{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Compton scattering\n",
    "## Introduction\n",
    "Plot the energy of a Compton scattered photon as a function of the scattering angle.\n",
    "## Load modules\n",
    "Load the Python modules needed for mathematical functions and plotting. The first command ensure plots are produced \"inline\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "from numpy import *\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constants\n",
    "Enter the values of any constants needed in the calculation and print out their values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mass of electron  511  keV.\n"
     ]
    }
   ],
   "source": [
    "m_e = 511 # keV\n",
    "print(\"mass of electron \",m_e,\" keV.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function\n",
    "Define Compton scattering function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def comptonE(energy_in,theta):\n",
    "    '''\n",
    "    Returns energy of Compton scattered photon at a given scattering angle and initial energy \n",
    "    '''\n",
    "    energy_out = energy_in/(1+energy_in*(1-math.cos(theta))/m_e)\n",
    "    return energy_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the plot\n",
    "Decide how many points are to be plotted, the energy of the incoming photon and the angular range to be covered. Define the arrays that will contain the scattering angles and energies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nIter = 100\n",
    "theta_bot = 0\n",
    "theta_top = 3.1415926\n",
    "theta_step = (theta_top-theta_bot)/nIter\n",
    "energy_in = 0.4*m_e\n",
    "theta = zeros((nIter+1))\n",
    "photonE = zeros((nIter+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fill the plot\n",
    "Now loop over the required number of iterations, calculating the angles energies and filling the plot. This is a \"Fortran-like\" approach. Later we will look at doing this using some of Python's features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2bc4a950f28>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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DM2XqhgnhG+14JSQiIvGJPSkh3Me9hTCkcNGAVGPNrF60fVNClezVhOrDIwgttEem7WcY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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2bc4a92f748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(0,nIter+1):\n",
    "    theta[i] = i*theta_step\n",
    "    photonE[i] = comptonE(energy_in,theta[i])\n",
    "plt.plot(theta,photonE)\n",
    "plt.title('Energy of Compton scattered photon');\n",
    "plt.xlabel('Angle (radians)')\n",
    "plt.ylabel('Energy (keV)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python solution\n",
    "Use the constants and function defined above, but change the way the arrays are set up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2bc4b2031d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HDqVz587ZjFdy5LzzoEkTOPVU+OEHePBBDUsvIpJtmb6oT58+nby8vKy/ViKS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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2bc4accc278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta_arr = linspace(theta_bot,theta_top,nIter+1)\n",
    "photonE_arr = array([comptonE(energy_in,theta_arr[i]) for i in range(0,nIter+1)])\n",
    "# print(\"nIter \",nIter)\n",
    "# print(\"theta array \",theta_arr)\n",
    "# print(\"photon array \",photonE_arr)\n",
    "plt.plot(theta_arr,photonE_arr)\n",
    "plt.title('Energy of Compton scattered photon');\n",
    "plt.xlabel('Angle (radians)')\n",
    "plt.ylabel('Energy (keV)')"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
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