236.42890625000558 3.202410257749679e-7\n",
      "5. 236.42887500000558 236.42890625000558 236.42889062500558 3.881784377089312e-7\n",
      "6. 236.42887500000558 236.42889062500558 236.42888281250558 4.221449126534495e-7\n",
      "7. 236.42887500000558 236.42888281250558 236.4288789062556 4.391294335749356e-7\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 4.4762144831838766e-7 for V_0/|E| = 236.42887695313058\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 158.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.0 158.0 157.5 -0.0007346645321262517\n",
      "1. 157.5 158.0 157.75 0.0008603173537895902\n",
      "2. 157.5 157.75 157.625 6.191961963004914e-5\n",
      "3. 157.5 157.625 157.5625 0.0004608916444434144\n",
      "4. 157.5 157.5625 157.53125 0.000660547769393114\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.0007604183761907288 for V_0/|E| = 157.515625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 157.769625000006\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.76862500000598 157.769625000006 157.769125000006 -6.778000592773207e-7\n",
      "1. 157.769125000006 157.769625000006 157.769375000006 9.168994685823564e-7\n",
      "2. 157.769125000006 157.769375000006 157.769250000006 1.1954889063902313e-7\n",
      "3. 157.769125000006 157.769250000006 157.769187500006 5.182250629765937e-7\n",
      "4. 157.769125000006 157.769187500006 157.769156250006 7.175629044708696e-7\n",
      "5. 157.769125000006 157.769156250006 157.769140625006 8.17230638560456e-7\n",
      "6. 157.769125000006 157.769140625006 157.769132812506 8.670657759527476e-7\n",
      "7. 157.769125000006 157.769132812506 157.76912890625601 8.919816440351692e-7\n",
      "8. 157.769125000006 157.76912890625601 157.769126953131 9.04441496687579e-7\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 9.106703171247113e-7 for V_0/|E| = 157.7691259765685\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 114.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.0 114.0 113.5 -0.003200900438735002\n",
      "1. 113.0 113.5 113.25 -0.0010368361815047526\n",
      "2. 113.25 113.5 113.375 5.052088812239477e-5\n",
      "3. 113.375 113.5 113.4375 -0.0004936020747602726\n",
      "4. 113.375 113.4375 113.40625 -0.0007653301844351821\n",
      "5. 113.375 113.40625 113.390625 -0.0006294939010130158\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0005615549308824672 for V_0/|E| = 113.3828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 113.2618125000042\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.26081250000419 113.2618125000042 113.2613125000042 -9.367842091368018e-7\n",
      "1. 113.2613125000042 113.2618125000042 113.2615625000042 1.241157015199581e-6\n",
      "2. 113.2613125000042 113.2615625000042 113.2614375000042 1.5218396341902453e-7\n",
      "3. 113.2613125000042 113.2614375000042 113.2613750000042 6.966700772651653e-7\n",
      "4. 113.2613125000042 113.2613750000042 113.26134375000419 9.689143943694475e-7\n",
      "5. 113.2613125000042 113.26134375000419 113.26132812500418 1.1050354116991558e-6\n",
      "6. 113.2613125000042 113.26132812500418 113.26132031250418 1.1730957080271444e-6\n",
      "7. 113.2613125000042 113.26132031250418 113.2613164062542 1.2071270571099966e-6\n",
      "8. 113.2613125000042 113.2613164062542 113.26131445312919 1.224141588593566e-6\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 1.2326494354712003e-6 for V_0/|E| = 113.2613134765667\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 86.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.0 86.0 85.5 -0.002079137134225096\n",
      "1. 85.5 86.0 85.75 0.0007425780563488308\n",
      "2. 85.75 86.0 85.875 -0.0006714189644561301\n",
      "3. 85.75 85.875 85.8125 -0.0013760619168066588\n",
      "4. 85.75 85.8125 85.78125 -0.0010239365316215073\n",
      "5. 85.75 85.78125 85.765625 -0.0008477267867774346\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0007595851371547249 for V_0/|E| = 85.7578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 85.63181250000417\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.63081250000417 85.63181250000417 85.63131250000417 -3.7353653627945688e-6\n",
      "1. 85.63081250000417 85.63131250000417 85.63106250000416 -9.077027526690032e-7\n",
      "2. 85.63106250000416 85.63131250000417 85.63118750000416 5.061381411320516e-7\n",
      "3. 85.63118750000416 85.63131250000417 85.63125000000417 -2.0078266481430725e-7\n",
      "4. 85.63118750000416 85.63125000000417 85.63121875000417 -5.54244022192921e-7\n",
      "5. 85.63118750000416 85.63121875000417 85.63120312500416 -3.775131551855836e-7\n",
      "6. 85.63118750000416 85.63120312500416 85.63119531250416 -2.891478030340776e-7\n",
      "7. 85.63118750000416 85.63119531250416 85.63119140625416 -2.449674717285791e-7\n",
      "8. 85.63118750000416 85.63119140625416 85.63118945312917 -2.2287383024704648e-7\n",
      "9. 85.63118750000416 85.63118945312917 85.63118847656666 -2.1182930521810908e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -2.0630593236879752e-7 for V_0/|E| = 85.6311879882854\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 68.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.0 68.0 67.5 -0.005025174286341681\n",
      "1. 67.0 67.5 67.25 -0.0015274822673099595\n",
      "2. 67.25 67.5 67.375 0.00023670810068545325\n",
      "3. 67.375 67.5 67.4375 -0.0006466692979989091\n",
      "4. 67.375 67.4375 67.40625 -0.001087396070808143\n",
      "5. 67.375 67.40625 67.390625 -0.0008671127898531627\n",
      "6. 67.375 67.390625 67.3828125 -0.0007569110746287873\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0007017951941369959 for V_0/|E| = 67.37890625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 67.28390625000432\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.28290625000432 67.28390625000432 67.28340625000432 -3.1617179602697826e-6\n",
      "1. 67.28340625000432 67.28390625000432 67.28365625000433 3.741594337828105e-7\n",
      "2. 67.28365625000433 67.28390625000432 67.28378125000432 -1.393783092959142e-6\n",
      "3. 67.28365625000433 67.28378125000432 67.28371875000433 -2.277752203337414e-6\n",
      "4. 67.28365625000433 67.28371875000433 67.28368750000433 -1.8357681962745546e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5. 67.28365625000433 67.28368750000433 67.28367187500433 -1.6147783584169675e-6\n",
      "6. 67.28365625000433 67.28367187500433 67.28366406250433 -1.5042791596611698e-6\n",
      "7. 67.28365625000433 67.28366406250433 67.28366015625433 -1.449032145695083e-6\n",
      "8. 67.28365625000433 67.28366015625433 67.28365820312933 -1.4214078530715197e-6\n",
      "9. 67.28365625000433 67.28365820312933 67.28365722656683 -1.407595609915493e-6\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -1.400689600183664e-6 for V_0/|E| = 67.28365673828557\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 55.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.0 55.0 54.5 -0.004591870443001571\n",
      "1. 54.0 54.5 54.25 -0.00033280707950481697\n",
      "2. 54.25 54.5 54.375 0.001820368832466088\n",
      "3. 54.25 54.375 54.3125 0.0007418036511896121\n",
      "4. 54.25 54.3125 54.28125 0.0012805914176925158\n",
      "5. 54.25 54.28125 54.265625 0.0015503563551218609\n",
      "6. 54.25 54.265625 54.2578125 0.001685331643494347\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = 0.0017528425009862227 for V_0/|E| = 54.25390625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 54.461906249997185\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.46090624999719 54.461906249997185 54.46140624999718 -5.737895369416914e-6\n",
      "1. 54.46090624999719 54.46140624999718 54.46115624999719 -1.4425047774047727e-6\n",
      "2. 54.46115624999719 54.46140624999718 54.461281249997185 7.052108694962251e-7\n",
      "3. 54.461281249997185 54.46140624999718 54.461343749997184 -3.6864800302952324e-7\n",
      "4. 54.461281249997185 54.461343749997184 54.461312499997184 -9.055784193252339e-7\n",
      "5. 54.461281249997185 54.461312499997184 54.46129687499719 -6.371139774724634e-7\n",
      "6. 54.461281249997185 54.46129687499719 54.46128906249719 -5.028818332142875e-7\n",
      "7. 54.461281249997185 54.46128906249719 54.461285156247186 -4.357663562083751e-7\n",
      "8. 54.461281249997185 54.461285156247186 54.461283203122186 -4.022056153338802e-7\n",
      "9. 54.461281249997185 54.461283203122186 54.46128222655969 -3.854269235663491e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -3.7703926493841327e-7 for V_0/|E| = 54.46128173827844\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 46.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.0 46.0 45.5 -0.008693984736728317\n",
      "1. 45.0 45.5 45.25 -0.0037073074066095706\n",
      "2. 45.0 45.25 45.125 -0.0011795590095504038\n",
      "3. 45.125 45.25 45.1875 9.296976270475279e-5\n",
      "4. 45.1875 45.25 45.21875 -0.0005440173937236134\n",
      "5. 45.1875 45.21875 45.203125 -0.0008619687770475329\n",
      "6. 45.1875 45.203125 45.1953125 -0.0007030382434065962\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.000623539110866491 for V_0/|E| = 45.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 45.1344062499978\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.133406249997805 45.1344062499978 45.13390624999781 -2.989283199262226e-6\n",
      "1. 45.13390624999781 45.1344062499978 45.1341562499978 2.1107031265295126e-6\n",
      "2. 45.1341562499978 45.1344062499978 45.1342812499978 -4.393004057916913e-7\n",
      "3. 45.1341562499978 45.1342812499978 45.1342187499978 -1.7142963275023737e-6\n",
      "4. 45.1341562499978 45.1342187499978 45.1341874999978 -1.076797854613403e-6\n",
      "5. 45.1341562499978 45.1341874999978 45.134171874997804 -7.580499391264076e-7\n",
      "6. 45.1341562499978 45.134171874997804 45.1341640624978 -5.986748198640857e-7\n",
      "7. 45.1341562499978 45.1341640624978 45.1341601562478 -5.189885919970901e-7\n",
      "8. 45.1341562499978 45.1341601562478 45.1341582031228 -4.791446035783234e-7\n",
      "9. 45.1341562499978 45.1341582031228 45.134157226560305 -4.592216062843782e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -4.4926120720922177e-7 for V_0/|E| = 45.13415673827905\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 39.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.0 39.0 38.5 -0.010180698290987332\n",
      "1. 38.0 38.5 38.25 -0.004398127752606141\n",
      "2. 38.0 38.25 38.125 -0.001458433148046693\n",
      "3. 38.125 38.25 38.1875 2.3605472851103665e-5\n",
      "4. 38.1875 38.25 38.21875 -0.0007184324395960776\n",
      "5. 38.1875 38.21875 38.203125 -0.0010886872463526304\n",
      "6. 38.1875 38.203125 38.1953125 -0.0009036234795695864\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0008110438708529125 for V_0/|E| = 38.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 38.12740624999782\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.12640624999782 38.12740624999782 38.126906249997816 -5.000729457186525e-6\n",
      "1. 38.126906249997816 38.12740624999782 38.12715624999782 9.431666788517482e-7\n",
      "2. 38.12715624999782 38.12740624999782 38.12728124999782 -2.028797361733825e-6\n",
      "3. 38.12715624999782 38.12728124999782 38.12721874999782 -3.514767922694259e-6\n",
      "4. 38.12715624999782 38.12721874999782 38.12718749999782 -2.771783203166219e-6\n",
      "5. 38.12715624999782 38.12718749999782 38.12717187499781 -2.4002917044699704e-6\n",
      "6. 38.12715624999782 38.12717187499781 38.12716406249781 -2.21454516728983e-6\n",
      "7. 38.12715624999782 38.12716406249781 38.12716015624781 -2.121671007879343e-6\n",
      "8. 38.12715624999782 38.12716015624781 38.12715820312282 -2.0752337052255414e-6\n",
      "9. 38.12715624999782 38.12715820312282 38.127157226560314 -2.0520156081411143e-6\n",
      "10. 38.12715624999782 38.127157226560314 38.12715673827907 -2.040407426076839e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -2.03460303346333e-6 for V_0/|E| = 38.12715649413845\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 33.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.0 33.0 32.5 -0.003774106141153586\n",
      "1. 32.5 33.0 32.75 0.003038092138340911\n",
      "2. 32.75 33.0 32.875 -0.0003902701473538549\n",
      "3. 32.75 32.875 32.8125 -0.002087733150723219\n",
      "4. 32.75 32.8125 32.78125 -0.0012403904933806211\n",
      "5. 32.75 32.78125 32.765625 -0.0008156778561881115\n",
      "6. 32.75 32.765625 32.7578125 -0.000603060924940366\n",
      "7. 32.75 32.7578125 32.75390625 -0.0004966872711203789\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.00044348414461355714 for V_0/|E| = 32.751953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 32.72195312499862\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.72095312499862 32.72195312499862 32.72145312499862 -7.874337568572597e-6\n",
      "1. 32.72095312499862 32.72145312499862 32.721203124998624 -1.0521666325097596e-6\n",
      "2. 32.721203124998624 32.72145312499862 32.72132812499862 2.3589854090258033e-6\n",
      "3. 32.721203124998624 32.72132812499862 32.72126562499862 6.534032785250884e-7\n",
      "4. 32.721203124998624 32.72126562499862 32.72123437499862 1.5061930820579718e-6\n",
      "5. 32.721203124998624 32.72123437499862 32.72121874999863 1.9325904636492353e-6\n",
      "6. 32.721203124998624 32.72121874999863 32.721210937498626 2.1457874777781337e-6\n",
      "7. 32.721203124998624 32.721210937498626 32.721207031248625 2.252386093934568e-6\n",
      "8. 32.721203124998624 32.721207031248625 32.721205078123624 2.305685633285029e-6\n",
      "9. 32.721203124998624 32.721205078123624 32.72120410156113 2.3323352651013505e-6\n",
      "10. 32.721203124998624 32.72120410156113 32.721203613279876 2.3456619399598204e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.352322533423854e-6 for V_0/|E| = 32.721203369139246\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 29.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.0 29.0 28.5 -0.008244776563017257\n",
      "1. 28.0 28.5 28.25 -0.0006517129290118321\n",
      "2. 28.25 28.5 28.375 0.003233241893476762\n",
      "3. 28.25 28.375 28.3125 0.0012833418840694812\n",
      "4. 28.25 28.3125 28.28125 0.0022564321708011944\n",
      "5. 28.25 28.28125 28.265625 0.0027443715927829766\n",
      "6. 28.25 28.265625 28.2578125 0.002988690320405552\n",
      "7. 28.25 28.2578125 28.25390625 0.0031109369927525793\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0031720821630686425 for V_0/|E| = 28.251953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 28.457953125001474\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.456953125001473 28.457953125001474 28.45745312500147 -2.4617663492193384e-6\n",
      "1. 28.45745312500147 28.457953125001474 28.457703125001473 5.268868855748401e-6\n",
      "2. 28.45745312500147 28.457703125001473 28.457578125001472 1.4035236202310938e-6\n",
      "3. 28.45745312500147 28.457578125001472 28.45751562500147 3.336190005335955e-6\n",
      "4. 28.45745312500147 28.45751562500147 28.45748437500147 4.302528695119269e-6\n",
      "5. 28.45745312500147 28.45748437500147 28.45746875000147 4.785697654474403e-6\n",
      "6. 28.45745312500147 28.45746875000147 28.457460937501473 5.0272825632011e-6\n",
      "7. 28.45745312500147 28.457460937501473 28.457457031251472 5.14807688670754e-6\n",
      "8. 28.45745312500147 28.457457031251472 28.457455078126472 5.20847275816397e-6\n",
      "9. 28.45745312500147 28.457455078126472 28.45745410156397 5.238672169303387e-6\n",
      "10. 28.45745312500147 28.45745410156397 28.457453613282723 5.253768843945562e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 5.2613203672588725e-6 for V_0/|E| = 28.457453369142097\n",
      "Locating Initial V_0.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Initial V_0/|E| = 26.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.0 26.0 25.5 -0.01622020786891308\n",
      "1. 25.0 25.5 25.25 -0.007990687697305633\n",
      "2. 25.0 25.25 25.125 -0.003763193529755455\n",
      "3. 25.0 25.125 25.0625 -0.0016209249456116898\n",
      "4. 25.0 25.0625 25.03125 -0.0005426177367513374\n",
      "5. 25.0 25.03125 25.015625 -1.6655677000335486e-6\n",
      "6. 25.015625 25.03125 25.0234375 0.00026926082727752356\n",
      "7. 25.015625 25.0234375 25.01953125 0.00013376008329115622\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00020150106865225994 for V_0/|E| = 25.017578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 25.03157812500124\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.030578125001238 25.03157812500124 25.031078125001237 -7.351802810628353e-6\n",
      "1. 25.031078125001237 25.03157812500124 25.031328125001238 1.312989731755172e-6\n",
      "2. 25.031328125001238 25.03157812500124 25.03145312500124 -3.0194453524747734e-6\n",
      "3. 25.031328125001238 25.03145312500124 25.031390625001237 -5.185632725762527e-6\n",
      "4. 25.031328125001238 25.031390625001237 25.031359375001237 -4.102539679506565e-6\n",
      "5. 25.031328125001238 25.031359375001237 25.031343750001238 -3.5609940876267927e-6\n",
      "6. 25.031328125001238 25.031343750001238 25.03133593750124 -3.2902200938432224e-6\n",
      "7. 25.031328125001238 25.03133593750124 25.03133203125124 -3.1548308758407244e-6\n",
      "8. 25.031328125001238 25.03133203125124 25.03133007812624 -3.0871407536242798e-6\n",
      "9. 25.031328125001238 25.03133007812624 25.03132910156374 -3.0532918381322255e-6\n",
      "10. 25.031328125001238 25.03132910156374 25.03132861328249 -3.0363679968421034e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -3.0279068781151635e-6 for V_0/|E| = 25.031328369141864\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 23.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.0 23.0 22.5 -0.014316333720672456\n",
      "1. 22.0 22.5 22.25 -0.0050945549108383\n",
      "2. 22.0 22.25 22.125 -0.00033930630573148054\n",
      "3. 22.125 22.25 22.1875 0.002074904062947613\n",
      "4. 22.125 22.1875 22.15625 0.0008647351689268105\n",
      "5. 22.125 22.15625 22.140625 0.0014690525707571037\n",
      "6. 22.125 22.140625 22.1328125 0.0017717864133272386\n",
      "7. 22.125 22.1328125 22.12890625 0.001923297244788738\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0019990886558381837 for V_0/|E| = 22.126953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 22.23295312500135\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.23195312500135 22.23295312500135 22.23245312500135 -1.1510683379105867e-5\n",
      "1. 22.23195312500135 22.23245312500135 22.232203125001348 -1.8892801251260566e-6\n",
      "2. 22.232203125001348 22.23245312500135 22.23232812500135 2.921567605895606e-6\n",
      "3. 22.232203125001348 22.23232812500135 22.232265625001347 5.16131195586755e-7\n",
      "4. 22.232203125001348 22.232265625001347 22.232234375001347 1.7188455918773443e-6\n",
      "5. 22.232203125001348 22.232234375001347 22.232218750001348 2.320206867211816e-6\n",
      "6. 22.232203125001348 22.232218750001348 22.23221093750135 2.6208867494430625e-6\n",
      "7. 22.232203125001348 22.23221093750135 22.23220703125135 2.771226672538138e-6\n",
      "8. 22.232203125001348 22.23220703125135 22.23220507812635 2.8463965447742603e-6\n",
      "9. 22.232203125001348 22.23220507812635 22.23220410156385 2.883980808718503e-6\n",
      "10. 22.232203125001348 22.23220410156385 22.2322036132826 2.902773787996293e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.912170779498914e-6 for V_0/|E| = 22.232203369141974\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 20.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.0 20.0 19.5 -0.001812961409514758\n",
      "1. 19.5 20.0 19.75 0.008946736690153346\n",
      "2. 19.5 19.75 19.625 0.003505161174652174\n",
      "3. 19.5 19.625 19.5625 0.006210414862921897\n",
      "4. 19.5 19.5625 19.53125 0.007574679398040226\n",
      "5. 19.5 19.53125 19.515625 0.008259732338346405\n",
      "6. 19.5 19.515625 19.5078125 0.00860299038641996\n",
      "7. 19.5 19.5078125 19.50390625 0.008774802480504537\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.008860754316199145 for V_0/|E| = 19.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 19.914953125001727\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.913953125001726 19.914953125001727 19.914453125001728 -1.7556198108280742e-5\n",
      "1. 19.913953125001726 19.914453125001728 19.914203125001727 -6.958999485337265e-6\n",
      "2. 19.913953125001726 19.914203125001727 19.914078125001726 -1.6602160065933528e-6\n",
      "3. 19.914078125001726 19.914203125001727 19.91414062500173 9.892201863466073e-7\n",
      "4. 19.91414062500173 19.914203125001727 19.914171875001728 -3.355026927744498e-7\n",
      "5. 19.91414062500173 19.914171875001728 19.914156250001728 -9.978598773545742e-7\n",
      "6. 19.91414062500173 19.914156250001728 19.91414843750173 -6.666828316482672e-7\n",
      "7. 19.91414062500173 19.91414843750173 19.91414453125173 -5.01092633250675e-7\n",
      "8. 19.91414062500173 19.91414453125173 19.91414257812673 -4.1829686702940284e-7\n",
      "9. 19.91414062500173 19.91414257812673 19.91414160156423 -3.768996358355668e-7\n",
      "10. 19.91414062500173 19.91414160156423 19.91414111328298 -3.5619978592636694e-7\n",
      "11. 19.91414062500173 19.91414111328298 19.914140869142354 -3.4585137625502495e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.4067555052352053e-7 for V_0/|E| = 19.91414074707204\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 18.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.0 18.0 17.5 -0.0006883716446519833\n",
      "1. 17.5 18.0 17.75 0.01117018424557909\n",
      "2. 17.5 17.75 17.625 0.005164513291920723\n",
      "3. 17.5 17.625 17.5625 0.008148107602537051\n",
      "4. 17.5 17.5625 17.53125 0.009654317683437757\n",
      "5. 17.5 17.53125 17.515625 0.010411041655669414\n",
      "6. 17.5 17.515625 17.5078125 0.010790310341530487\n",
      "7. 17.5 17.5078125 17.50390625 0.01098017160575371\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.011075158998888831 for V_0/|E| = 17.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.970953125001795\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.969953125001794 17.970953125001795 17.970453125001796 -1.6110771246085825e-5\n",
      "1. 17.969953125001794 17.970453125001796 17.970203125001795 -4.520961194711439e-6\n",
      "2. 17.970203125001795 17.970453125001796 17.970328125001796 1.2741693147222926e-6\n",
      "3. 17.970328125001796 17.970453125001796 17.970390625001798 -1.6234149554451596e-6\n",
      "4. 17.970328125001796 17.970390625001798 17.9703593750018 -3.072192419852844e-6\n",
      "5. 17.970328125001796 17.9703593750018 17.970343750001796 -2.347804223469166e-6\n",
      "6. 17.970328125001796 17.970343750001796 17.970335937501794 -1.9856105468812603e-6\n",
      "7. 17.970328125001796 17.970335937501794 17.970332031251793 -1.8045131753647284e-6\n",
      "8. 17.970328125001796 17.970332031251793 17.970330078126793 -1.713964059698879e-6\n",
      "9. 17.970328125001796 17.970330078126793 17.970329101564296 -1.6686898045621498e-6\n",
      "10. 17.970328125001796 17.970329101564296 17.970328613283044 -1.6460535323151975e-6\n",
      "11. 17.970328125001796 17.970328613283044 17.970328369142422 -1.6347326438750322e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.6290742210560759e-6 for V_0/|E| = 17.97032824707211\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.0 17.0 16.5 -0.01640433886256945\n",
      "1. 16.0 16.5 16.25 -0.004424298753944133\n",
      "2. 16.25 16.5 16.375 0.0018358956710131681\n",
      "3. 16.375 16.5 16.4375 -0.0013170336871778567\n",
      "4. 16.375 16.4375 16.40625 -0.0028763502721138447\n",
      "5. 16.375 16.40625 16.390625 -0.0020981159841827555\n",
      "6. 16.375 16.390625 16.3828125 -0.0017079312132987719\n",
      "7. 16.375 16.3828125 16.37890625 -0.0015125715919677297\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.001414824929867105 for V_0/|E| = 16.376953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 16.322953125000048\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.321953125000046 16.322953125000048 16.322453125000045 -9.803138761074663e-6\n",
      "1. 16.322453125000045 16.322953125000048 16.322703125000046 2.7935470455105537e-6\n",
      "2. 16.322703125000046 16.322953125000048 16.322828125000047 -3.5048875994506017e-6\n",
      "3. 16.322703125000046 16.322828125000047 16.322765625000045 -6.65403804453515e-6\n",
      "4. 16.322703125000046 16.322765625000045 16.322734375000046 -5.079467174207904e-6\n",
      "5. 16.322703125000046 16.322734375000046 16.322718750000046 -4.292178375727183e-6\n",
      "6. 16.322703125000046 16.322718750000046 16.322710937500048 -3.898533227218031e-6\n",
      "7. 16.322703125000046 16.322710937500048 16.322707031250047 -3.7017094848527514e-6\n",
      "8. 16.322703125000046 16.322707031250047 16.322705078125047 -3.6032991638940305e-6\n",
      "9. 16.322703125000046 16.322705078125047 16.322704101562547 -3.554091072845998e-6\n",
      "10. 16.322703125000046 16.322704101562547 16.3227036132813 -3.5294898183209602e-6\n",
      "11. 16.322703125000046 16.3227036132813 16.322703369140672 -3.517186501329225e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.5110392664827358e-6 for V_0/|E| = 16.322703247070358\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 15.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.0 15.0 14.5 -0.0023714609817110962\n",
      "1. 14.5 15.0 14.75 0.011532900603983869\n",
      "2. 14.5 14.75 14.625 0.00446927633115871\n",
      "3. 14.5 14.625 14.5625 0.007972967465175639\n",
      "4. 14.5 14.5625 14.53125 0.00974587107615276\n",
      "5. 14.5 14.53125 14.515625 0.010637615998094239\n",
      "6. 14.5 14.515625 14.5078125 0.011084815327497756\n",
      "7. 14.5 14.5078125 14.50390625 0.011308747158280723\n",
      "8. 14.5 14.50390625 14.501953125 0.011420796171382967\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.011476841458952317 for V_0/|E| = 14.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.912976562499217\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.911976562499218 14.912976562499217 14.912476562499219 -1.5273308713269637e-5\n",
      "1. 14.911976562499218 14.912476562499219 14.912226562499217 -1.6587292728695113e-6\n",
      "2. 14.912226562499217 14.912476562499219 14.912351562499218 5.148891219017478e-6\n",
      "3. 14.912226562499217 14.912351562499218 14.912289062499218 1.7450539354583961e-6\n",
      "4. 14.912226562499217 14.912289062499218 14.912257812499217 3.446964708790948e-6\n",
      "5. 14.912226562499217 14.912257812499217 14.912242187499217 4.297928219344302e-6\n",
      "6. 14.912226562499217 14.912242187499217 14.912234374999217 4.7234092061677025e-6\n",
      "7. 14.912226562499217 14.912234374999217 14.912230468749218 4.936150656096719e-6\n",
      "8. 14.912226562499217 14.912230468749218 14.912228515624218 5.0425214229542415e-6\n",
      "9. 14.912226562499217 14.912228515624218 14.912227539061718 5.095704978860746e-6\n",
      "10. 14.912226562499217 14.912227539061718 14.912227050780468 5.122297849187927e-6\n",
      "11. 14.912226562499217 14.912227050780468 14.912226806639843 5.135594649486092e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 5.142242963232831e-6 for V_0/|E| = 14.91222668456953\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.0 14.0 13.5 -0.008735326376409565\n",
      "1. 13.5 14.0 13.75 0.005794892201445049\n",
      "2. 13.75 14.0 13.875 -0.0016004802310585976\n",
      "3. 13.75 13.875 13.8125 -0.005200132251209783\n",
      "4. 13.75 13.8125 13.78125 -0.0034084053854297374\n",
      "5. 13.75 13.78125 13.765625 -0.002506472849377347\n",
      "6. 13.75 13.765625 13.7578125 -0.002053984708558525\n",
      "7. 13.75 13.7578125 13.75390625 -0.0018273595928624826\n",
      "8. 13.75 13.75390625 13.751953125 -0.0017139517042082544\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0016572239163060705 for V_0/|E| = 13.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.695976562499476\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.694976562499477 13.695976562499476 13.695476562499476 -2.463822602554696e-5\n",
      "1. 13.694976562499477 13.695476562499476 13.695226562499476 -9.996435745191336e-6\n",
      "2. 13.694976562499477 13.695226562499476 13.695101562499477 -2.675151000473901e-6\n",
      "3. 13.695101562499477 13.695226562499476 13.695164062499476 9.855903397209292e-7\n",
      "4. 13.695164062499476 13.695226562499476 13.695195312499475 -8.447889887615453e-7\n",
      "5. 13.695164062499476 13.695195312499475 13.695179687499476 -1.7599711663798073e-6\n",
      "6. 13.695164062499476 13.695179687499476 13.695171874999476 -1.3023781050308107e-6\n",
      "7. 13.695164062499476 13.695171874999476 13.695167968749477 -1.0735852923868327e-6\n",
      "8. 13.695164062499476 13.695167968749477 13.695166015624476 -9.591854157043214e-7\n",
      "9. 13.695164062499476 13.695166015624476 13.695165039061976 -9.01987328293914e-7\n",
      "10. 13.695164062499476 13.695165039061976 13.695164550780726 -8.733878706999898e-7\n",
      "11. 13.695164062499476 13.695164550780726 13.695164306640102 -8.590879054205129e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -8.519376678238813e-7 for V_0/|E| = 13.695164184569789\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.0 13.0 12.5 -0.011085952266526339\n",
      "1. 12.5 13.0 12.75 0.0043160485678469815\n",
      "2. 12.75 13.0 12.875 -0.0035374007515335884\n",
      "3. 12.75 12.875 12.8125 -0.007349354117532007\n",
      "4. 12.75 12.8125 12.78125 -0.005452850882341437\n",
      "5. 12.75 12.78125 12.765625 -0.004497500960384431\n",
      "6. 12.75 12.765625 12.7578125 -0.004018045490436686\n",
      "7. 12.75 12.7578125 12.75390625 -0.003777871885196448\n",
      "8. 12.75 12.75390625 12.751953125 -0.0036576735232582975\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0035975464400170853 for V_0/|E| = 12.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.636976562499509\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.63597656249951 12.636976562499509 12.63647656249951 -2.508627493360085e-5\n",
      "1. 12.63597656249951 12.63647656249951 12.636226562499509 -9.408876182965466e-6\n",
      "2. 12.63597656249951 12.636226562499509 12.636101562499508 -1.5697132251319396e-6\n",
      "3. 12.636101562499508 12.636226562499509 12.636164062499509 2.3499816731966983e-6\n",
      "4. 12.636101562499508 12.636164062499509 12.636132812499508 3.9012462468662115e-7\n",
      "5. 12.636101562499508 12.636132812499508 12.636117187499508 1.3700512543776446e-6\n",
      "6. 12.636101562499508 12.636117187499508 12.636109374999508 1.8600147052069982e-6\n",
      "7. 12.636101562499508 12.636109374999508 12.63610546874951 2.1049963018973655e-6\n",
      "8. 12.636101562499508 12.63610546874951 12.636103515624509 2.2274888574620175e-6\n",
      "9. 12.636101562499508 12.636103515624509 12.636102539062009 2.288735413884376e-6\n",
      "10. 12.636101562499508 12.636102539062009 12.636102050780758 2.319358768520483e-6\n",
      "11. 12.636101562499508 12.636102050780758 12.636101806640134 2.334668979156965e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 2.3423251752570876e-6 for V_0/|E| = 12.636101684569821\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.0 12.0 11.5 -0.009506896666894716\n",
      "1. 11.5 12.0 11.75 0.007097571803956231\n",
      "2. 11.75 12.0 11.875 -0.001383684722721908\n",
      "3. 11.75 11.875 11.8125 -0.005489488076665313\n",
      "4. 11.75 11.8125 11.78125 -0.003447705123208797\n",
      "5. 11.75 11.78125 11.765625 -0.002418483312684088\n",
      "6. 11.75 11.765625 11.7578125 -0.0019017822041812553\n",
      "7. 11.75 11.7578125 11.75390625 -0.0016429081475083814\n",
      "8. 11.75 11.75390625 11.751953125 -0.0015133401246595066\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.001448523347026245 for V_0/|E| = 11.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.708976562499469\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.70797656249947 11.708976562499469 11.70847656249947 -1.6757878898266566e-5\n",
      "1. 11.70797656249947 11.70847656249947 11.708226562499469 -3.7934543202623084e-8\n",
      "2. 11.708226562499469 11.70847656249947 11.70835156249947 8.322575537605558e-6\n",
      "3. 11.708226562499469 11.70835156249947 11.70828906249947 4.1422754725013835e-6\n",
      "4. 11.708226562499469 11.70828906249947 11.708257812499468 6.232413915939015e-6\n",
      "5. 11.708226562499469 11.708257812499468 11.708242187499469 7.277493345480609e-6\n",
      "6. 11.708226562499469 11.708242187499469 11.708234374999469 7.800032749673331e-6\n",
      "7. 11.708226562499469 11.708234374999469 11.70823046874947 8.06130500322274e-6\n",
      "8. 11.708226562499469 11.70823046874947 11.70822851562447 8.191943168377364e-6\n",
      "9. 11.708226562499469 11.70822851562447 11.70822753906197 8.257259783795295e-6\n",
      "10. 11.708226562499469 11.70822753906197 11.70822705078072 8.28991810513862e-6\n",
      "11. 11.708226562499469 11.70822705078072 11.708226806640095 8.306247414137763e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 8.314412275257862e-6 for V_0/|E| = 11.708226684569782\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.0038485895855383105\n",
      "1. 10.5 11.0 10.75 0.014394263931217613\n",
      "2. 10.5 10.75 10.625 0.005061488342880755\n",
      "3. 10.5 10.625 10.5625 0.009674320299789405\n",
      "4. 10.5 10.5625 10.53125 0.012020812548488462\n",
      "5. 10.5 10.53125 10.515625 0.013204156972183476\n",
      "6. 10.5 10.515625 10.5078125 0.013798363709370475\n",
      "7. 10.5 10.5078125 10.50390625 0.01409610195688356\n",
      "8. 10.5 10.50390625 10.501953125 0.01424512995482937\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.014319683692696115 for V_0/|E| = 10.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.89097656249923\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.88997656249923 10.89097656249923 10.89047656249923 -1.4201206631321955e-5\n",
      "1. 10.89047656249923 10.89097656249923 10.89072656249923 3.5655870087482364e-6\n",
      "2. 10.89072656249923 10.89097656249923 10.890851562499229 -5.318017642655561e-6\n",
      "3. 10.89072656249923 10.890851562499229 10.89078906249923 -9.759664182217121e-6\n",
      "4. 10.89072656249923 10.89078906249923 10.890757812499231 -7.5388532137270655e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5. 10.89072656249923 10.890757812499231 10.890742187499232 -6.428439714983601e-6\n",
      "6. 10.89072656249923 10.890742187499232 10.89073437499923 -5.8732305417685796e-6\n",
      "7. 10.89072656249923 10.89073437499923 10.89073046874923 -5.595623823317267e-6\n",
      "8. 10.89072656249923 10.89073046874923 10.890728515624229 -5.456821504872135e-6\n",
      "9. 10.89072656249923 10.890728515624229 10.890727539061729 -5.387419471610885e-6\n",
      "10. 10.89072656249923 10.890727539061729 10.89072705078048 -5.35272022476084e-6\n",
      "11. 10.89072656249923 10.89072705078048 10.890726806639854 -5.33536868928467e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -5.326693520925795e-6 for V_0/|E| = 10.890726684569543\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.028833161303242663\n",
      "1. 10.0 10.5 10.25 -0.012173496808619783\n",
      "2. 10.0 10.25 10.125 -0.0031607144363806523\n",
      "3. 10.125 10.25 10.1875 0.0015224537368185751\n",
      "4. 10.1875 10.25 10.21875 -0.0008340446899142722\n",
      "5. 10.1875 10.21875 10.203125 -0.0020010943459372885\n",
      "6. 10.1875 10.203125 10.1953125 -0.001418499936688654\n",
      "7. 10.1875 10.1953125 10.19140625 -0.0011265051346332172\n",
      "8. 10.1875 10.19140625 10.189453125 -0.0009803331442130385\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0009072034775340485 for V_0/|E| = 10.1884765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.165476562499459\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.164476562499459 10.165476562499459 10.164976562499458 -7.088485596427766e-6\n",
      "1. 10.164976562499458 10.165476562499459 10.165226562499459 1.172904553533163e-5\n",
      "2. 10.164976562499458 10.165226562499459 10.165101562499459 2.3200412163464714e-6\n",
      "3. 10.164976562499458 10.165101562499459 10.165039062499458 7.024485311735834e-6\n",
      "4. 10.164976562499458 10.165039062499458 10.165007812499457 9.376750746903795e-6\n",
      "5. 10.164976562499458 10.165007812499457 10.164992187499458 1.0552895184651766e-5\n",
      "6. 10.164976562499458 10.164992187499458 10.164984374999458 1.1140968522629269e-5\n",
      "7. 10.164976562499458 10.164984374999458 10.164980468749459 1.1435008557634039e-5\n",
      "8. 10.164976562499458 10.164980468749459 10.164978515624458 1.1582027464152907e-5\n",
      "9. 10.164976562499458 10.164978515624458 10.164977539061958 1.165553619698114e-5\n",
      "10. 10.164976562499458 10.164977539061958 10.164977050780708 1.1692290922674808e-5\n",
      "11. 10.164976562499458 10.164977050780708 10.164976806640084 1.1710669291527632e-5\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 1.1719858624514263e-5 for V_0/|E| = 10.16497668456977\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.0 10.0 9.5 -0.018134400155594362\n",
      "1. 9.5 10.0 9.75 0.0007444910585047671\n",
      "2. 9.75 10.0 9.875 -0.008960185169677287\n",
      "3. 9.75 9.875 9.8125 -0.013612531603870047\n",
      "4. 9.75 9.8125 9.78125 -0.011302800730570333\n",
      "5. 9.75 9.78125 9.765625 -0.01013562019814927\n",
      "6. 9.75 9.765625 9.7578125 -0.009548936583111038\n",
      "7. 9.75 9.7578125 9.75390625 -0.009254819613782155\n",
      "8. 9.75 9.75390625 9.751953125 -0.009107567108200945\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.009033892322820168 for V_0/|E| = 9.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.518976562499574\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.517976562499575 9.518976562499574 9.518476562499576 -1.11468551436656e-5\n",
      "1. 9.518476562499576 9.518976562499574 9.518726562499575 8.722493377086204e-6\n",
      "2. 9.518726562499575 9.518976562499574 9.518851562499574 -1.2124545861961996e-6\n",
      "3. 9.518726562499575 9.518851562499574 9.518789062499575 -6.179723316368842e-6\n",
      "4. 9.518726562499575 9.518789062499575 9.518757812499576 -3.6961064624281968e-6\n",
      "5. 9.518726562499575 9.518757812499576 9.518742187499576 -2.454284573225721e-6\n",
      "6. 9.518726562499575 9.518742187499576 9.518734374999575 -1.833370359967768e-6\n",
      "7. 9.518726562499575 9.518734374999575 9.518730468749574 -1.522912350384676e-6\n",
      "8. 9.518726562499575 9.518730468749574 9.518728515624574 -1.3676828570820549e-6\n",
      "9. 9.518726562499575 9.518728515624574 9.518727539062073 -1.2900697823571263e-6\n",
      "10. 9.518726562499575 9.518727539062073 9.518727050780825 -1.2512602981555576e-6\n",
      "11. 9.518726562499575 9.518727050780825 9.518726806640199 -1.231857563867971e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.2221549047252224e-6 for V_0/|E| = 9.518726684569888\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.0025160558758893906\n",
      "1. 8.5 9.0 8.75 0.019366512022565598\n",
      "2. 8.5 8.75 8.625 0.008106835826878635\n",
      "3. 8.5 8.625 8.5625 0.01365570364495579\n",
      "4. 8.5 8.5625 8.53125 0.016490691844531686\n",
      "5. 8.5 8.53125 8.515625 0.017923476141016585\n",
      "6. 8.5 8.515625 8.5078125 0.01864370989997124\n",
      "7. 8.5 8.5078125 8.50390625 0.0190047895746868\n",
      "8. 8.5 8.50390625 8.501953125 0.019185570409100454\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.019276021115974533 for V_0/|E| = 8.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.939976562499647\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.938976562499647 8.939976562499647 8.939476562499646 -2.2490551280042357e-5\n",
      "1. 8.938976562499647 8.939476562499646 8.939226562499647 -1.5692033204187745e-6\n",
      "2. 8.939226562499647 8.939476562499646 8.939351562499645 8.892399716355815e-6\n",
      "3. 8.939226562499647 8.939351562499645 8.939289062499647 3.6615210360788517e-6\n",
      "4. 8.939226562499647 8.939289062499647 8.939257812499648 6.276942150432989e-6\n",
      "5. 8.939226562499647 8.939257812499648 8.939242187499648 7.584665886088398e-6\n",
      "6. 8.939226562499647 8.939242187499648 8.939234374999646 8.238532656604035e-6\n",
      "7. 8.939226562499647 8.939234374999646 8.939230468749646 8.565465997721549e-6\n",
      "8. 8.939226562499647 8.939230468749646 8.939228515624645 8.728935066771376e-6\n",
      "9. 8.939226562499647 8.939228515624645 8.939227539062145 8.810666910075438e-6\n",
      "10. 8.939226562499647 8.939227539062145 8.939227050780897 8.85153368581419e-6\n",
      "11. 8.939226562499647 8.939227050780897 8.93922680664027 8.871965886525452e-6\n",
      "12. 8.939226562499647 8.93922680664027 8.93922668456996 8.88218378335504e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 8.887292078559563e-6 for V_0/|E| = 8.939226623534804\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.023730694121465425\n",
      "1. 8.0 8.5 8.25 -0.0035595919042749253\n",
      "2. 8.25 8.5 8.375 0.007550885566598947\n",
      "3. 8.25 8.375 8.3125 0.0019075525669472269\n",
      "4. 8.25 8.3125 8.28125 0.00470699043164333\n",
      "5. 8.25 8.28125 8.265625 0.00612335505500063\n",
      "6. 8.25 8.265625 8.2578125 0.006835721339856636\n",
      "7. 8.25 8.2578125 8.25390625 0.007192953305770137\n",
      "8. 8.25 8.25390625 8.251953125 0.0073718318491889515\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.0074613368063066055 for V_0/|E| = 8.2509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.418976562500019\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.41797656250002 8.418976562500019 8.418476562500018 -3.577816761585003e-5\n",
      "1. 8.41797656250002 8.418476562500018 8.418226562500019 -1.3805121353284112e-5\n",
      "2. 8.41797656250002 8.418226562500019 8.41810156250002 -2.817549739622476e-6\n",
      "3. 8.41810156250002 8.418226562500019 8.418164062500018 2.6765007675153357e-6\n",
      "4. 8.418164062500018 8.418226562500019 8.418195312500018 -7.054638048736933e-8\n",
      "5. 8.418164062500018 8.418195312500018 8.418179687500018 -1.4440534492640452e-6\n",
      "6. 8.418164062500018 8.418179687500018 8.418171875000018 -7.572996734003321e-7\n",
      "7. 8.418164062500018 8.418171875000018 8.41816796875002 -4.139231114669871e-7\n",
      "8. 8.418164062500018 8.41816796875002 8.418166015625019 -2.4223527561567203e-7\n",
      "9. 8.418164062500018 8.418166015625019 8.418165039062519 -1.5638896494675868e-7\n",
      "10. 8.418164062500018 8.418165039062519 8.418164550781269 -1.1346943462522036e-7\n",
      "11. 8.418164062500018 8.418164550781269 8.418164306640644 -9.200783770573985e-8\n",
      "12. 8.418164062500018 8.418164306640644 8.418164184570331 -8.127716917553326e-8\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -7.591221796009058e-8 for V_0/|E| = 8.418164123535174\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.0024187005278395886\n",
      "1. 7.5 8.0 7.75 0.021880601745154018\n",
      "2. 7.5 7.75 7.625 0.009325188460550884\n",
      "3. 7.5 7.625 7.5625 0.015499437236984917\n",
      "4. 7.5 7.5625 7.53125 0.01866389964509842\n",
      "5. 7.5 7.53125 7.515625 0.020265688608782393\n",
      "6. 7.5 7.515625 7.5078125 0.02107150062906323\n",
      "7. 7.5 7.5078125 7.50390625 0.02147563954457037\n",
      "8. 7.5 7.50390625 7.501953125 0.02167801767141276\n",
      "9. 7.5 7.501953125 7.5009765625 0.021779283957694438\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = 0.021829936412646828 for V_0/|E| = 7.50048828125\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.947488281250483\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.946488281250483 7.947488281250483 7.9469882812504835 -1.7677489419555844e-5\n",
      "1. 7.9469882812504835 7.947488281250483 7.947238281250483 5.350571075490115e-6\n",
      "2. 7.947238281250483 7.947488281250483 7.9473632812504835 -6.163852658970561e-6\n",
      "3. 7.947238281250483 7.9473632812504835 7.947300781250483 -1.1920769750668375e-5\n",
      "4. 7.947238281250483 7.947300781250483 7.947269531250483 -9.042335622057348e-6\n",
      "5. 7.947238281250483 7.947269531250483 7.947253906250483 -7.603100131770984e-6\n",
      "6. 7.947238281250483 7.947253906250483 7.947246093750483 -6.883479210610899e-6\n",
      "7. 7.947238281250483 7.947246093750483 7.947242187500483 -6.5236677703451e-6\n",
      "8. 7.947238281250483 7.947242187500483 7.947240234375483 -6.343758960235362e-6\n",
      "9. 7.947238281250483 7.947240234375483 7.947239257812983 -6.253806983754946e-6\n",
      "10. 7.947238281250483 7.947239257812983 7.947238769531733 -6.20882981900352e-6\n",
      "11. 7.947238281250483 7.947238769531733 7.947238525391108 -6.186341712001963e-6\n",
      "12. 7.947238281250483 7.947238525391108 7.947238403320796 -6.1750975506005305e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -6.169475188632171e-6 for V_0/|E| = 7.947238342285639\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.021549715321948562\n",
      "1. 7.5 8.0 7.75 0.0009553222048762354\n",
      "2. 7.75 8.0 7.875 -0.010719651415212954\n",
      "3. 7.75 7.875 7.8125 -0.016238023332713753\n",
      "4. 7.75 7.8125 7.78125 -0.013504953787679574\n",
      "5. 7.75 7.78125 7.765625 -0.012118867124958754\n",
      "6. 7.75 7.765625 7.7578125 -0.011420904843736415\n",
      "7. 7.75 7.7578125 7.75390625 -0.011070690079605643\n",
      "8. 7.75 7.75390625 7.751953125 -0.010895273804403048\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.010807488382491081 for V_0/|E| = 7.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.519976562500257\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.5189765625002565 7.519976562500257 7.519476562500257 -9.506130309835983e-6\n",
      "1. 7.519476562500257 7.519976562500257 7.5197265625002565 1.4574325745644937e-5\n",
      "2. 7.519476562500257 7.5197265625002565 7.519601562500257 2.5336565309106918e-6\n",
      "3. 7.519476562500257 7.519601562500257 7.519539062500257 8.553881144566461e-6\n",
      "4. 7.519476562500257 7.519539062500257 7.519507812500257 1.1564077701997017e-5\n",
      "5. 7.519476562500257 7.519507812500257 7.519492187500257 1.3069193251523072e-5\n",
      "6. 7.519476562500257 7.519492187500257 7.519484375000257 1.382175635128173e-5\n",
      "7. 7.519476562500257 7.519484375000257 7.519480468750257 1.4198040157020133e-5\n",
      "8. 7.519476562500257 7.519480468750257 7.5194785156252575 1.4386183866239793e-5\n",
      "9. 7.519476562500257 7.5194785156252575 7.519477539062757 1.4480254163898433e-5\n",
      "10. 7.519476562500257 7.519477539062757 7.519477050781507 1.4527288266997952e-5\n",
      "11. 7.519476562500257 7.519477050781507 7.519476806640882 1.4550807236999955e-5\n",
      "12. 7.519476562500257 7.519476806640882 7.51947668457057 1.4562564980217714e-5\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 1.456844648502386e-5 for V_0/|E| = 7.519476623535414\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 237.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.0 237.0 236.5 -0.0012390662293665798\n",
      "1. 236.0 236.5 236.25 -0.0001541342394906389\n",
      "2. 236.25 236.5 236.375 0.00038952657670873004\n",
      "3. 236.25 236.375 236.3125 0.00011759653242886772\n",
      "4. 236.25 236.3125 236.28125 0.00025353664039350993\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.00032152537875570564 for V_0/|E| = 236.265625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 236.42962500000556\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.42862500000555 236.42962500000556 236.42912500000557 -1.1743230026192083e-6\n",
      "1. 236.42862500000555 236.42912500000557 236.42887500000558 -8.734959263726385e-8\n",
      "2. 236.42887500000558 236.42912500000557 236.42900000000557 4.561405288785048e-7\n",
      "3. 236.42887500000558 236.42900000000557 236.4289375000056 1.8439461155839111e-7\n",
      "4. 236.42887500000558 236.4289375000056 236.42890625000558 3.20267860547907e-7\n",
      "5. 236.42887500000558 236.42890625000558 236.42889062500558 3.8820445267930496e-7\n",
      "6. 236.42887500000558 236.42889062500558 236.42888281250558 4.221710173266415e-7\n",
      "7. 236.42887500000558 236.42888281250558 236.4288789062556 4.3915497033843306e-7\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 4.476473980437265e-7 for V_0/|E| = 236.42887695313058\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 158.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.0 158.0 157.5 -0.0007346645104006296\n",
      "1. 157.5 158.0 157.75 0.0008603173759793248\n",
      "2. 157.5 157.75 157.625 6.191964179707119e-5\n",
      "3. 157.5 157.625 157.5625 0.00046089166661800705\n",
      "4. 157.5 157.5625 157.53125 0.0006605477920398164\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.0007604183983428395 for V_0/|E| = 157.515625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 157.769625000006\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.76862500000598 157.769625000006 157.769125000006 -6.777780313147536e-7\n",
      "1. 157.769125000006 157.769625000006 157.769375000006 9.169216248718841e-7\n",
      "2. 157.769125000006 157.769375000006 157.769250000006 1.1957102159367274e-7\n",
      "3. 157.769125000006 157.769250000006 157.769187500006 5.182468874904994e-7\n",
      "4. 157.769125000006 157.769187500006 157.769156250006 7.175847690612293e-7\n",
      "5. 157.769125000006 157.769156250006 157.769140625006 8.172521390522809e-7\n",
      "6. 157.769125000006 157.769140625006 157.769132812506 8.67087579397726e-7\n",
      "7. 157.769125000006 157.769132812506 157.76912890625601 8.920038253526377e-7\n",
      "8. 157.769125000006 157.76912890625601 157.769126953131 9.044631804361801e-7\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 9.106924392398146e-7 for V_0/|E| = 157.7691259765685\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 114.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.0 114.0 113.5 -0.0032009004201898404\n",
      "1. 113.0 113.5 113.25 -0.0010368361618411294\n",
      "2. 113.25 113.5 113.375 5.052090702653975e-5\n",
      "3. 113.375 113.5 113.4375 -0.0004936020556479196\n",
      "4. 113.375 113.4375 113.40625 -0.0007653301648233077\n",
      "5. 113.375 113.40625 113.390625 -0.000629493881457342\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0005615549124487517 for V_0/|E| = 113.3828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 113.2618125000042\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.26081250000419 113.2618125000042 113.2613125000042 -9.367645513505311e-7\n",
      "1. 113.2613125000042 113.2618125000042 113.2615625000042 1.241175567872112e-6\n",
      "2. 113.2613125000042 113.2615625000042 113.2614375000042 1.52203345267143e-7\n",
      "3. 113.2613125000042 113.2614375000042 113.2613750000042 6.966898217960321e-7\n",
      "4. 113.2613125000042 113.2613750000042 113.26134375000419 9.689329382276655e-7\n",
      "5. 113.2613125000042 113.26134375000419 113.26132812500418 1.1050547694912996e-6\n",
      "6. 113.2613125000042 113.26132812500418 113.26132031250418 1.1731153126093717e-6\n",
      "7. 113.2613125000042 113.26132031250418 113.2613164062542 1.2071460908067472e-6\n",
      "8. 113.2613125000042 113.2613164062542 113.26131445312919 1.2241607560497732e-6\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 1.2326685455720244e-6 for V_0/|E| = 113.2613134765667\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 86.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.0 86.0 85.5 -0.00207913711728161\n",
      "1. 85.5 86.0 85.75 0.0007425780737537882\n",
      "2. 85.75 86.0 85.875 -0.0006714189472551245\n",
      "3. 85.75 85.875 85.8125 -0.001376061899028185\n",
      "4. 85.75 85.8125 85.78125 -0.0010239365141503304\n",
      "5. 85.75 85.78125 85.765625 -0.0008477267697102856\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.00075958512021027 for V_0/|E| = 85.7578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 85.63181250000417\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.63081250000417 85.63181250000417 85.63131250000417 -3.73534848782002e-6\n",
      "1. 85.63081250000417 85.63131250000417 85.63106250000416 -9.076854782611034e-7\n",
      "2. 85.63106250000416 85.63131250000417 85.63118750000416 5.06154967552463e-7\n",
      "3. 85.63118750000416 85.63131250000417 85.63125000000417 -2.007661902464014e-7\n",
      "4. 85.63118750000416 85.63125000000417 85.63121875000417 -5.542270776778092e-7\n",
      "5. 85.63118750000416 85.63121875000417 85.63120312500416 -3.774959817758548e-7\n",
      "6. 85.63118750000416 85.63120312500416 85.63119531250416 -2.8913051261308933e-7\n",
      "7. 85.63118750000416 85.63119531250416 85.63119140625416 -2.449504620978393e-7\n",
      "8. 85.63118750000416 85.63119140625416 85.63118945312917 -2.22856706680107e-7\n",
      "9. 85.63118750000416 85.63118945312917 85.63118847656666 -2.1181189813667966e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -2.0628843572371656e-7 for V_0/|E| = 85.6311879882854\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 68.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.0 68.0 67.5 -0.005025174270735835\n",
      "1. 67.0 67.5 67.25 -0.0015274822514394584\n",
      "2. 67.25 67.5 67.375 0.0002367081175280595\n",
      "3. 67.375 67.5 67.4375 -0.0006466692823778498\n",
      "4. 67.375 67.4375 67.40625 -0.0010873960557750335\n",
      "5. 67.375 67.40625 67.390625 -0.000867112774771708\n",
      "6. 67.375 67.390625 67.3828125 -0.0007569110586580387\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0007017951784877559 for V_0/|E| = 67.37890625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 67.28390625000432\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.28290625000432 67.28390625000432 67.28340625000432 -3.1617026450999904e-6\n",
      "1. 67.28340625000432 67.28390625000432 67.28365625000433 3.7417576968873094e-7\n",
      "2. 67.28365625000433 67.28390625000432 67.28378125000432 -1.3937674146539976e-6\n",
      "3. 67.28365625000433 67.28378125000432 67.28371875000433 -2.277736584552695e-6\n",
      "4. 67.28365625000433 67.28371875000433 67.28368750000433 -1.8357517486188704e-6\n",
      "5. 67.28365625000433 67.28368750000433 67.28367187500433 -1.6147623452730123e-6\n",
      "6. 67.28365625000433 67.28367187500433 67.28366406250433 -1.5042639937734062e-6\n",
      "7. 67.28365625000433 67.28366406250433 67.28366015625433 -1.4490175646884588e-6\n",
      "8. 67.28365625000433 67.28366015625433 67.28365820312933 -1.4213913906821012e-6\n",
      "9. 67.28365625000433 67.28365820312933 67.28365722656683 -1.4075803776001526e-6\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -1.4006749005204789e-6 for V_0/|E| = 67.28365673828557\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 55.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.0 55.0 54.5 -0.004591870430473518\n",
      "1. 54.0 54.5 54.25 -0.0003328070647424085\n",
      "2. 54.25 54.5 54.375 0.0018203688483759922\n",
      "3. 54.25 54.375 54.3125 0.0007418036648403698\n",
      "4. 54.25 54.3125 54.28125 0.0012805914316067468\n",
      "5. 54.25 54.28125 54.265625 0.0015503563695856387\n",
      "6. 54.25 54.265625 54.2578125 0.0016853316579201255\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = 0.001752842513914104 for V_0/|E| = 54.25390625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 54.461906249997185\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.46090624999719 54.461906249997185 54.46140624999718 -5.737879081208504e-6\n",
      "1. 54.46090624999719 54.46140624999718 54.46115624999719 -1.4424920217722947e-6\n",
      "2. 54.46115624999719 54.46140624999718 54.461281249997185 7.052263959942002e-7\n",
      "3. 54.461281249997185 54.46140624999718 54.461343749997184 -3.686350088255166e-7\n",
      "4. 54.461281249997185 54.461343749997184 54.461312499997184 -9.055637774433277e-7\n",
      "5. 54.461281249997185 54.461312499997184 54.46129687499719 -6.37099868153981e-7\n",
      "6. 54.461281249997185 54.46129687499719 54.46128906249719 -5.028673076753259e-7\n",
      "7. 54.461281249997185 54.46128906249719 54.461285156247186 -4.3575125354920326e-7\n",
      "8. 54.461281249997185 54.461285156247186 54.461283203122186 -4.021924582758011e-7\n",
      "9. 54.461281249997185 54.461283203122186 54.46128222655969 -3.8541348449285003e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -3.770237829301985e-7 for V_0/|E| = 54.46128173827844\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 46.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.0 46.0 45.5 -0.008693984758791606\n",
      "1. 45.0 45.5 45.25 -0.0037073074081671624\n",
      "2. 45.0 45.25 45.125 -0.001179559001386227\n",
      "3. 45.125 45.25 45.1875 9.296977609589978e-5\n",
      "4. 45.1875 45.25 45.21875 -0.0005440173827527701\n",
      "5. 45.1875 45.21875 45.203125 -0.0008619687684322894\n",
      "6. 45.1875 45.203125 45.1953125 -0.000703038233683609\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0006235391006047435 for V_0/|E| = 45.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 45.1344062499978\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.133406249997805 45.1344062499978 45.13390624999781 -2.9892709515431265e-6\n",
      "1. 45.13390624999781 45.1344062499978 45.1341562499978 2.110716557452454e-6\n",
      "2. 45.1341562499978 45.1344062499978 45.1342812499978 -4.3928717707470554e-7\n",
      "3. 45.1341562499978 45.1342812499978 45.1342187499978 -1.714282329144705e-6\n",
      "4. 45.1341562499978 45.1342187499978 45.1341874999978 -1.0767865871075162e-6\n",
      "5. 45.1341562499978 45.1341874999978 45.134171874997804 -7.580374812954036e-7\n",
      "6. 45.1341562499978 45.134171874997804 45.1341640624978 -5.986622837478468e-7\n",
      "7. 45.1341562499978 45.1341640624978 45.1341601562478 -5.189749989115567e-7\n",
      "8. 45.1341562499978 45.1341601562478 45.1341582031228 -4.79131907281752e-7\n",
      "9. 45.1341562499978 45.1341582031228 45.134157226560305 -4.5920931226936414e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -4.492488157600367e-7 for V_0/|E| = 45.13415673827905\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 39.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.0 39.0 38.5 -0.010180698458064187\n",
      "1. 38.0 38.5 38.25 -0.004398127817138402\n",
      "2. 38.0 38.25 38.125 -0.0014584331622797596\n",
      "3. 38.125 38.25 38.1875 2.3605485745037548e-5\n",
      "4. 38.1875 38.25 38.21875 -0.0007184324386176999\n",
      "5. 38.1875 38.21875 38.203125 -0.0010886872515902181\n",
      "6. 38.1875 38.203125 38.1953125 -0.0009036234814176549\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.000811043872074909 for V_0/|E| = 38.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 38.12740624999782\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.12640624999782 38.12740624999782 38.126906249997816 -5.000719112563737e-6\n",
      "1. 38.126906249997816 38.12740624999782 38.12715624999782 9.431794968288935e-7\n",
      "2. 38.12715624999782 38.12740624999782 38.12728124999782 -2.0287861508289847e-6\n",
      "3. 38.12715624999782 38.12728124999782 38.12721874999782 -3.514756697051801e-6\n",
      "4. 38.12715624999782 38.12721874999782 38.12718749999782 -2.7717741835565984e-6\n",
      "5. 38.12715624999782 38.12718749999782 38.12717187499781 -2.4002803795544527e-6\n",
      "6. 38.12715624999782 38.12717187499781 38.12716406249781 -2.214532068289839e-6\n",
      "7. 38.12715624999782 38.12716406249781 38.12716015624781 -2.121659893112276e-6\n",
      "8. 38.12715624999782 38.12716015624781 38.12715820312282 -2.075222675226074e-6\n",
      "9. 38.12715624999782 38.12715820312282 38.127157226560314 -2.0520028063565532e-6\n",
      "10. 38.12715624999782 38.127157226560314 38.12715673827907 -2.040394845644758e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -2.0345928786447214e-6 for V_0/|E| = 38.12715649413845\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 33.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.0 33.0 32.5 -0.003774106365358664\n",
      "1. 32.5 33.0 32.75 0.0030380923421590854\n",
      "2. 32.75 33.0 32.875 -0.00039027015760072594\n",
      "3. 32.75 32.875 32.8125 -0.0020877332711005682\n",
      "4. 32.75 32.8125 32.78125 -0.0012403905590710237\n",
      "5. 32.75 32.78125 32.765625 -0.0008156778948361634\n",
      "6. 32.75 32.765625 32.7578125 -0.0006030609503925293\n",
      "7. 32.75 32.7578125 32.75390625 -0.0004966872890159992\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.0004434841582877651 for V_0/|E| = 32.751953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 32.72195312499862\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.72095312499862 32.72195312499862 32.72145312499862 -7.87432573478769e-6\n",
      "1. 32.72095312499862 32.72145312499862 32.721203124998624 -1.0521528952381685e-6\n",
      "2. 32.721203124998624 32.72145312499862 32.72132812499862 2.3589971618236683e-6\n",
      "3. 32.721203124998624 32.72132812499862 32.72126562499862 6.534178179737262e-7\n",
      "4. 32.721203124998624 32.72126562499862 32.72123437499862 1.5062066344691205e-6\n",
      "5. 32.721203124998624 32.72123437499862 32.72121874999863 1.932603038145152e-6\n",
      "6. 32.721203124998624 32.72121874999863 32.721210937498626 2.1458010943944986e-6\n",
      "7. 32.721203124998624 32.721210937498626 32.721207031248625 2.2524002722335655e-6\n",
      "8. 32.721203124998624 32.721207031248625 32.721205078123624 2.305698983977048e-6\n",
      "9. 32.721203124998624 32.721205078123624 32.72120410156113 2.332348336308944e-6\n",
      "10. 32.721203124998624 32.72120410156113 32.721203613279876 2.3456742557291634e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.352335477988858e-6 for V_0/|E| = 32.721203369139246\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 29.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.0 29.0 28.5 -0.008244778136742278\n",
      "1. 28.0 28.5 28.25 -0.0006517130376607217\n",
      "2. 28.25 28.5 28.375 0.0032332425170744747\n",
      "3. 28.25 28.375 28.3125 0.0012833421428979338\n",
      "4. 28.25 28.3125 28.28125 0.00225643261153029\n",
      "5. 28.25 28.28125 28.265625 0.0027443721253708874\n",
      "6. 28.25 28.265625 28.2578125 0.0029886908996592425\n",
      "7. 28.25 28.2578125 28.25390625 0.003110937594237057\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0031720827772707583 for V_0/|E| = 28.251953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 28.457953125001474\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.456953125001473 28.457953125001474 28.45745312500147 -2.461748026377085e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. 28.45745312500147 28.457953125001474 28.457703125001473 5.268887904737167e-6\n",
      "2. 28.45745312500147 28.457703125001473 28.457578125001472 1.4035382254744137e-6\n",
      "3. 28.45745312500147 28.457578125001472 28.45751562500147 3.336205429428759e-6\n",
      "4. 28.45745312500147 28.45751562500147 28.45748437500147 4.3025446628927265e-6\n",
      "5. 28.45745312500147 28.45748437500147 28.45746875000147 4.785715826327172e-6\n",
      "6. 28.45745312500147 28.45746875000147 28.457460937501473 5.027301615849543e-6\n",
      "7. 28.45745312500147 28.457460937501473 28.457457031251472 5.148093490714918e-6\n",
      "8. 28.45745312500147 28.457457031251472 28.457455078126472 5.208491443328911e-6\n",
      "9. 28.45745312500147 28.457455078126472 28.45745410156397 5.2386897910918356e-6\n",
      "10. 28.45745312500147 28.45745410156397 28.457453613282723 5.253788733141751e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 5.2613365081935096e-6 for V_0/|E| = 28.457453369142097\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 26.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.0 26.0 25.5 -0.016220216153311942\n",
      "1. 25.0 25.5 25.25 -0.007990691687247309\n",
      "2. 25.0 25.25 25.125 -0.0037631953778254606\n",
      "3. 25.0 25.125 25.0625 -0.0016209257218293537\n",
      "4. 25.0 25.0625 25.03125 -0.0005426179782973482\n",
      "5. 25.0 25.03125 25.015625 -1.6655411300478918e-6\n",
      "6. 25.015625 25.03125 25.0234375 0.0002692609842457212\n",
      "7. 25.015625 25.0234375 25.01953125 0.00013376017590041193\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00020150119461307986 for V_0/|E| = 25.017578125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 25.03157812500124\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.030578125001238 25.03157812500124 25.031078125001237 -7.351780244618042e-6\n",
      "1. 25.031078125001237 25.03157812500124 25.031328125001238 1.313015076189439e-6\n",
      "2. 25.031328125001238 25.03157812500124 25.03145312500124 -3.0194196316247283e-6\n",
      "3. 25.031328125001238 25.03145312500124 25.031390625001237 -5.1856099649583975e-6\n",
      "4. 25.031328125001238 25.031390625001237 25.031359375001237 -4.102517321528771e-6\n",
      "5. 25.031328125001238 25.031359375001237 25.031343750001238 -3.5609701777465757e-6\n",
      "6. 25.031328125001238 25.031343750001238 25.03133593750124 -3.2901936195205383e-6\n",
      "7. 25.031328125001238 25.03133593750124 25.03133203125124 -3.1548082301939145e-6\n",
      "8. 25.031328125001238 25.03133203125124 25.03133007812624 -3.0871152748320597e-6\n",
      "9. 25.031328125001238 25.03133007812624 25.03132910156374 -3.053266801419156e-6\n",
      "10. 25.031328125001238 25.03132910156374 25.03132861328249 -3.036343872137614e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -3.0278817759092936e-6 for V_0/|E| = 25.031328369141864\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 23.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.0 23.0 22.5 -0.014316350582685673\n",
      "1. 22.0 22.5 22.25 -0.005094560750958697\n",
      "2. 22.0 22.25 22.125 -0.00033930664466607556\n",
      "3. 22.125 22.25 22.1875 0.0020749064692319455\n",
      "4. 22.125 22.1875 22.15625 0.0008647362037685758\n",
      "5. 22.125 22.15625 22.140625 0.0014690542905586741\n",
      "6. 22.125 22.140625 22.1328125 0.0017717884778147752\n",
      "7. 22.125 22.1328125 22.12890625 0.0019232994805156887\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0019990909743366272 for V_0/|E| = 22.126953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 22.23295312500135\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.23195312500135 22.23295312500135 22.23245312500135 -1.1510647049720785e-5\n",
      "1. 22.23195312500135 22.23245312500135 22.232203125001348 -1.8892338531547558e-6\n",
      "2. 22.232203125001348 22.23245312500135 22.23232812500135 2.9216191856423234e-6\n",
      "3. 22.232203125001348 22.23232812500135 22.232265625001347 5.161792671412715e-7\n",
      "4. 22.232203125001348 22.232265625001347 22.232234375001347 1.7188961654271737e-6\n",
      "5. 22.232203125001348 22.232234375001347 22.232218750001348 2.3202582167086257e-6\n",
      "6. 22.232203125001348 22.232218750001348 22.23221093750135 2.6209384122065055e-6\n",
      "7. 22.232203125001348 22.23221093750135 22.23220703125135 2.7712781714502363e-6\n",
      "8. 22.232203125001348 22.23220703125135 22.23220507812635 2.846448493037629e-6\n",
      "9. 22.232203125001348 22.23220507812635 22.23220410156385 2.8840317075960276e-6\n",
      "10. 22.232203125001348 22.23220410156385 22.2322036132826 2.902825565617095e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 2.9122220886691314e-6 for V_0/|E| = 22.232203369141974\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 20.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.0 20.0 19.5 -0.0018129656799201724\n",
      "1. 19.5 20.0 19.75 0.008946757785400276\n",
      "2. 19.5 19.75 19.625 0.003505169603363553\n",
      "3. 19.5 19.625 19.5625 0.00621042962872055\n",
      "4. 19.5 19.5625 19.53125 0.007574697330815905\n",
      "5. 19.5 19.53125 19.515625 0.008259751852069105\n",
      "6. 19.5 19.515625 19.5078125 0.008603010690592671\n",
      "7. 19.5 19.5078125 19.50390625 0.008774823181770263\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.008860775215283844 for V_0/|E| = 19.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 19.914953125001727\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.913953125001726 19.914953125001727 19.914453125001728 -1.755614771461412e-5\n",
      "1. 19.913953125001726 19.914453125001728 19.914203125001727 -6.958922506410275e-6\n",
      "2. 19.913953125001726 19.914203125001727 19.914078125001726 -1.6601289751065163e-6\n",
      "3. 19.914078125001726 19.914203125001727 19.91414062500173 9.89316097422806e-7\n",
      "4. 19.91414062500173 19.914203125001727 19.914171875001728 -3.354092100364352e-7\n",
      "5. 19.91414062500173 19.914171875001728 19.914156250001728 -9.977691847765395e-7\n",
      "6. 19.91414062500173 19.914156250001728 19.91414843750173 -6.665900232564096e-7\n",
      "7. 19.91414062500173 19.91414843750173 19.91414453125173 -5.009985349959948e-7\n",
      "8. 19.91414062500173 19.91414453125173 19.91414257812673 -4.18206019852743e-7\n",
      "9. 19.91414062500173 19.91414257812673 19.91414160156423 -3.768083277153283e-7\n",
      "10. 19.91414062500173 19.91414160156423 19.91414111328298 -3.5610817823127254e-7\n",
      "11. 19.91414062500173 19.91414111328298 19.914140869142354 -3.4576042133119474e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.4058406616907e-7 for V_0/|E| = 19.91414074707204\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 18.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.0 18.0 17.5 -0.0006883746659626189\n",
      "1. 17.5 18.0 17.75 0.011170234898671054\n",
      "2. 17.5 17.75 17.625 0.005164537142216446\n",
      "3. 17.5 17.625 17.5625 0.008148144863910457\n",
      "4. 17.5 17.5625 17.53125 0.009654361642470383\n",
      "5. 17.5 17.53125 17.515625 0.010411088961999692\n",
      "6. 17.5 17.515625 17.5078125 0.010790359321831375\n",
      "7. 17.5 17.5078125 17.50390625 0.010980221422968698\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.011075209234997578 for V_0/|E| = 17.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.970953125001795\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.969953125001794 17.970953125001795 17.970453125001796 -1.6110667799155746e-5\n",
      "1. 17.969953125001794 17.970453125001796 17.970203125001795 -4.520805485305584e-6\n",
      "2. 17.970203125001795 17.970453125001796 17.970328125001796 1.2743530325405831e-6\n",
      "3. 17.970328125001796 17.970453125001796 17.970390625001798 -1.6232440624331444e-6\n",
      "4. 17.970328125001796 17.970390625001798 17.9703593750018 -3.0720302452856702e-6\n",
      "5. 17.970328125001796 17.9703593750018 17.970343750001796 -2.347639230688289e-6\n",
      "6. 17.970328125001796 17.970343750001796 17.970335937501794 -1.985442463996271e-6\n",
      "7. 17.970328125001796 17.970335937501794 17.970332031251793 -1.8043440775708131e-6\n",
      "8. 17.970328125001796 17.970332031251793 17.970330078126793 -1.7137946266811005e-6\n",
      "9. 17.970328125001796 17.970330078126793 17.970329101564296 -1.6685199036510305e-6\n",
      "10. 17.970328125001796 17.970329101564296 17.970328613283044 -1.6458832919707078e-6\n",
      "11. 17.970328125001796 17.970328613283044 17.970328369142422 -1.6345640309545963e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.6289049816424372e-6 for V_0/|E| = 17.97032824707211\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.0 17.0 16.5 -0.01640448183344647\n",
      "1. 16.0 16.5 16.25 -0.00442433593995587\n",
      "2. 16.25 16.5 16.375 0.001835911321932743\n",
      "3. 16.375 16.5 16.4375 -0.001317044446124704\n",
      "4. 16.375 16.4375 16.40625 -0.0028763742434695537\n",
      "5. 16.375 16.40625 16.390625 -0.0020981333509988904\n",
      "6. 16.375 16.390625 16.3828125 -0.0017079452734816102\n",
      "7. 16.375 16.3828125 16.37890625 -0.0015125840020082748\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.001414836514912346 for V_0/|E| = 16.376953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 16.322953125000048\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.321953125000046 16.322953125000048 16.322453125000045 -9.802899013845456e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. 16.322453125000045 16.322953125000048 16.322703125000046 2.793892782951299e-6\n",
      "2. 16.322703125000046 16.322953125000048 16.322828125000047 -3.5045944709454462e-6\n",
      "3. 16.322703125000046 16.322828125000047 16.322765625000045 -6.6537693549895845e-6\n",
      "4. 16.322703125000046 16.322765625000045 16.322734375000046 -5.079187353723595e-6\n",
      "5. 16.322703125000046 16.322734375000046 16.322718750000046 -4.291892051871566e-6\n",
      "6. 16.322703125000046 16.322718750000046 16.322710937500048 -3.898243757960597e-6\n",
      "7. 16.322703125000046 16.322710937500048 16.322707031250047 -3.701418772950805e-6\n",
      "8. 16.322703125000046 16.322707031250047 16.322705078125047 -3.60300644310335e-6\n",
      "9. 16.322703125000046 16.322705078125047 16.322704101562547 -3.553801475574519e-6\n",
      "10. 16.322703125000046 16.322704101562547 16.3227036132813 -3.5291992484524387e-6\n",
      "11. 16.322703125000046 16.3227036132813 16.322703369140672 -3.5168968647458873e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -3.5107445282610995e-6 for V_0/|E| = 16.322703247070358\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 15.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.0 15.0 14.5 -0.0023714945340226794\n",
      "1. 14.5 15.0 14.75 0.011533061512366369\n",
      "2. 14.5 14.75 14.625 0.004469340100378359\n",
      "3. 14.5 14.625 14.5625 0.007973079833289015\n",
      "4. 14.5 14.5625 14.53125 0.009746007719398013\n",
      "5. 14.5 14.53125 14.515625 0.010637764777749697\n",
      "6. 14.5 14.515625 14.5078125 0.011084970171406429\n",
      "7. 14.5 14.5078125 14.50390625 0.011308905033745497\n",
      "8. 14.5 14.50390625 14.501953125 0.011420955561412897\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.011477001608894933 for V_0/|E| = 14.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.912976562499217\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.911976562499218 14.912976562499217 14.912476562499219 -1.527297188454275e-5\n",
      "1. 14.911976562499218 14.912476562499219 14.912226562499217 -1.6581947122265849e-6\n",
      "2. 14.912226562499217 14.912476562499219 14.912351562499218 5.149523327243748e-6\n",
      "3. 14.912226562499217 14.912351562499218 14.912289062499218 1.7456359758219805e-6\n",
      "4. 14.912226562499217 14.912289062499218 14.912257812499217 3.447571839731447e-6\n",
      "5. 14.912226562499217 14.912257812499217 14.912242187499217 4.298544817699941e-6\n",
      "6. 14.912226562499217 14.912242187499217 14.912234374999217 4.724034115850863e-6\n",
      "7. 14.912226562499217 14.912234374999217 14.912230468749218 4.936778880873104e-6\n",
      "8. 14.912226562499217 14.912230468749218 14.912228515624218 5.043150657985492e-6\n",
      "9. 14.912226562499217 14.912228515624218 14.912227539061718 5.096335900043265e-6\n",
      "10. 14.912226562499217 14.912227539061718 14.912227050780468 5.12292942574067e-6\n",
      "11. 14.912226562499217 14.912227050780468 14.912226806639843 5.136225724167662e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 5.142873471400488e-6 for V_0/|E| = 14.91222668456953\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.0 14.0 13.5 -0.008735532532576614\n",
      "1. 13.5 14.0 13.75 0.005795025587731459\n",
      "2. 13.75 14.0 13.875 -0.0016005165710875863\n",
      "3. 13.75 13.875 13.8125 -0.005200253500596066\n",
      "4. 13.75 13.8125 13.78125 -0.0034084841795695596\n",
      "5. 13.75 13.78125 13.765625 -0.0025065304159996625\n",
      "6. 13.75 13.765625 13.7578125 -0.002054031662579265\n",
      "7. 13.75 13.7578125 13.75390625 -0.001827401243127811\n",
      "8. 13.75 13.75390625 13.751953125 -0.0017139906975949725\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0016572615840326392 for V_0/|E| = 13.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.695976562499476\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.694976562499477 13.695976562499476 13.695476562499476 -2.463787348071979e-5\n",
      "1. 13.694976562499477 13.695476562499476 13.695226562499476 -9.995746508300496e-6\n",
      "2. 13.694976562499477 13.695226562499476 13.695101562499477 -2.6742917982085984e-6\n",
      "3. 13.695101562499477 13.695226562499476 13.695164062499476 9.865350826180801e-7\n",
      "4. 13.695164062499476 13.695226562499476 13.695195312499475 -8.438851948641275e-7\n",
      "5. 13.695164062499476 13.695195312499475 13.695179687499476 -1.7590896195085638e-6\n",
      "6. 13.695164062499476 13.695179687499476 13.695171874999476 -1.3014871846797146e-6\n",
      "7. 13.695164062499476 13.695171874999476 13.695167968749477 -1.0726872662285599e-6\n",
      "8. 13.695164062499476 13.695167968749477 13.695166015624476 -9.582877612153585e-7\n",
      "9. 13.695164062499476 13.695166015624476 13.695165039061976 -9.010880558013374e-7\n",
      "10. 13.695164062499476 13.695165039061976 13.695164550780726 -8.72486219928647e-7\n",
      "11. 13.695164062499476 13.695164550780726 13.695164306640102 -8.581862204890036e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -8.510373026460997e-7 for V_0/|E| = 13.695164184569789\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.0 13.0 12.5 -0.011086361544124856\n",
      "1. 12.5 13.0 12.75 0.004316203788765515\n",
      "2. 12.75 13.0 12.875 -0.0035375278301516887\n",
      "3. 12.75 12.875 12.8125 -0.00734962233421706\n",
      "4. 12.75 12.8125 12.78125 -0.005453048536968868\n",
      "5. 12.75 12.78125 12.765625 -0.004497663327005138\n",
      "6. 12.75 12.765625 12.7578125 -0.004018190214456383\n",
      "7. 12.75 12.7578125 12.75390625 -0.0037780077873835554\n",
      "8. 12.75 12.75390625 12.751953125 -0.003657805014572179\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0035976757263898457 for V_0/|E| = 12.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.636976562499509\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.63597656249951 12.636976562499509 12.63647656249951 -2.5085717416667642e-5\n",
      "1. 12.63597656249951 12.63647656249951 12.636226562499509 -9.407754840424124e-6\n",
      "2. 12.63597656249951 12.636226562499509 12.636101562499508 -1.5683106709584934e-6\n",
      "3. 12.636101562499508 12.636226562499509 12.636164062499509 2.3515266765940556e-6\n",
      "4. 12.636101562499508 12.636164062499509 12.636132812499508 3.915991305626845e-7\n",
      "5. 12.636101562499508 12.636132812499508 12.636117187499508 1.3715595868298285e-6\n",
      "6. 12.636101562499508 12.636117187499508 12.636109374999508 1.8615434682907479e-6\n",
      "7. 12.636101562499508 12.636109374999508 12.63610546874951 2.1065346756017603e-6\n",
      "8. 12.636101562499508 12.63610546874951 12.636103515624509 2.229029441578268e-6\n",
      "9. 12.636101562499508 12.636103515624509 12.636102539062009 2.290277489658013e-6\n",
      "10. 12.636101562499508 12.636102539062009 12.636102050780758 2.3209022814494367e-6\n",
      "11. 12.636101562499508 12.636102050780758 12.636101806640134 2.33621433588067e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 2.3438698401122856e-6 for V_0/|E| = 12.636101684569821\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.0 12.0 11.5 -0.009507419233283677\n",
      "1. 11.5 12.0 11.75 0.007097949498874168\n",
      "2. 11.75 12.0 11.875 -0.0013837572828969836\n",
      "3. 11.75 11.875 11.8125 -0.005489785716140584\n",
      "4. 11.75 11.8125 11.78125 -0.0034478902357997416\n",
      "5. 11.75 11.78125 11.765625 -0.002418612148509448\n",
      "6. 11.75 11.765625 11.7578125 -0.0019018829036949\n",
      "7. 11.75 11.7578125 11.75390625 -0.0016429947762472954\n",
      "8. 11.75 11.75390625 11.751953125 -0.0015134197178159514\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0014485994250987237 for V_0/|E| = 11.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.708976562499469\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.70797656249947 11.708976562499469 11.70847656249947 -1.675655379712388e-5\n",
      "1. 11.70797656249947 11.70847656249947 11.708226562499469 -3.5706826663131726e-8\n",
      "2. 11.708226562499469 11.70847656249947 11.70835156249947 8.325255513515635e-6\n",
      "3. 11.708226562499469 11.70835156249947 11.70828906249947 4.144730140727681e-6\n",
      "4. 11.708226562499469 11.70828906249947 11.708257812499468 6.234983415878142e-6\n",
      "5. 11.708226562499469 11.708257812499468 11.708242187499469 7.280116649221459e-6\n",
      "6. 11.708226562499469 11.708242187499469 11.708234374999469 7.802686202361047e-6\n",
      "7. 11.708226562499469 11.708234374999469 11.70823046874947 8.063972190078723e-6\n",
      "8. 11.708226562499469 11.70823046874947 11.70822851562447 8.194613634639703e-6\n",
      "9. 11.708226562499469 11.70822851562447 11.70822753906197 8.25993392782669e-6\n",
      "10. 11.708226562499469 11.70822753906197 11.70822705078072 8.292595907179018e-6\n",
      "11. 11.708226562499469 11.70822705078072 11.708226806640095 8.308925931681067e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 8.317090264190226e-6 for V_0/|E| = 11.708226684569782\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.003848889245846926\n",
      "1. 10.5 11.0 10.75 0.01439534878892551\n",
      "2. 10.5 10.75 10.625 0.005061881009091558\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3. 10.5 10.625 10.5625 0.009675059165612591\n",
      "4. 10.5 10.5625 10.53125 0.012021724448305024\n",
      "5. 10.5 10.53125 10.515625 0.013205155361849834\n",
      "6. 10.5 10.515625 10.5078125 0.01379940533771557\n",
      "7. 10.5 10.5078125 10.50390625 0.014097165200870823\n",
      "8. 10.5 10.50390625 10.501953125 0.014246204006277925\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.014320763147179012 for V_0/|E| = 10.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.89097656249923\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.88997656249923 10.89097656249923 10.89047656249923 -1.4199019607209684e-5\n",
      "1. 10.89047656249923 10.89097656249923 10.89072656249923 3.5691596891527737e-6\n",
      "2. 10.89072656249923 10.89097656249923 10.890851562499229 -5.315137963784104e-6\n",
      "3. 10.89072656249923 10.890851562499229 10.89078906249923 -9.757129824167238e-6\n",
      "4. 10.89072656249923 10.89078906249923 10.890757812499231 -7.536147996019616e-6\n",
      "5. 10.89072656249923 10.890757812499231 10.890742187499232 -6.425647576511349e-6\n",
      "6. 10.89072656249923 10.890742187499232 10.89073437499923 -5.870393188008932e-6\n",
      "7. 10.89072656249923 10.89073437499923 10.89073046874923 -5.592765137388911e-6\n",
      "8. 10.89072656249923 10.89073046874923 10.890728515624229 -5.453951976115058e-6\n",
      "9. 10.89072656249923 10.890728515624229 10.890727539061729 -5.384545704357741e-6\n",
      "10. 10.89072656249923 10.890727539061729 10.89072705078048 -5.349840512665793e-6\n",
      "11. 10.89072656249923 10.89072705078048 10.890726806639854 -5.332490642058614e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -5.323814266860547e-6 for V_0/|E| = 10.890726684569543\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.028836574412894667\n",
      "1. 10.0 10.5 10.25 -0.012174869476781135\n",
      "2. 10.0 10.25 10.125 -0.0031610588186764973\n",
      "3. 10.125 10.25 10.1875 0.0015226245644534373\n",
      "4. 10.1875 10.25 10.21875 -0.0008341315262063292\n",
      "5. 10.1875 10.21875 10.203125 -0.0020013099716688896\n",
      "6. 10.1875 10.203125 10.1953125 -0.0014186511705308916\n",
      "7. 10.1875 10.1953125 10.19140625 -0.001126624169891836\n",
      "8. 10.1875 10.19140625 10.189453125 -0.00098043608092751\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.000907298366240556 for V_0/|E| = 10.1884765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.165476562499459\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.164476562499459 10.165476562499459 10.164976562499458 -7.084537583800908e-6\n",
      "1. 10.164976562499458 10.165476562499459 10.165226562499459 1.173505443996028e-5\n",
      "2. 10.164976562499458 10.165226562499459 10.165101562499459 2.325017731298012e-6\n",
      "3. 10.164976562499458 10.165101562499459 10.165039062499458 7.029977286854125e-6\n",
      "4. 10.164976562499458 10.165039062499458 10.165007812499457 9.38249978551849e-6\n",
      "5. 10.164976562499458 10.165007812499457 10.164992187499458 1.0558774239927675e-5\n",
      "6. 10.164976562499458 10.164992187499458 10.164984374999458 1.1146912586096333e-5\n",
      "7. 10.164976562499458 10.164984374999458 10.164980468749459 1.144098499168691e-5\n",
      "8. 10.164976562499458 10.164980468749459 10.164978515624458 1.1588020414246885e-5\n",
      "9. 10.164976562499458 10.164978515624458 10.164977539061958 1.1661537388393114e-5\n",
      "10. 10.164976562499458 10.164977539061958 10.164977050780708 1.1698295623491822e-5\n",
      "11. 10.164976562499458 10.164977050780708 10.164976806640084 1.1716674880191392e-5\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 1.172586359018686e-5 for V_0/|E| = 10.16497668456977\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.0 10.0 9.5 -0.018137252097180007\n",
      "1. 9.5 10.0 9.75 0.0007446091378228881\n",
      "2. 9.75 10.0 9.875 -0.00896155563748704\n",
      "3. 9.75 9.875 9.8125 -0.013614643919065642\n",
      "4. 9.75 9.8125 9.78125 -0.011304542373047267\n",
      "5. 9.75 9.78125 9.765625 -0.010137176311816206\n",
      "6. 9.75 9.765625 9.7578125 -0.009550399887810214\n",
      "7. 9.75 9.7578125 9.75390625 -0.009256236503327278\n",
      "8. 9.75 9.75390625 9.751953125 -0.009108960787265367\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.009035274396583257 for V_0/|E| = 9.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.518976562499574\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.517976562499575 9.518976562499574 9.518476562499576 -1.1141931882828387e-5\n",
      "1. 9.518476562499576 9.518976562499574 9.518726562499575 8.730398559020862e-6\n",
      "2. 9.518726562499575 9.518976562499574 9.518851562499574 -1.2060402433952215e-6\n",
      "3. 9.518726562499575 9.518851562499574 9.518789062499575 -6.174053588202285e-6\n",
      "4. 9.518726562499575 9.518789062499575 9.518757812499576 -3.6900640092439224e-6\n",
      "5. 9.518726562499575 9.518757812499576 9.518742187499576 -2.4480558140940752e-6\n",
      "6. 9.518726562499575 9.518742187499576 9.518734374999575 -1.8270489972375923e-6\n",
      "7. 9.518726562499575 9.518734374999575 9.518730468749574 -1.516544333631155e-6\n",
      "8. 9.518726562499575 9.518730468749574 9.518728515624574 -1.3612916971916334e-6\n",
      "9. 9.518726562499575 9.518728515624574 9.518727539062073 -1.283666074180234e-6\n",
      "10. 9.518726562499575 9.518727539062073 9.518727050780825 -1.244851450808099e-6\n",
      "11. 9.518726562499575 9.518727050780825 9.518726806640199 -1.2254484806941533e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.215741777792394e-6 for V_0/|E| = 9.518726684569888\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.0025165556651065035\n",
      "1. 8.5 9.0 8.75 0.019370219495420178\n",
      "2. 8.5 8.75 8.625 0.00810843858122242\n",
      "3. 8.5 8.625 8.5625 0.013658358889026992\n",
      "4. 8.5 8.5625 8.53125 0.016493873288751522\n",
      "5. 8.5 8.53125 8.515625 0.017926920625310004\n",
      "6. 8.5 8.515625 8.5078125 0.0186472858893671\n",
      "7. 8.5 8.5078125 8.50390625 0.019008431307843354\n",
      "8. 8.5 8.50390625 8.501953125 0.019189245014252943\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.019279712152652208 for V_0/|E| = 8.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.939976562499647\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.938976562499647 8.939976562499647 8.939476562499646 -2.248607116701729e-5\n",
      "1. 8.938976562499647 8.939476562499646 8.939226562499647 -1.560520898347766e-6\n",
      "2. 8.939226562499647 8.939476562499646 8.939351562499645 8.903183272987169e-6\n",
      "3. 8.939226562499647 8.939351562499645 8.939289062499647 3.671253181236885e-6\n",
      "4. 8.939226562499647 8.939289062499647 8.939257812499648 6.287200321020044e-6\n",
      "5. 8.939226562499647 8.939257812499648 8.939242187499648 7.595186858723546e-6\n",
      "6. 8.939226562499647 8.939242187499648 8.939234374999646 8.249184642672158e-6\n",
      "7. 8.939226562499647 8.939234374999646 8.939230468749646 8.576183936726882e-6\n",
      "8. 8.939226562499647 8.939230468749646 8.939228515624645 8.739683799467706e-6\n",
      "9. 8.939226562499647 8.939228515624645 8.939227539062145 8.821433508405376e-6\n",
      "10. 8.939226562499647 8.939227539062145 8.939227050780897 8.862308937849082e-6\n",
      "11. 8.939226562499647 8.939227050780897 8.93922680664027 8.88274663239625e-6\n",
      "12. 8.939226562499647 8.93922680664027 8.93922668456996 8.892966603306538e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 8.898076460477303e-6 for V_0/|E| = 8.939226623534804\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.02373736581995915\n",
      "1. 8.0 8.5 8.25 -0.0035605266893386904\n",
      "2. 8.25 8.5 8.375 0.007552846890261149\n",
      "3. 8.25 8.375 8.3125 0.0019080644968374931\n",
      "4. 8.25 8.3125 8.28125 0.004708226801146105\n",
      "5. 8.25 8.28125 8.265625 0.006124953845411783\n",
      "6. 8.25 8.265625 8.2578125 0.006837501384338747\n",
      "7. 8.25 8.2578125 8.25390625 0.007194823987664913\n",
      "8. 8.25 8.25390625 8.251953125 0.007373747851395948\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.007463275467289775 for V_0/|E| = 8.2509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.418976562500019\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.41797656250002 8.418976562500019 8.418476562500018 -3.577557513002431e-5\n",
      "1. 8.41797656250002 8.418476562500018 8.418226562500019 -1.3796740825482044e-5\n",
      "2. 8.41797656250002 8.418226562500019 8.41810156250002 -2.8062749806159954e-6\n",
      "3. 8.41810156250002 8.418226562500019 8.418164062500018 2.6892228094275764e-6\n",
      "4. 8.418164062500018 8.418226562500019 8.418195312500018 -5.8547618105841366e-8\n",
      "5. 8.418164062500018 8.418195312500018 8.418179687500018 -1.4324157173431305e-6\n",
      "6. 8.418164062500018 8.418179687500018 8.418171875000018 -7.454840329327364e-7\n",
      "7. 8.418164062500018 8.418171875000018 8.41816796875002 -4.020158816474467e-7\n",
      "8. 8.418164062500018 8.41816796875002 8.418166015625019 -2.302815601437392e-7\n",
      "9. 8.418164062500018 8.418166015625019 8.418165039062519 -1.444147295743015e-7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10. 8.418164062500018 8.418165039062519 8.418164550781269 -1.0148184298455136e-7\n",
      "11. 8.418164062500018 8.418164550781269 8.418164306640644 -8.001428719307188e-8\n",
      "12. 8.418164062500018 8.418164306640644 8.418164184570331 -6.928087884730828e-8\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -6.391398744404039e-8 for V_0/|E| = 8.418164123535174\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.0024195106264864\n",
      "1. 7.5 8.0 7.75 0.021887621048834918\n",
      "2. 7.5 7.75 7.625 0.009328288620139161\n",
      "3. 7.5 7.625 7.5625 0.015504496823764964\n",
      "4. 7.5 7.5625 7.53125 0.018669939176225385\n",
      "5. 7.5 7.53125 7.515625 0.020272218063861595\n",
      "6. 7.5 7.515625 7.5078125 0.021078275016490008\n",
      "7. 7.5 7.5078125 7.50390625 0.021482536393318732\n",
      "8. 7.5 7.50390625 7.501953125 0.02168497574768229\n",
      "9. 7.5 7.501953125 7.5009765625 0.021786272645771328\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = 0.02183694040849212 for V_0/|E| = 7.50048828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.947488281250483\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.946488281250483 7.947488281250483 7.9469882812504835 -1.76677377933765e-5\n",
      "1. 7.9469882812504835 7.947488281250483 7.947238281250483 5.368135346032172e-6\n",
      "2. 7.947238281250483 7.947488281250483 7.9473632812504835 -6.150194392884838e-6\n",
      "3. 7.947238281250483 7.9473632812504835 7.947300781250483 -1.1909061821763633e-5\n",
      "4. 7.947238281250483 7.947300781250483 7.947269531250483 -9.029653379306535e-6\n",
      "5. 7.947238281250483 7.947269531250483 7.947253906250483 -7.589930486621581e-6\n",
      "6. 7.947238281250483 7.947253906250483 7.947246093750483 -6.870065031923013e-6\n",
      "7. 7.947238281250483 7.947246093750483 7.947242187500483 -6.510128231935579e-6\n",
      "8. 7.947238281250483 7.947242187500483 7.947240234375483 -6.3301622354734434e-6\n",
      "9. 7.947238281250483 7.947240234375483 7.947239257812983 -6.2401777725574835e-6\n",
      "10. 7.947238281250483 7.947239257812983 7.947238769531733 -6.195187158200514e-6\n",
      "11. 7.947238281250483 7.947238769531733 7.947238525391108 -6.172691564416772e-6\n",
      "12. 7.947238281250483 7.947238525391108 7.947238403320796 -6.1614427624579915e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -6.15581735943665e-6 for V_0/|E| = 7.947238342285639\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.02155954357680434\n",
      "1. 7.5 8.0 7.75 0.0009557517690778903\n",
      "2. 7.75 8.0 7.875 -0.010724376871859618\n",
      "3. 7.75 7.875 7.8125 -0.01624530795874055\n",
      "4. 7.75 7.8125 7.78125 -0.013510960620511565\n",
      "5. 7.75 7.78125 7.765625 -0.012124233699877042\n",
      "6. 7.75 7.765625 7.7578125 -0.011425950965057033\n",
      "7. 7.75 7.7578125 7.75390625 -0.01107557589493607\n",
      "8. 7.75 7.75390625 7.751953125 -0.010900079447893904\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.010812253934338758 for V_0/|E| = 7.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.519976562500257\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.5189765625002565 7.519976562500257 7.519476562500257 -9.489922806322706e-6\n",
      "1. 7.519476562500257 7.519976562500257 7.5197265625002565 1.460087561947264e-5\n",
      "2. 7.519476562500257 7.5197265625002565 7.519601562500257 2.5550362499596445e-6\n",
      "3. 7.519476562500257 7.519601562500257 7.519539062500257 8.57784580973895e-6\n",
      "4. 7.519476562500257 7.519539062500257 7.519507812500257 1.1589333211541066e-5\n",
      "5. 7.519476562500257 7.519507812500257 7.519492187500257 1.3095098114817004e-5\n",
      "6. 7.519476562500257 7.519492187500257 7.519484375000257 1.3847984305380905e-5\n",
      "7. 7.519476562500257 7.519484375000257 7.519480468750257 1.4224429543901051e-5\n",
      "8. 7.519476562500257 7.519480468750257 7.5194785156252575 1.441265198119182e-5\n",
      "9. 7.519476562500257 7.5194785156252575 7.519477539062757 1.4506764176249558e-5\n",
      "10. 7.519476562500257 7.519477539062757 7.519477050781507 1.4553821073854185e-5\n",
      "11. 7.519476562500257 7.519477050781507 7.519476806640882 1.457734807093176e-5\n",
      "12. 7.519476562500257 7.519476806640882 7.51947668457057 1.4589110972779357e-5\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = 1.4594992637888583e-5 for V_0/|E| = 7.519476623535414\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 237.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.0 237.0 236.5 -0.001239066225578745\n",
      "1. 236.0 236.5 236.25 -0.0001541342337060473\n",
      "2. 236.25 236.5 236.375 0.0003895265836204892\n",
      "3. 236.25 236.375 236.3125 0.00011759653807454972\n",
      "4. 236.25 236.3125 236.28125 0.0002535366459581386\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.0003215253849452023 for V_0/|E| = 236.265625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 236.42962500000556\n",
      "Starting Bisection.\n",
      "\n",
      "0. 236.42862500000555 236.42962500000556 236.42912500000557 -1.1743182155219045e-6\n",
      "1. 236.42862500000555 236.42912500000557 236.42887500000558 -8.734365942266694e-8\n",
      "2. 236.42887500000558 236.42912500000557 236.42900000000557 4.5614511227834844e-7\n",
      "3. 236.42887500000558 236.42900000000557 236.4289375000056 1.8440067059786614e-7\n",
      "4. 236.42887500000558 236.4289375000056 236.42890625000558 3.202721304679873e-7\n",
      "5. 236.42887500000558 236.42890625000558 236.42889062500558 3.882086689933798e-7\n",
      "6. 236.42887500000558 236.42889062500558 236.42888281250558 4.221765723070221e-7\n",
      "7. 236.42887500000558 236.42888281250558 236.4288789062556 4.3916145584620403e-7\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 4.476540495577997e-7 for V_0/|E| = 236.42887695313058\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 158.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.0 158.0 157.5 -0.000734664462538766\n",
      "1. 157.5 158.0 157.75 0.0008603174787014253\n",
      "2. 157.5 157.75 157.625 6.191971840843183e-5\n",
      "3. 157.5 157.625 157.5625 0.0004608917555720696\n",
      "4. 157.5 157.5625 157.53125 0.0006605478893102739\n",
      "\n",
      "After 5 steps, convergent value found.\n",
      "U(r_0) = 0.0007604184986670928 for V_0/|E| = 157.515625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 157.769625000006\n",
      "Starting Bisection.\n",
      "\n",
      "0. 157.76862500000598 157.769625000006 157.769125000006 -6.777054397747816e-7\n",
      "1. 157.769125000006 157.769625000006 157.769375000006 9.169949524806853e-7\n",
      "2. 157.769125000006 157.769375000006 157.769250000006 1.1964416011554388e-7\n",
      "3. 157.769125000006 157.769250000006 157.769187500006 5.183205941568557e-7\n",
      "4. 157.769125000006 157.769187500006 157.769156250006 7.176569903947696e-7\n",
      "5. 157.769125000006 157.769156250006 157.769140625006 8.173250791641629e-7\n",
      "6. 157.769125000006 157.769140625006 157.769132812506 8.671605496681187e-7\n",
      "7. 157.769125000006 157.769132812506 157.76912890625601 8.920773017817652e-7\n",
      "8. 157.769125000006 157.76912890625601 157.769126953131 9.045354758134454e-7\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 9.107652444835202e-7 for V_0/|E| = 157.7691259765685\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 114.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.0 114.0 113.5 -0.003200900797492377\n",
      "1. 113.0 113.5 113.25 -0.0010368357262582526\n",
      "2. 113.25 113.5 113.375 5.052174915157152e-5\n",
      "3. 113.375 113.5 113.4375 -0.0004936014170731768\n",
      "4. 113.375 113.4375 113.40625 -0.0007653296265639781\n",
      "5. 113.375 113.40625 113.390625 -0.0006294932918397648\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0005615542974714792 for V_0/|E| = 113.3828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 113.2618125000042\n",
      "Starting Bisection.\n",
      "\n",
      "0. 113.26081250000419 113.2618125000042 113.2613125000042 -9.359418224400111e-7\n",
      "1. 113.2613125000042 113.2618125000042 113.2615625000042 1.242000243510239e-6\n",
      "2. 113.2613125000042 113.2615625000042 113.2614375000042 1.5302696555527482e-7\n",
      "3. 113.2613125000042 113.2614375000042 113.2613750000042 6.975140332839005e-7\n",
      "4. 113.2613125000042 113.2613750000042 113.26134375000419 9.697566675773415e-7\n",
      "5. 113.2613125000042 113.26134375000419 113.26132812500418 1.1058777129192236e-6\n",
      "6. 113.2613125000042 113.26132812500418 113.26132031250418 1.1739397736683743e-6\n",
      "7. 113.2613125000042 113.26132031250418 113.2613164062542 1.2079693129937685e-6\n",
      "8. 113.2613125000042 113.2613164062542 113.26131445312919 1.2249853777915065e-6\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 1.2334945141251205e-6 for V_0/|E| = 113.2613134765667\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 86.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.0 86.0 85.5 -0.0020791364318109265\n",
      "1. 85.5 86.0 85.75 0.0007425849231253636\n",
      "2. 85.75 86.0 85.875 -0.000671415177249337\n",
      "3. 85.75 85.875 85.8125 -0.0013760596726907204\n",
      "4. 85.75 85.8125 85.78125 -0.001023933515539493\n",
      "5. 85.75 85.78125 85.765625 -0.0008477233834581082\n",
      "\n",
      "After 6 steps, convergent value found.\n",
      "U(r_0) = -0.0007595815426055686 for V_0/|E| = 85.7578125\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 85.63181250000417\n",
      "Starting Bisection.\n",
      "\n",
      "0. 85.63081250000417 85.63181250000417 85.63131250000417 -3.730122252769844e-6\n",
      "1. 85.63081250000417 85.63131250000417 85.63106250000416 -9.024526846730826e-7\n",
      "2. 85.63106250000416 85.63131250000417 85.63118750000416 5.113921109215382e-7\n",
      "3. 85.63118750000416 85.63131250000417 85.63125000000417 -1.9553095270591307e-7\n",
      "4. 85.63118750000416 85.63125000000417 85.63121875000417 -5.489917536705312e-7\n",
      "5. 85.63118750000416 85.63121875000417 85.63120312500416 -3.722616373862044e-7\n",
      "6. 85.63118750000416 85.63120312500416 85.63119531250416 -2.838975276132359e-7\n",
      "7. 85.63118750000416 85.63119531250416 85.63119140625416 -2.3971489563992613e-7\n",
      "8. 85.63118750000416 85.63119140625416 85.63118945312917 -2.1762314770059262e-7\n",
      "9. 85.63118750000416 85.63118945312917 85.63118847656666 -2.0657764421512918e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -2.0105489855765446e-7 for V_0/|E| = 85.6311879882854\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 68.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.0 68.0 67.5 -0.0050251957411519485\n",
      "1. 67.0 67.5 67.25 -0.0015274731514267677\n",
      "2. 67.25 67.5 67.375 0.00023673246574744045\n",
      "3. 67.375 67.5 67.4375 -0.0006466525541923158\n",
      "4. 67.375 67.4375 67.40625 -0.0010873831413910151\n",
      "5. 67.375 67.40625 67.390625 -0.0008670979505467563\n",
      "6. 67.375 67.390625 67.3828125 -0.000756895282938904\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0007017789270656123 for V_0/|E| = 67.37890625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 67.28390625000432\n",
      "Starting Bisection.\n",
      "\n",
      "0. 67.28290625000432 67.28390625000432 67.28340625000432 -3.1394204926217855e-6\n",
      "1. 67.28340625000432 67.28390625000432 67.28365625000433 3.964889464682449e-7\n",
      "2. 67.28365625000433 67.28390625000432 67.28378125000432 -1.3714713113252487e-6\n",
      "3. 67.28365625000433 67.28378125000432 67.28371875000433 -2.255445724082443e-6\n",
      "4. 67.28365625000433 67.28371875000433 67.28368750000433 -1.8134589490576187e-6\n",
      "5. 67.28365625000433 67.28368750000433 67.28367187500433 -1.5924657375550873e-6\n",
      "6. 67.28365625000433 67.28367187500433 67.28366406250433 -1.4819684903294287e-6\n",
      "7. 67.28365625000433 67.28366406250433 67.28366015625433 -1.4267181251063363e-6\n",
      "8. 67.28365625000433 67.28366015625433 67.28365820312933 -1.399094933723981e-6\n",
      "9. 67.28365625000433 67.28365820312933 67.28365722656683 -1.3852829171643969e-6\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -1.3783776725462155e-6 for V_0/|E| = 67.28365673828557\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 55.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.0 55.0 54.5 -0.004591919135723447\n",
      "1. 54.0 54.5 54.25 -0.00033274398656043505\n",
      "2. 54.25 54.5 54.375 0.0018204876619559488\n",
      "3. 54.25 54.375 54.3125 0.0007418946235092474\n",
      "4. 54.25 54.3125 54.28125 0.0012806963227710527\n",
      "5. 54.25 54.28125 54.265625 0.0015504682233875955\n",
      "6. 54.25 54.265625 54.2578125 0.0016854469925278593\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = 0.001752959586190081 for V_0/|E| = 54.25390625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 54.461906249997185\n",
      "Starting Bisection.\n",
      "\n",
      "0. 54.46090624999719 54.461906249997185 54.46140624999718 -5.666303309107335e-6\n",
      "1. 54.46090624999719 54.46140624999718 54.46115624999719 -1.3708021801303437e-6\n",
      "2. 54.46115624999719 54.46140624999718 54.461281249997185 7.769707449677606e-7\n",
      "3. 54.461281249997185 54.46140624999718 54.461343749997184 -2.969173842184467e-7\n",
      "4. 54.461281249997185 54.461343749997184 54.461312499997184 -8.338624494319877e-7\n",
      "5. 54.461281249997185 54.461312499997184 54.46129687499719 -5.653891637336748e-7\n",
      "6. 54.461281249997185 54.46129687499719 54.46128906249719 -4.3115354940532623e-7\n",
      "7. 54.461281249997185 54.46128906249719 54.461285156247186 -3.640356562382426e-7\n",
      "8. 54.461281249997185 54.461285156247186 54.461283203122186 -3.304775011475883e-7\n",
      "9. 54.461281249997185 54.461283203122186 54.46128222655969 -3.1369726025520136e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -3.0530773197531175e-7 for V_0/|E| = 54.46128173827844\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 46.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.0 46.0 45.5 -0.008694365671189658\n",
      "1. 45.0 45.5 45.25 -0.0037073595126783164\n",
      "2. 45.0 45.25 45.125 -0.0011794471722606224\n",
      "3. 45.125 45.25 45.1875 9.316344700465736e-5\n",
      "4. 45.1875 45.25 45.21875 -0.0005438646225965506\n",
      "5. 45.1875 45.21875 45.203125 -0.0008618364700635099\n",
      "6. 45.1875 45.203125 45.1953125 -0.0007028957045462937\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.000623391455216982 for V_0/|E| = 45.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 45.1344062499978\n",
      "Starting Bisection.\n",
      "\n",
      "0. 45.133406249997805 45.1344062499978 45.13390624999781 -2.8017564000601184e-6\n",
      "1. 45.13390624999781 45.1344062499978 45.1341562499978 2.2985596726871565e-6\n",
      "2. 45.1341562499978 45.1344062499978 45.1342812499978 -2.5161042318266336e-7\n",
      "3. 45.1341562499978 45.1342812499978 45.1342187499978 -1.5266853214632823e-6\n",
      "4. 45.1341562499978 45.1342187499978 45.1341874999978 -8.891483213144666e-7\n",
      "5. 45.1341562499978 45.1341874999978 45.134171874997804 -5.703795521626203e-7\n",
      "6. 45.1341562499978 45.134171874997804 45.1341640624978 -4.1099375276036703e-7\n",
      "7. 45.1341562499978 45.1341640624978 45.1341601562478 -3.3130323968751346e-7\n",
      "8. 45.1341562499978 45.1341601562478 45.1341582031228 -2.9145656174793794e-7\n",
      "9. 45.1341562499978 45.1341582031228 45.134157226560305 -2.7153545262575213e-7\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = -2.615724352725387e-7 for V_0/|E| = 45.13415673827905\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 39.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.0 39.0 38.5 -0.010181700803385782\n",
      "1. 38.0 38.5 38.25 -0.004398313905952277\n",
      "2. 38.0 38.25 38.125 -0.0014582123442525596\n",
      "3. 38.125 38.25 38.1875 2.4029430415711803e-5\n",
      "4. 38.1875 38.25 38.21875 -0.0007181100316573492\n",
      "5. 38.1875 38.21875 38.203125 -0.0010884156302567616\n",
      "6. 38.1875 38.203125 38.1953125 -0.0009033264666792995\n",
      "\n",
      "After 7 steps, convergent value found.\n",
      "U(r_0) = -0.0008107341629442053 for V_0/|E| = 38.19140625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 38.12740624999782\n",
      "Starting Bisection.\n",
      "\n",
      "0. 38.12640624999782 38.12740624999782 38.126906249997816 -4.580686323904179e-6\n",
      "1. 38.126906249997816 38.12740624999782 38.12715624999782 1.3640246640194492e-6\n",
      "2. 38.12715624999782 38.12740624999782 38.12728124999782 -1.6083472340539458e-6\n",
      "3. 38.12715624999782 38.12728124999782 38.12721874999782 -3.094519992958631e-6\n",
      "4. 38.12715624999782 38.12721874999782 38.12718749999782 -2.3514355226438564e-6\n",
      "5. 38.12715624999782 38.12718749999782 38.12717187499781 -1.979890354924793e-6\n",
      "6. 38.12715624999782 38.12717187499781 38.12716406249781 -1.7941185918592905e-6\n",
      "7. 38.12715624999782 38.12716406249781 38.12716015624781 -1.70123458421309e-6\n",
      "8. 38.12715624999782 38.12716015624781 38.12715820312282 -1.654790762619287e-6\n",
      "9. 38.12715624999782 38.12715820312282 38.127157226560314 -1.6315669194211714e-6\n",
      "10. 38.12715624999782 38.127157226560314 38.12715673827907 -1.6199575043669624e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -1.6141531192086187e-6 for V_0/|E| = 38.12715649413845\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 33.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.0 33.0 32.5 -0.0037742572781203614\n",
      "1. 32.5 33.0 32.75 0.003039711844471117\n",
      "2. 32.75 33.0 32.875 -0.000389534807058909\n",
      "3. 32.75 32.875 32.8125 -0.0020874407988886318\n",
      "4. 32.75 32.8125 32.78125 -0.0012398765837673882\n",
      "5. 32.75 32.78125 32.765625 -0.0008150532173459461\n",
      "6. 32.75 32.765625 32.7578125 -0.0006023809300494573\n",
      "7. 32.75 32.7578125 32.75390625 -0.0004959796054545753\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.00044276264229817084 for V_0/|E| = 32.751953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 32.72195312499862\n",
      "Starting Bisection.\n",
      "\n",
      "0. 32.72095312499862 32.72195312499862 32.72145312499862 -7.039676980267876e-6\n",
      "1. 32.72095312499862 32.72145312499862 32.721203124998624 -2.1573528630844824e-7\n",
      "2. 32.721203124998624 32.72145312499862 32.72132812499862 3.1963015087109674e-6\n",
      "3. 32.721203124998624 32.72132812499862 32.72126562499862 1.4902782610816846e-6\n",
      "4. 32.721203124998624 32.72126562499862 32.72123437499862 2.343288479818267e-6\n",
      "5. 32.721203124998624 32.72123437499862 32.72121874999863 2.769794614765088e-6\n",
      "6. 32.721203124998624 32.72121874999863 32.721210937498626 2.9830492573210025e-6\n",
      "7. 32.721203124998624 32.721210937498626 32.721207031248625 3.0896759125097983e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8. 32.721203124998624 32.721207031248625 32.721205078123624 3.1429894661755598e-6\n",
      "9. 32.721203124998624 32.721205078123624 32.72120410156113 3.1696461563781674e-6\n",
      "10. 32.721203124998624 32.72120410156113 32.721203613279876 3.18297499195243e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 3.1896378365812674e-6 for V_0/|E| = 32.721203369139246\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 29.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.0 29.0 28.5 -0.008247048277169674\n",
      "1. 28.0 28.5 28.25 -0.0006504926975670213\n",
      "2. 28.25 28.5 28.375 0.0032362019414481965\n",
      "3. 28.25 28.375 28.3125 0.0012854325874121868\n",
      "4. 28.25 28.3125 28.28125 0.002258957689225333\n",
      "5. 28.25 28.28125 28.265625 0.0027471144138378053\n",
      "6. 28.25 28.265625 28.2578125 0.002991541763223914\n",
      "7. 28.25 28.2578125 28.25390625 0.0031138427400433286\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00317501506284885 for V_0/|E| = 28.251953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 28.457953125001474\n",
      "Starting Bisection.\n",
      "\n",
      "0. 28.456953125001473 28.457953125001474 28.45745312500147 -9.4860513013078e-7\n",
      "1. 28.45745312500147 28.457953125001474 28.457703125001473 6.785511812890972e-6\n",
      "2. 28.45745312500147 28.457703125001473 28.457578125001472 2.918425342414475e-6\n",
      "3. 28.45745312500147 28.457578125001472 28.45751562500147 4.851962452964478e-6\n",
      "4. 28.45745312500147 28.45751562500147 28.45748437500147 5.818735779595956e-6\n",
      "5. 28.45745312500147 28.45748437500147 28.45746875000147 6.302122350171453e-6\n",
      "6. 28.45745312500147 28.45746875000147 28.457460937501473 6.543817693570065e-6\n",
      "7. 28.45745312500147 28.457460937501473 28.457457031251472 6.6646653466689495e-6\n",
      "8. 28.45745312500147 28.457457031251472 28.457455078126472 6.72508969034104e-6\n",
      "9. 28.45745312500147 28.457455078126472 28.45745410156397 6.755301411212616e-6\n",
      "10. 28.45745312500147 28.45745410156397 28.457453613282723 6.77040685868709e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 6.777961161442585e-6 for V_0/|E| = 28.457453369142097\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 26.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.0 26.0 25.5 -0.016229935969406913\n",
      "1. 25.0 25.5 25.25 -0.007994072978638663\n",
      "2. 25.0 25.25 25.125 -0.0037634158232208205\n",
      "3. 25.0 25.125 25.0625 -0.0016195683176459799\n",
      "4. 25.0 25.0625 25.03125 -0.0005404723513862892\n",
      "5. 25.03125 25.0625 25.046875 8.740110488271067e-7\n",
      "6. 25.046875 25.0625 25.0546875 -0.00026994919480026507\n",
      "7. 25.046875 25.0546875 25.05078125 -0.00040524826845535694\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.0003376081061278022 for V_0/|E| = 25.048828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 25.0318281250012\n",
      "Starting Bisection.\n",
      "\n",
      "0. 25.0308281250012 25.0318281250012 25.031328125001203 -9.1517939980723e-6\n",
      "1. 25.0308281250012 25.031328125001203 25.0310781250012 -4.8084962089016e-7\n",
      "2. 25.0310781250012 25.031328125001203 25.031203125001202 3.854735331874727e-6\n",
      "3. 25.0310781250012 25.031203125001202 25.0311406250012 1.6869339594437112e-6\n",
      "4. 25.0310781250012 25.0311406250012 25.0311093750012 2.7708335370599566e-6\n",
      "5. 25.0310781250012 25.0311093750012 25.0310937500012 3.3127838723440476e-6\n",
      "6. 25.0310781250012 25.0310937500012 25.031085937501203 3.583759319076188e-6\n",
      "7. 25.0310781250012 25.031085937501203 25.031082031251202 3.7192486340170117e-6\n",
      "8. 25.0310781250012 25.031082031251202 25.0310800781262 3.7869916992383703e-6\n",
      "9. 25.0310781250012 25.0310800781262 25.0310791015637 3.820863718138222e-6\n",
      "10. 25.0310781250012 25.0310791015637 25.031078613282453 3.837799417254216e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = 3.846266083001317e-6 for V_0/|E| = 25.031078369141827\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 23.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.0 23.0 22.5 -0.014328760087302545\n",
      "1. 22.0 22.5 22.25 -0.005096265768269758\n",
      "2. 22.0 22.25 22.125 -0.00033567478719792875\n",
      "3. 22.125 22.25 22.1875 0.0020812019013681207\n",
      "4. 22.125 22.1875 22.15625 0.0008697002869338428\n",
      "5. 22.125 22.15625 22.140625 0.001474684156787253\n",
      "6. 22.125 22.140625 22.1328125 0.0017777511584009984\n",
      "7. 22.125 22.1328125 22.12890625 0.0019294285434427725\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.0020053032252041864 for V_0/|E| = 22.126953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 22.23295312500135\n",
      "Starting Bisection.\n",
      "\n",
      "0. 22.23195312500135 22.23295312500135 22.23245312500135 -7.515339706006234e-6\n",
      "1. 22.23245312500135 22.23295312500135 22.23270312500135 2.1167339689055146e-6\n",
      "2. 22.23270312500135 22.23295312500135 22.23282812500135 -2.699352782691293e-6\n",
      "3. 22.23270312500135 22.23282812500135 22.23276562500135 -5.1073586714076525e-6\n",
      "4. 22.23270312500135 22.23276562500135 22.23273437500135 -3.903358239625337e-6\n",
      "5. 22.23270312500135 22.23273437500135 22.23271875000135 -3.301355571005917e-6\n",
      "6. 22.23270312500135 22.23271875000135 22.232710937501352 -3.000353602570461e-6\n",
      "7. 22.23270312500135 22.232710937501352 22.23270703125135 -2.8498522918672955e-6\n",
      "8. 22.23270312500135 22.23270703125135 22.23270507812635 -2.7746022056187706e-6\n",
      "9. 22.23270312500135 22.23270507812635 22.23270410156385 -2.736977033625592e-6\n",
      "10. 22.23270312500135 22.23270410156385 22.232703613282602 -2.718165205330608e-6\n",
      "\n",
      "After 11 steps, convergent value found.\n",
      "U(r_0) = -2.7087579109557956e-6 for V_0/|E| = 22.232703369141976\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 20.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.0 20.0 19.5 -0.0018098853928232058\n",
      "1. 19.5 20.0 19.75 0.00896684808347765\n",
      "2. 19.5 19.75 19.625 0.003516767102448624\n",
      "3. 19.5 19.625 19.5625 0.006226276882987827\n",
      "4. 19.5 19.5625 19.53125 0.007592666985402125\n",
      "5. 19.5 19.53125 19.515625 0.008278782055132489\n",
      "6. 19.5 19.515625 19.5078125 0.008622570998322638\n",
      "7. 19.5 19.5078125 19.50390625 0.008794648499254744\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.00888073302534848 for V_0/|E| = 19.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 19.914953125001727\n",
      "Starting Bisection.\n",
      "\n",
      "0. 19.913953125001726 19.914953125001727 19.914453125001728 -1.1575970047078715e-5\n",
      "1. 19.913953125001726 19.914453125001728 19.914203125001727 -9.617063810994595e-7\n",
      "2. 19.914203125001727 19.914453125001728 19.914328125001727 4.3456111562038e-6\n",
      "3. 19.914203125001727 19.914328125001727 19.914265625001725 1.6919378014391663e-6\n",
      "4. 19.914203125001727 19.914265625001725 19.914234375001726 3.018769769923171e-6\n",
      "5. 19.914203125001727 19.914234375001726 19.914218750001726 3.682188040595543e-6\n",
      "6. 19.914203125001727 19.914218750001726 19.91421093750173 4.0139007857912825e-6\n",
      "7. 19.914203125001727 19.91421093750173 19.914207031251728 4.1797554096410385e-6\n",
      "8. 19.914203125001727 19.914207031251728 19.914205078126727 4.262684878922344e-6\n",
      "9. 19.914203125001727 19.914205078126727 19.914204101564227 4.304146433707919e-6\n",
      "10. 19.914203125001727 19.914204101564227 19.91420361328298 4.3248774479908955e-6\n",
      "11. 19.914203125001727 19.91420361328298 19.914203369142353 4.335244375165088e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 4.340426269862048e-6 for V_0/|E| = 19.914203247072038\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 18.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.0 18.0 17.5 -0.0006812895155117006\n",
      "1. 17.5 18.0 17.75 0.011203240645258976\n",
      "2. 17.5 17.75 17.625 0.005184602179699957\n",
      "3. 17.5 17.625 17.5625 0.008174685730709407\n",
      "4. 17.5 17.5625 17.53125 0.009684136389598632\n",
      "5. 17.5 17.53125 17.515625 0.010442479580321183\n",
      "6. 17.5 17.515625 17.5078125 0.010822557598505488\n",
      "7. 17.5 17.5078125 17.50390625 0.011012823459189282\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = 0.011108013130619989 for V_0/|E| = 17.501953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.970953125001795\n",
      "Starting Bisection.\n",
      "\n",
      "0. 17.969953125001794 17.970953125001795 17.970453125001796 -7.515700304240623e-6\n",
      "1. 17.970453125001796 17.970953125001795 17.970703125001798 4.100147062115185e-6\n",
      "2. 17.970703125001798 17.970953125001795 17.970828125001795 -1.7078522137833913e-6\n",
      "3. 17.970703125001798 17.970828125001795 17.970765625001796 -4.611794863468017e-6\n",
      "4. 17.970703125001798 17.970765625001796 17.970734375001797 -3.159828220645862e-6\n",
      "5. 17.970703125001798 17.970734375001797 17.970718750001797 -2.43384327358291e-6\n",
      "6. 17.970703125001798 17.970718750001797 17.9707109375018 -2.070846500460583e-6\n",
      "7. 17.970703125001798 17.9707109375018 17.9707070312518 -1.8893503557718737e-6\n",
      "8. 17.970703125001798 17.9707070312518 17.970705078126798 -1.7986017413990576e-6\n",
      "9. 17.970703125001798 17.970705078126798 17.970704101564298 -1.7532273120894676e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10. 17.970703125001798 17.970704101564298 17.97070361328305 -1.7305391790838829e-6\n",
      "11. 17.970703125001798 17.97070361328305 17.970703369142424 -1.719195730674462e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.7135246368435148e-6 for V_0/|E| = 17.97070324707211\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 17.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.0 17.0 16.5 -0.01644419736748503\n",
      "1. 16.0 16.5 16.25 -0.004425893565664549\n",
      "2. 16.25 16.5 16.375 0.0018533931881355567\n",
      "3. 16.375 16.5 16.4375 -0.001309077397985977\n",
      "4. 16.375 16.4375 16.40625 -0.0028731684247910645\n",
      "5. 16.375 16.40625 16.390625 -0.0020925466237768716\n",
      "6. 16.375 16.390625 16.3828125 -0.001701168311711159\n",
      "7. 16.375 16.3828125 16.37890625 -0.0015052119776482644\n",
      "\n",
      "After 8 steps, convergent value found.\n",
      "U(r_0) = -0.001407166973813828 for V_0/|E| = 16.376953125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 16.32395312500005\n",
      "Starting Bisection.\n",
      "\n",
      "0. 16.322953125000048 16.32395312500005 16.32345312500005 -2.3140317649429298e-5\n",
      "1. 16.322953125000048 16.32345312500005 16.32320312500005 -1.0506928985646256e-5\n",
      "2. 16.322953125000048 16.32320312500005 16.32307812500005 -4.18995811191802e-6\n",
      "3. 16.322953125000048 16.32307812500005 16.323015625000046 -1.0314054328127177e-6\n",
      "4. 16.323015625000046 16.32307812500005 16.323046875000045 5.478884657376781e-7\n",
      "5. 16.323046875000045 16.32307812500005 16.32306250000005 -2.4176052327388896e-7\n",
      "6. 16.323046875000045 16.32306250000005 16.323054687500047 -6.365844362015414e-7\n",
      "7. 16.323046875000045 16.323054687500047 16.323050781250046 -4.391725326227504e-7\n",
      "8. 16.323046875000045 16.323050781250046 16.323048828125046 -3.404665542678189e-7\n",
      "9. 16.323046875000045 16.323048828125046 16.323047851562546 -2.9111390868661206e-7\n",
      "10. 16.323046875000045 16.323047851562546 16.323047363281297 -2.664368709956066e-7\n",
      "11. 16.323046875000045 16.323047363281297 16.32304711914067 -2.5409846452473397e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -2.4792840117208363e-7 for V_0/|E| = 16.323046997070357\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 15.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.0 15.0 14.5 -0.002364863320707359\n",
      "1. 14.5 15.0 14.75 0.011593467572036614\n",
      "2. 14.5 14.75 14.625 0.004502895367594226\n",
      "3. 14.5 14.625 14.5625 0.008020071410534181\n",
      "4. 14.5 14.5625 14.53125 0.009799709490052676\n",
      "5. 14.5 14.53125 14.515625 0.010694819459103838\n",
      "6. 14.5 14.515625 14.5078125 0.011143700737499408\n",
      "7. 14.5 14.5078125 14.50390625 0.011368473397873023\n",
      "8. 14.5 14.50390625 14.501953125 0.011480942786103322\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.011537198254530999 for V_0/|E| = 14.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.913976562499217\n",
      "Starting Bisection.\n",
      "\n",
      "0. 14.912976562499217 14.913976562499217 14.913476562499216 -2.6597736423747097e-5\n",
      "1. 14.912976562499217 14.913476562499216 14.913226562499217 -1.2930855396359766e-5\n",
      "2. 14.912976562499217 14.913226562499217 14.913101562499218 -6.0970845928187925e-6\n",
      "3. 14.912976562499217 14.913101562499218 14.913039062499218 -2.6801152973642816e-6\n",
      "4. 14.912976562499217 14.913039062499218 14.913007812499217 -9.716100917353576e-7\n",
      "5. 14.912976562499217 14.913007812499217 14.912992187499217 -1.1735189140105638e-7\n",
      "6. 14.912992187499217 14.913007812499217 14.912999999999217 3.097765119670474e-7\n",
      "7. 14.912992187499217 14.912999999999217 14.912996093749218 9.621125631063343e-8\n",
      "8. 14.912992187499217 14.912996093749218 14.912994140624217 2.0299472474247147e-7\n",
      "9. 14.912992187499217 14.912994140624217 14.912993164061717 2.563872208665694e-7\n",
      "10. 14.912992187499217 14.912993164061717 14.912992675780467 2.8308045956907066e-7\n",
      "11. 14.912992187499217 14.912992675780467 14.912992431639843 2.9642915220308145e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 3.031040868655428e-7 for V_0/|E| = 14.91299230956953\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 14.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.0 14.0 13.5 -0.008759659157562298\n",
      "1. 13.5 14.0 13.75 0.005844912273245815\n",
      "2. 13.75 14.0 13.875 -0.0015876081277120166\n",
      "3. 13.75 13.875 13.8125 -0.005205858263394402\n",
      "4. 13.75 13.8125 13.78125 -0.0034048309134432067\n",
      "5. 13.75 13.78125 13.765625 -0.002498249161769576\n",
      "6. 13.75 13.765625 13.7578125 -0.0020434367076021033\n",
      "7. 13.75 13.7578125 13.75390625 -0.0018156495146398972\n",
      "8. 13.75 13.75390625 13.751953125 -0.001701660605515596\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0016446423141491836 for V_0/|E| = 13.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.695976562499476\n",
      "Starting Bisection.\n",
      "\n",
      "0. 13.694976562499477 13.695976562499476 13.695476562499476 -3.732316183781939e-6\n",
      "1. 13.695476562499476 13.695976562499476 13.695726562499477 1.0983813005681748e-5\n",
      "2. 13.695476562499476 13.695726562499477 13.695601562499476 3.625617312785513e-6\n",
      "3. 13.695476562499476 13.695601562499476 13.695539062499476 7.30468108368948e-6\n",
      "4. 13.695476562499476 13.695539062499476 13.695507812499475 9.144238946084779e-6\n",
      "5. 13.695476562499476 13.695507812499475 13.695492187499475 1.0064024178448449e-5\n",
      "6. 13.695476562499476 13.695492187499475 13.695484374999475 1.052391798216765e-5\n",
      "7. 13.695476562499476 13.695484374999475 13.695480468749476 1.0753863815491566e-5\n",
      "8. 13.695476562499476 13.695480468749476 13.695478515624476 1.0868836308375989e-5\n",
      "9. 13.695476562499476 13.695478515624476 13.695477539061976 1.0926326396013592e-5\n",
      "10. 13.695476562499476 13.695477539061976 13.695477050780726 1.0955068956610493e-5\n",
      "11. 13.695476562499476 13.695477050780726 13.695476806640102 1.0969439993947573e-5\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 1.0976625571892762e-5 for V_0/|E| = 13.695476684569789\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 13.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.0 13.0 12.5 -0.011131590404590856\n",
      "1. 12.5 13.0 12.75 0.004370067842697068\n",
      "2. 12.75 13.0 12.875 -0.003533189112921062\n",
      "3. 12.75 12.875 12.8125 -0.007370066463794656\n",
      "4. 12.75 12.8125 12.78125 -0.005461100469990896\n",
      "5. 12.75 12.78125 12.765625 -0.004499519673993253\n",
      "6. 12.75 12.765625 12.7578125 -0.004016948955301046\n",
      "7. 12.75 12.7578125 12.75390625 -0.003775217778128909\n",
      "8. 12.75 12.75390625 12.751953125 -0.0036542406451623155\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.00359372417917444 for V_0/|E| = 12.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.637976562499508\n",
      "Starting Bisection.\n",
      "\n",
      "0. 12.636976562499509 12.637976562499508 12.637476562499508 -2.9897829802606696e-5\n",
      "1. 12.636976562499509 12.637476562499508 12.637226562499508 -1.4123267846765018e-5\n",
      "2. 12.636976562499509 12.637226562499508 12.63710156249951 -6.23552193808229e-6\n",
      "3. 12.636976562499509 12.63710156249951 12.63703906249951 -2.291538509124994e-6\n",
      "4. 12.636976562499509 12.63703906249951 12.637007812499508 -3.195147386780898e-7\n",
      "5. 12.637007812499508 12.63703906249951 12.637023437499508 6.665049305534919e-7\n",
      "6. 12.637007812499508 12.637023437499508 12.637015624999508 1.7349363907078344e-7\n",
      "7. 12.637007812499508 12.637015624999508 12.637011718749509 4.1999940436954773e-7\n",
      "8. 12.637007812499508 12.637011718749509 12.637009765624509 5.432528380148205e-7\n",
      "9. 12.637007812499508 12.637009765624509 12.637008789062008 6.048788743681861e-7\n",
      "10. 12.637007812499508 12.637008789062008 12.637008300780758 6.356914114465459e-7\n",
      "11. 12.637007812499508 12.637008300780758 12.637008056640134 6.510971036845348e-7\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 6.588013483733932e-7 for V_0/|E| = 12.637007934569821\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 12.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.0 12.0 11.5 -0.009549309896733681\n",
      "1. 11.5 12.0 11.75 0.007185685629913423\n",
      "2. 11.75 12.0 11.875 -0.0013608063962993453\n",
      "3. 11.75 11.875 11.8125 -0.0054992552746582464\n",
      "4. 11.75 11.8125 11.78125 -0.003441148661898264\n",
      "5. 11.75 11.78125 11.765625 -0.0024037655859785977\n",
      "6. 11.75 11.765625 11.7578125 -0.001882984083236815\n",
      "7. 11.75 11.7578125 11.75390625 -0.0016220698988355273\n",
      "8. 11.75 11.75390625 11.751953125 -0.00149148182661966\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0014261550348899656 for V_0/|E| = 11.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.709976562499468\n",
      "Starting Bisection.\n",
      "\n",
      "0. 11.708976562499469 11.709976562499468 11.709476562499468 -1.6864738845901794e-5\n",
      "1. 11.708976562499469 11.709476562499468 11.709226562499468 -1.712615134486777e-8\n",
      "2. 11.709226562499468 11.709476562499468 11.709351562499467 8.407219792152275e-6\n",
      "3. 11.709226562499468 11.709351562499467 11.709289062499469 4.19500202604947e-6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4. 11.709226562499468 11.709289062499469 11.70925781249947 6.301099883498456e-6\n",
      "5. 11.709226562499468 11.70925781249947 11.70924218749947 7.354157127786156e-6\n",
      "6. 11.709226562499468 11.70924218749947 11.709234374999468 7.880688737534617e-6\n",
      "7. 11.709226562499468 11.709234374999468 11.709230468749467 8.143954237990696e-6\n",
      "8. 11.709226562499468 11.709230468749467 11.709228515624467 8.275587076301145e-6\n",
      "9. 11.709226562499468 11.709228515624467 11.709227539061967 8.341402994613344e-6\n",
      "10. 11.709226562499468 11.709227539061967 11.709227050780719 8.374311875591094e-6\n",
      "11. 11.709226562499468 11.709227050780719 11.709226806640093 8.390764315892834e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 8.398992128518442e-6 for V_0/|E| = 11.709226684569781\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.0038437535633645587\n",
      "1. 10.5 11.0 10.75 0.014566609979722808\n",
      "2. 10.5 10.75 10.625 0.005150156291817447\n",
      "3. 10.5 10.625 10.5625 0.009804857031973507\n",
      "4. 10.5 10.5625 10.53125 0.012172262711342967\n",
      "5. 10.5 10.53125 10.515625 0.013366057439312485\n",
      "6. 10.5 10.515625 10.5078125 0.013965487580968017\n",
      "7. 10.5 10.5078125 10.50390625 0.014265837070299388\n",
      "8. 10.5 10.50390625 10.501953125 0.014416170575587361\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.014491377038207744 for V_0/|E| = 10.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.891976562499229\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.89097656249923 10.891976562499229 10.891476562499228 -8.662306521531452e-6\n",
      "1. 10.891476562499228 10.891976562499229 10.89172656249923 9.26884482681668e-6\n",
      "2. 10.891476562499228 10.89172656249923 10.891601562499229 3.0306117246834075e-7\n",
      "3. 10.891476562499228 10.891601562499229 10.891539062499229 4.785901280471221e-6\n",
      "4. 10.891476562499228 10.891539062499229 10.891507812499228 7.0273586504811e-6\n",
      "5. 10.891476562499228 10.891507812499228 10.891492187499228 8.148096831794054e-6\n",
      "6. 10.891476562499228 10.891492187499228 10.891484374999228 8.708470693060089e-6\n",
      "7. 10.891476562499228 10.891484374999228 10.89148046874923 8.988658544920575e-6\n",
      "8. 10.891476562499228 10.89148046874923 10.891478515624229 9.128752081014422e-6\n",
      "9. 10.891476562499228 10.891478515624229 10.891477539061729 9.19879635551346e-6\n",
      "10. 10.891476562499228 10.891477539061729 10.891477050780479 9.233821513598338e-6\n",
      "11. 10.891476562499228 10.891477050780479 10.891476806639854 9.251333945559897e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 9.26008908324295e-6 for V_0/|E| = 10.891476684569541\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 11.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.0 11.0 10.5 -0.029134846891670226\n",
      "1. 10.0 10.5 10.25 -0.012264730202538411\n",
      "2. 10.0 10.25 10.125 -0.0031461952598506016\n",
      "3. 10.125 10.25 10.1875 0.0015898831616216757\n",
      "4. 10.1875 10.25 10.21875 -0.0007930701971854655\n",
      "5. 10.1875 10.21875 10.203125 -0.001973347690679341\n",
      "6. 10.1875 10.203125 10.1953125 -0.0013841393760501658\n",
      "7. 10.1875 10.1953125 10.19140625 -0.0010888376078473144\n",
      "8. 10.1875 10.19140625 10.189453125 -0.0009410121340105486\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.0008670557253728782 for V_0/|E| = 10.1884765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.167476562499457\n",
      "Starting Bisection.\n",
      "\n",
      "0. 10.166476562499458 10.167476562499457 10.166976562499457 -3.288926010211547e-5\n",
      "1. 10.166476562499458 10.166976562499457 10.166726562499457 -1.386774087415256e-5\n",
      "2. 10.166476562499458 10.166726562499457 10.166601562499459 -4.356262328815959e-6\n",
      "3. 10.166601562499459 10.166726562499457 10.166664062499457 3.996551583050991e-7\n",
      "4. 10.166664062499457 10.166726562499457 10.166695312499456 -1.9783186491133973e-6\n",
      "5. 10.166664062499457 10.166695312499456 10.166679687499457 -3.1672939423509393e-6\n",
      "6. 10.166664062499457 10.166679687499457 10.166671874999457 -2.5728050301830383e-6\n",
      "7. 10.166664062499457 10.166671874999457 10.166667968749458 -2.2755626780912977e-6\n",
      "8. 10.166664062499457 10.166667968749458 10.166666015624457 -2.1269414903947905e-6\n",
      "9. 10.166664062499457 10.166666015624457 10.166665039061957 -2.0526298971713946e-6\n",
      "10. 10.166664062499457 10.166665039061957 10.166664550780707 -2.015474157780405e-6\n",
      "11. 10.166664062499457 10.166664550780707 10.166664306640083 -1.996897441995155e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = -1.987607725553711e-6 for V_0/|E| = 10.16666418456977\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 10.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.0 10.0 9.5 -0.01832682490999905\n",
      "1. 9.5 10.0 9.75 0.0008145846858227873\n",
      "2. 9.75 10.0 9.875 -0.009021519073733806\n",
      "3. 9.75 9.875 9.8125 -0.013739472923871232\n",
      "4. 9.75 9.8125 9.78125 -0.011396951394708404\n",
      "5. 9.75 9.78125 9.765625 -0.010213365435109013\n",
      "6. 9.75 9.765625 9.7578125 -0.009618476853336529\n",
      "7. 9.75 9.7578125 9.75390625 -0.009320256871304384\n",
      "8. 9.75 9.75390625 9.751953125 -0.009170952730065327\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.009096252095801807 for V_0/|E| = 9.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.520976562499573\n",
      "Starting Bisection.\n",
      "\n",
      "0. 9.519976562499574 9.520976562499573 9.520476562499574 -3.154132597458698e-5\n",
      "1. 9.519976562499574 9.520476562499574 9.520226562499573 -1.1417748271861383e-5\n",
      "2. 9.519976562499574 9.520226562499573 9.520101562499573 -1.3551419735569566e-6\n",
      "3. 9.520101562499573 9.520226562499573 9.520164062499573 3.676368445950434e-6\n",
      "4. 9.520101562499573 9.520164062499573 9.520132812499572 1.1605980259276056e-6\n",
      "5. 9.520101562499573 9.520132812499572 9.520117187499572 2.41847835369093e-6\n",
      "6. 9.520101562499573 9.520117187499572 9.520109374999572 3.04742287140673e-6\n",
      "7. 9.520101562499573 9.520109374999572 9.520105468749573 3.361894623196503e-6\n",
      "8. 9.520101562499573 9.520105468749573 9.520103515624573 3.5191316118551716e-6\n",
      "9. 9.520101562499573 9.520103515624573 9.520102539062073 3.597748700428123e-6\n",
      "10. 9.520101562499573 9.520102539062073 9.520102050780823 3.6370598311905697e-6\n",
      "11. 9.520101562499573 9.520102050780823 9.520101806640199 3.656714009470111e-6\n",
      "\n",
      "After 12 steps, convergent value found.\n",
      "U(r_0) = 3.6665410799713884e-6 for V_0/|E| = 9.520101684569886\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.002483874563897887\n",
      "1. 8.5 9.0 8.75 0.019720659577072305\n",
      "2. 8.5 8.75 8.625 0.00830011670118882\n",
      "3. 8.5 8.625 8.5625 0.013929477821749874\n",
      "4. 8.5 8.5625 8.53125 0.016804671655607385\n",
      "5. 8.5 8.53125 8.515625 0.01825754505728354\n",
      "6. 8.5 8.515625 8.5078125 0.018987819508710504\n",
      "7. 8.5 8.5078125 8.50390625 0.019353918509132997\n",
      "8. 8.5 8.50390625 8.501953125 0.01953720874217506\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.019628914078026877 for V_0/|E| = 8.5009765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.941976562499645\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.940976562499646 8.941976562499645 8.941476562499645 -3.658433192452053e-5\n",
      "1. 8.940976562499646 8.941476562499645 8.941226562499645 -1.535070811943136e-5\n",
      "2. 8.940976562499646 8.941226562499645 8.941101562499647 -4.732966633251896e-6\n",
      "3. 8.941101562499647 8.941226562499645 8.941164062499645 5.761378921578669e-7\n",
      "4. 8.941164062499645 8.941226562499645 8.941195312499644 -2.0784351947683456e-6\n",
      "5. 8.941164062499645 8.941195312499644 8.941179687499645 -3.405705741129622e-6\n",
      "6. 8.941164062499645 8.941179687499645 8.941171874999645 -2.742070329567545e-6\n",
      "7. 8.941164062499645 8.941171874999645 8.941167968749646 -2.410253904188855e-6\n",
      "8. 8.941164062499645 8.941167968749646 8.941166015624646 -2.244345391035889e-6\n",
      "9. 8.941164062499645 8.941166015624646 8.941165039062145 -2.1613880387971234e-6\n",
      "10. 8.941164062499645 8.941165039062145 8.941164550780895 -2.119911190549499e-6\n",
      "11. 8.941164062499645 8.941164550780895 8.941164306640271 -2.0991718202739436e-6\n",
      "12. 8.941164062499645 8.941164306640271 8.941164184569958 -2.0888039590472215e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -2.0836192774084437e-6 for V_0/|E| = 8.9411641235348\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 9.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.0 9.0 8.5 -0.024099057865754902\n",
      "1. 8.0 8.5 8.25 -0.0035401715265140233\n",
      "2. 8.25 8.5 8.375 0.007765232822294934\n",
      "3. 8.25 8.375 8.3125 0.0020244152306684374\n",
      "4. 8.25 8.3125 8.28125 0.004872595197371561\n",
      "5. 8.25 8.28125 8.265625 0.00631333166114901\n",
      "6. 8.25 8.265625 8.2578125 0.007037883504134127\n",
      "7. 8.25 8.2578125 8.25390625 0.007401208083952413\n",
      "8. 8.25 8.25390625 8.251953125 0.007583132884004418\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = 0.007674160953984788 for V_0/|E| = 8.2509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.420976562500018\n",
      "Starting Bisection.\n",
      "\n",
      "0. 8.419976562500018 8.420976562500018 8.420476562500017 -4.262937766009868e-5\n",
      "1. 8.419976562500018 8.420476562500017 8.420226562500018 -2.027771046894155e-5\n",
      "2. 8.419976562500018 8.420226562500018 8.420101562500019 -9.100826061754945e-6\n",
      "3. 8.419976562500018 8.420101562500019 8.420039062500019 -3.5121212051739157e-6\n",
      "4. 8.419976562500018 8.420039062500019 8.420007812500018 -7.177025188473954e-7\n",
      "5. 8.420007812500018 8.420039062500019 8.420023437500017 6.79521710119798e-7\n",
      "6. 8.420023437500017 8.420039062500019 8.420031250000019 -1.9092405170416547e-8\n",
      "7. 8.420023437500017 8.420031250000019 8.420027343750018 -3.683968110972051e-7\n",
      "8. 8.420023437500017 8.420027343750018 8.420025390625018 -1.937452725551389e-7\n",
      "9. 8.420023437500017 8.420025390625018 8.420024414062517 -1.0641989109522879e-7\n",
      "10. 8.420023437500017 8.420024414062517 8.420023925781267 -6.275535321805058e-8\n",
      "11. 8.420023437500017 8.420023925781267 8.420023681640643 -4.092285318083239e-8\n",
      "12. 8.420023437500017 8.420023681640643 8.42002355957033 -3.0008373012616823e-8\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -2.4549082334863464e-8 for V_0/|E| = 8.420023498535173\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.0023717455283039177\n",
      "1. 7.5 8.0 7.75 0.02239380476915737\n",
      "2. 7.5 7.75 7.625 0.009605373237541827\n",
      "3. 7.5 7.625 7.5625 0.015896214947063576\n",
      "4. 7.5 7.5625 7.53125 0.019118918339107296\n",
      "5. 7.5 7.53125 7.515625 0.020749807482293853\n",
      "6. 7.5 7.515625 7.5078125 0.02157016369766885\n",
      "7. 7.5 7.5078125 7.50390625 0.02198157313466501\n",
      "8. 7.5 7.50390625 7.501953125 0.022187586115579475\n",
      "9. 7.5 7.501953125 7.5009765625 0.022290669724908587\n",
      "\n",
      "After 10 steps, convergent value found.\n",
      "U(r_0) = 0.022342230814970113 for V_0/|E| = 7.50048828125\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.949488281250484\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.948488281250484 7.949488281250484 7.948988281250484 -1.5706308009813176e-5\n",
      "1. 7.948988281250484 7.949488281250484 7.949238281250484 7.775484199479195e-6\n",
      "2. 7.949238281250484 7.949488281250484 7.949363281250484 -3.9658055480859895e-6\n",
      "3. 7.949238281250484 7.949363281250484 7.949300781250484 -9.836155505983635e-6\n",
      "4. 7.949238281250484 7.949300781250484 7.949269531250484 -6.901004608685993e-6\n",
      "5. 7.949238281250484 7.949269531250484 7.949253906250483 -5.4334114765024405e-6\n",
      "6. 7.949238281250484 7.949253906250483 7.949246093750483 -4.699608641831335e-6\n",
      "7. 7.949238281250484 7.949246093750483 7.9492421875004835 -4.332709003860595e-6\n",
      "8. 7.949238281250484 7.9492421875004835 7.949240234375484 -4.149256010112499e-6\n",
      "9. 7.949238281250484 7.949240234375484 7.949239257812984 -4.057531222625832e-6\n",
      "10. 7.949238281250484 7.949239257812984 7.949238769531734 -4.011668013958853e-6\n",
      "11. 7.949238281250484 7.949238769531734 7.949238525391109 -3.988736227702563e-6\n",
      "12. 7.949238281250484 7.949238525391109 7.949238403320797 -3.977268021086657e-6\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -3.971538375185666e-6 for V_0/|E| = 7.94923834228564\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 8.0\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.0 8.0 7.5 -0.021966827097597244\n",
      "1. 7.5 8.0 7.75 0.0010875655661370873\n",
      "2. 7.75 8.0 7.875 -0.010862984305366714\n",
      "3. 7.75 7.875 7.8125 -0.016518536769351437\n",
      "4. 7.75 7.8125 7.78125 -0.013716941612374977\n",
      "5. 7.75 7.78125 7.765625 -0.012296542618958442\n",
      "6. 7.75 7.765625 7.7578125 -0.011581412690373603\n",
      "7. 7.75 7.7578125 7.75390625 -0.011222611345167877\n",
      "8. 7.75 7.75390625 7.751953125 -0.011042901105026268\n",
      "\n",
      "After 9 steps, convergent value found.\n",
      "U(r_0) = -0.010952968533700487 for V_0/|E| = 7.7509765625\n",
      "\n",
      "Locating Initial V_0.\n",
      "\n",
      "Initial V_0/|E| = 7.522976562500258\n",
      "Starting Bisection.\n",
      "\n",
      "0. 7.5219765625002575 7.522976562500258 7.522476562500257 -4.704492441227627e-5\n",
      "1. 7.5219765625002575 7.522476562500257 7.522226562500258 -2.243346889624555e-5\n",
      "2. 7.5219765625002575 7.522226562500258 7.522101562500257 -1.0126427007887561e-5\n",
      "3. 7.5219765625002575 7.522101562500257 7.522039062500257 -3.972573187137491e-6\n",
      "4. 7.5219765625002575 7.522039062500257 7.522007812500258 -8.955642487255644e-7\n",
      "5. 7.522007812500258 7.522039062500257 7.522023437500257 6.429600045692163e-7\n",
      "6. 7.522023437500257 7.522039062500257 7.522031250000257 -1.2630319141376413e-7\n",
      "7. 7.522023437500257 7.522031250000257 7.522027343750257 -5.109326251128252e-7\n",
      "8. 7.522023437500257 7.522027343750257 7.522025390625258 -3.1861692590311706e-7\n",
      "9. 7.522023437500257 7.522025390625258 7.5220244140627575 -2.2245997282313174e-7\n",
      "10. 7.522023437500257 7.5220244140627575 7.522023925781507 -1.7438262008191712e-7\n",
      "11. 7.522023437500257 7.522023925781507 7.522023681640882 -1.5034132087749046e-7\n",
      "12. 7.522023437500257 7.522023681640882 7.52202355957057 -1.3832310401682554e-7\n",
      "\n",
      "After 13 steps, convergent value found.\n",
      "U(r_0) = -1.3231408519254654e-7 for V_0/|E| = 7.522023498535414\n"
     ]
    }
   ],
   "source": [
    "a_values = .5:.1:3\n",
    "\n",
    "open(\"vr_50.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .001, 50, file)\n",
    "    end\n",
    "end\n",
    "\n",
    "open(\"vr_40.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .001, 40, file)\n",
    "    end\n",
    "end\n",
    "\n",
    "open(\"vr_30.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .001, 30, file)\n",
    "    end\n",
    "end\n",
    "open(\"vr_20.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .001, 20, file)\n",
    "    end\n",
    "end\n",
    "\n",
    "open(\"vr_10.dat\", \"w\") do file\n",
    "    for a in a_values\n",
    "        export_r_V0(a, .001, 10, file)\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing $U(r)$ vs. $r$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1.3\n",
    "V_0 = 32.7212\n",
    "\n",
    "self_50 = System(.1, a, V_0, 50, .001)#System(r_0, a, V_0, r_max, ∆r, ∆V)\n",
    "initialize(self_50)\n",
    "U_integration(self_50)\n",
    "\n",
    "r_50 = collect(self_50.r_0:self_50.∆r:self_50.r_max)\n",
    "\n",
    "open(\"data/r_max/U_50.dat\", \"w\") do file\n",
    "    for i=1:length(r_50)\n",
    "        println(file, r_50[i], \" \", self_50.U[i])\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "self_40 = System(.1, a, V_0, 40, .001)#System(r_0, a, V_0, r_max, ∆r, ∆V)\n",
    "initialize(self_40)\n",
    "U_integration(self_40)\n",
    "\n",
    "r_40 = collect(self_40.r_0:self_40.∆r:self_40.r_max)\n",
    "\n",
    "open(\"data/r_max/U_40.dat\", \"w\") do file\n",
    "    for i=1:length(r_40)\n",
    "        println(file, r_40[i], \" \", self_40.U[i])\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "self_30 = System(.1, a, V_0, 30, .001)#System(r_0, a, V_0, r_max, ∆r, ∆V)\n",
    "initialize(self_30)\n",
    "U_integration(self_30)\n",
    "\n",
    "r_30 = collect(self_30.r_0:self_30.∆r:self_30.r_max)\n",
    "\n",
    "open(\"data/r_max/U_30.dat\", \"w\") do file\n",
    "    for i=1:length(r_30)\n",
    "        println(file, r_30[i], \" \", self_30.U[i])\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "self_20 = System(.1, a, V_0, 20, .001)#System(r_0, a, V_0, r_max, ∆r, ∆V)\n",
    "initialize(self_20)\n",
    "U_integration(self_20)\n",
    "\n",
    "r_20 = collect(self_20.r_0:self_20.∆r:self_20.r_max)\n",
    "\n",
    "open(\"data/r_max/U_20.dat\", \"w\") do file\n",
    "    for i=1:length(r_20)\n",
    "        println(file, r_20[i], \" \", self_20.U[i])\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exporting $U(r)$ for true value of $a$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, V_0 = 1.258, 34.8307\n",
    "self_0 = System(.1, a, V_0, 30, 1e-3)\n",
    "\n",
    "r_values = collect(self_0.r_0:self_0.∆r:self_0.r_max)\n",
    "\n",
    "initialize(self_0)\n",
    "U_integration(self_0)\n",
    "\n",
    "norm_0= calculate_norm(self_0)\n",
    "\n",
    "open(\"data/U_vs_r.dat\", \"w\") do file\n",
    "    for i=1:length(r_values)\n",
    "        println(file, r_values[i], \" \", self_0.U[i]/sqrt(norm))\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing Impact of initial conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, V_0 = 1.258, 34.8307\n",
    "self = System(.1, a, V_0, 30, 1e-3)\n",
    "\n",
    "r_values = collect(self.r_0:self.∆r:self.r_max)\n",
    "\n",
    "initialize(self)\n",
    "\n",
    "#set value of U at r = r_max first\n",
    "self.U[self.n_total] = .001\n",
    "#set corresponding vaue of phi_0\n",
    "self.phi_0 = self.U[self.n_total] * (1-((self.∆r^2) * f(self, self.r_max) / 12))\n",
    "\n",
    "#set value of U at r = r_max - ∆r next\n",
    "self.U[self.n_total-1] = 100000000000000\n",
    "#set corresponding vaue of phi_1\n",
    "self.phi_1 = self.U[self.n_total-1] * (1-((self.∆r^2) * f(self, self.r_max - self.∆r) / 12))\n",
    "\n",
    "U_integration(self)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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