06-transmutation.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Transmutation\n",
      "\n",
      "As of v0.3, PyNE has a nascent support for native transmutation.  The only implementation right now is a recursive chain solver, though we envision a suite of tools. To enable this future vision each solver will have a `Transmute` class which has a `transmute()` method.  Though this may seem like extra work from the users perspective, it enables rapid speedups by pre-loading cross section data and/or pre-computing decay chains.  \n",
      "\n",
      "The `transmute()` method accepts a material, as well as other parameters.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import time\n",
      "import sys\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pyne import nucname\n",
      "from pyne.material import Material\n",
      "from pyne.transmute.chainsolve import Transmuter"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First make a transmuter instance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "transmuter = Transmuter(t=365.25 * 24 * 3600, phi=4e14)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then make a dictionary to represent a material"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "imat = {'H1': 1.0}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Transmuting the material returns another material:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print transmuter.transmute(imat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Material:\n",
        "mass = 1.00008087683\n",
        "density= -1.0\n",
        "atoms per molecule = 1.0\n",
        "------------------------\n",
        "H1     0.999838134994\n",
        "H2     0.000161864985416\n",
        "H3     2.09351322228e-11\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can also specify a flux using the EAF group structure:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phi = np.array([  # fluxin1 from ALARA\n",
      "    0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00,\n",
      "    0.00000E+00, 8.98755E+13, 9.77446E+12, 8.06925E+12, 1.70726E+12, 1.28302E+12,\n",
      "    1.89143E+12, 2.04175E+12, 2.07250E+12, 1.80384E+12, 1.54256E+12, 1.42579E+12,\n",
      "    1.24872E+12, 1.17419E+12, 1.14707E+12, 1.19572E+12, 1.22437E+12, 1.26141E+12,\n",
      "    4.38938E+11, 9.07635E+11, 1.39910E+12, 1.45818E+12, 1.48523E+12, 1.43566E+12,\n",
      "    1.41561E+12, 1.40784E+12, 1.35321E+12, 2.71459E+12, 2.62508E+12, 2.66233E+12,\n",
      "    1.40292E+12, 1.42487E+12, 1.37130E+12, 1.37665E+12, 1.52025E+12, 1.59680E+12,\n",
      "    1.07723E+12, 2.77969E+11, 2.78790E+11, 5.53898E+11, 1.09314E+12, 1.64561E+12,\n",
      "    1.68331E+12, 1.74677E+12, 1.80254E+12, 1.93480E+12, 1.96231E+12, 1.93938E+12,\n",
      "    1.92934E+12, 1.93774E+12, 1.90789E+12, 1.82967E+12, 1.88061E+12, 1.89368E+12,\n",
      "    1.81907E+12, 3.42703E+12, 1.43106E+12, 2.05052E+12, 1.78729E+12, 1.86431E+12,\n",
      "    1.83209E+12, 1.87158E+12, 1.80219E+12, 1.73173E+12, 1.60686E+12, 1.29878E+12,\n",
      "    1.48781E+12, 1.61671E+12, 1.60349E+12, 1.59722E+12, 3.03722E+12, 2.90241E+12,\n",
      "    1.42928E+12, 1.35835E+12, 2.69252E+12, 2.55807E+12, 2.86956E+11, 1.05539E+11,\n",
      "    2.25492E+11, 5.88210E+11, 1.19440E+12, 2.20287E+12, 1.08398E+12, 1.03200E+12,\n",
      "    9.75760E+11, 9.46015E+11, 9.12835E+11, 9.29522E+11, 8.90411E+11, 8.30228E+11,\n",
      "    8.45313E+11, 8.07049E+11, 7.71896E+11, 7.07755E+11, 8.21782E+11, 7.22692E+11,\n",
      "    7.33346E+11, 6.91441E+11, 1.63354E+12, 1.56807E+12, 5.29641E+11, 4.48653E+11,\n",
      "    1.07702E+12, 8.07461E+11, 1.82087E+12, 7.58110E+11, 1.26259E+12, 1.12779E+12,\n",
      "    1.54243E+12, 6.74366E+11, 8.42541E+11, 4.34202E+11, 2.89471E+11, 3.71251E+11,\n",
      "    2.64038E+11, 2.30016E+11, 5.82748E+11, 9.47843E+11, 1.71492E+12, 1.80379E+12,\n",
      "    5.48701E+11, 8.73235E+11, 1.82674E+12, 1.52497E+12, 1.48336E+12, 9.67624E+11,\n",
      "    6.31697E+11, 6.03210E+11, 5.84716E+11, 1.49733E+11, 1.84075E+11, 7.72799E+11,\n",
      "    1.82977E+11, 1.80083E+12, 1.48029E+12, 1.45254E+12, 1.44214E+12, 1.34832E+12,\n",
      "    1.10171E+12, 1.27549E+12, 1.33060E+12, 1.27163E+12, 1.32883E+12, 1.32596E+12,\n",
      "    1.35429E+12, 1.34940E+12, 1.34862E+12, 1.34699E+12, 1.32883E+12, 1.33697E+12,\n",
      "    1.33352E+12, 1.32882E+12, 1.32283E+12, 1.31655E+12, 1.30955E+12, 1.30178E+12,\n",
      "    1.29327E+12, 1.28377E+12, 1.27355E+12, 1.26193E+12, 1.24944E+12, 1.23535E+12,\n",
      "    1.21970E+12, 1.20272E+12, 1.18312E+12, 1.16152E+12, 1.13736E+12, 2.82140E+12,\n",
      "    5.36871E+13])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Having the `log` set will produce fancy output."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tm = Transmuter(phi=phi, tol=1e-10, log=sys.stdout)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "inp = Material({'FE56': 1.0}, mass=1.0)\n",
      "t1 = time.time()\n",
      "out = tm.transmute(inp, t=31536000.0, tol=1e-7)\n",
      "dt = time.time() - t1\n",
      "print 'Transmutation time: {0}'.format(dt)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "--> Fe56 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Fe57 [ 0.00438046]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Fe57 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe56 [  8.55972423e-06]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe56 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe57 [  1.25875636e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn55 [  4.94094467e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr52 [  3.87491320e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn54 [  3.38033850e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe55 [  3.24252005e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn56 [  1.59905049e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  3.71225677e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn57 [  5.29448233e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe58 [  9.18336666e-06]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe58 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr56 [  8.48355844e-23]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn57 [  3.32510519e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe57 [  9.32443551e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn58 [  5.50579059e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr55 [  5.18805000e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe59 [  2.42666743e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn58M [  5.39244677e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr54 [  5.18991130e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn56 [  8.01386265e-19]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr56 [  1.66874942e-20]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr53 [  1.21595729e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn55 [  7.74655993e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr54 [  2.35240098e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr54 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V52 [  6.44852455e-20]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti50 [  2.69566822e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V53 [  5.32034599e-18]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  2.81950119e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V54 [  2.55387164e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti51 [  1.79352912e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr55 [  1.40945438e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr55 [  1.19819151e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn56 [  6.72436461e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Mn55 [ 0.00017116]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Mn55 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn56 [  1.74489151e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr54 [  1.20633097e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr55 [  2.39406026e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V52 [  1.79426349e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V51 [  3.06438194e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V53 [  1.75536085e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn54 [  1.68383934e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn54 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr52 [  4.39773662e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V51 [  6.93564656e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V50 [  4.80612381e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V52 [  1.47767256e-21]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe54 [  4.51302168e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V53 [  3.45313498e-25]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn53 [  1.61107481e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr54 [  4.85981083e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn55 [  1.08024686e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  1.28688325e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr53 [  2.41876795e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Cr52 [  1.35040579e-06]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Cr52 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti48 [  2.66741826e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V51 [  1.51384510e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti50 [  2.07097938e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V52 [  4.27284275e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti49 [  7.92519715e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr51 [  1.09072537e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr53 [  8.89591993e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti51 [  2.85300050e-23]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Mn54 [  9.72921990e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Fe55 [ 0.00105972]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Fe55 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe56 [  6.22048126e-06]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe56 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe57 [  9.34023045e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn55 [  3.66607049e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr52 [  2.87531711e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn54 [  2.50222717e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe55 [  2.40410966e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn56 [  1.16209472e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  2.75434266e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr54 [  1.70537115e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn53 [  1.95492583e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr51 [  1.01013449e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn54 [  1.07010032e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr53 [  1.51280374e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe54 [  6.21810640e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe54 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn52 [  3.11634445e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr50 [  1.79244516e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn53 [  4.64570346e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn52M [  7.15530513e-18]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr52 [  1.96993819e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn54 [  3.23514650e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr51 [  1.75120966e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe53 [  1.68786921e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe55 [  7.66412987e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  1.97548348e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr52 [  1.30221707e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr52 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti48 [  1.75295891e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V51 [  9.94592049e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti50 [  1.35963708e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V52 [  4.12032917e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti49 [  5.20510264e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr51 [  9.57762086e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  5.85551932e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti51 [  2.75115238e-24]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn55 [ 0.00013905]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Mn55 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn56 [  1.41705352e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr54 [  6.66065700e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr55 [  1.94499632e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V52 [  1.45770504e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V51 [  1.69294963e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V53 [  1.42610748e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn54 [  9.87971943e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  1.33878231e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Mn56 [  1.85782312e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Mn56 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe56 [ 0.00043724]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Fe56 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe57 [  9.63708652e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe57 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Fe56 [  1.25467330e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Mn57 [  1.16478929e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Fe58 [  1.34596443e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr56 [  3.67121315e-24]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr53 [  1.78657394e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Mn55 [  1.13742807e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr54 [  3.44753726e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr55 [  2.63601348e-21]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Mn56 [  1.47874121e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn55 [  3.77703949e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr52 [  2.96806630e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn54 [  2.43117073e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe55 [  2.43136515e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Fe55 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Fe56 [  9.31024176e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr54 [  2.55199144e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Mn53 [  2.95532308e-13]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr51 [  2.08480107e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Mn54 [  1.71084565e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr53 [  2.26986158e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Fe54 [  9.30827174e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Cr52 [  1.94843187e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |   |--> Mn55 [  2.08496906e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Mn56 [  8.17149537e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  2.83591353e-08]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Cr53 [ 0.00012834]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |--> Cr53 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V52 [  4.26296948e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti50 [  5.78481821e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti49 [  1.95066140e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V51 [  1.50342873e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti51 [  6.02570968e-19]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr52 [  2.61458516e-07]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr52 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti48 [  3.45464382e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V51 [  1.96007372e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti50 [  2.67941074e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V52 [  8.27277081e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti49 [  1.02577389e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr51 [  1.91077670e-11]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  1.15404141e-10]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti51 [  5.52374408e-24]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> V53 [  8.76560312e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr54 [  1.97194095e-06]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Cr54 1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V52 [  5.40558810e-19]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti50 [  2.26464551e-12]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V53 [  4.45987252e-17]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr53 [  2.36865302e-09]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> V54 [  2.14082727e-16]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Ti51 [  1.50345712e-15]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |   |--> Cr55 [  1.18149969e-14]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   |   |--> Ti52 [  1.28370431e-23]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Transmutation time: 0.384331941605\n"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}