1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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4 | // * * |
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5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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7 | // * conditions of the Geant4 Software License, included in the file * |
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8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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9 | // * include a list of copyright holders. * |
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10 | // * * |
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11 | // * Neither the authors of this software system, nor their employing * |
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12 | // * institutes,nor the agencies providing financial support for this * |
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13 | // * work make any representation or warranty, express or implied, * |
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14 | // * regarding this software system or assume any liability for its * |
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15 | // * use. Please see the license in the file LICENSE and URL above * |
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16 | // * for the full disclaimer and the limitation of liability. * |
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17 | // * * |
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18 | // * This code implementation is the result of the scientific and * |
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19 | // * technical work of the GEANT4 collaboration. * |
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20 | // * By using, copying, modifying or distributing the software (or * |
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21 | // * any work based on the software) you agree to acknowledge its * |
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22 | // * use in resulting scientific publications, and indicate your * |
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23 | // * acceptance of all terms of the Geant4 Software license. * |
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24 | // ******************************************************************** |
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25 | // |
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26 | //$Id: G4ecpssrCrossSection.cc,v 1.6.2.2 2009/12/11 18:44:44 japost Exp $ |
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27 | // GEANT4 tag $Name: geant4-09-03 $ |
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28 | // |
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29 | // Author: Haifa Ben Abdelouahed |
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30 | // |
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31 | // |
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32 | // History: |
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33 | // ----------- |
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34 | // 21 Apr 2008 H. Ben Abdelouahed 1st implementation |
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35 | // 21 Apr 2008 MGP Major revision according to a design iteration |
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36 | // |
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37 | // ------------------------------------------------------------------- |
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38 | // Class description: |
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39 | // Low Energy Electromagnetic Physics, Cross section, p ionisation, K shell |
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40 | // Further documentation available from http://www.ge.infn.it/geant4/lowE |
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41 | // ------------------------------------------------------------------- |
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42 | |
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43 | |
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44 | #include "globals.hh" |
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45 | #include "G4ecpssrCrossSection.hh" |
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46 | #include "G4AtomicTransitionManager.hh" |
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47 | #include "G4NistManager.hh" |
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48 | #include "G4Proton.hh" |
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49 | #include "G4Alpha.hh" |
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50 | #include <math.h> |
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51 | |
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52 | G4ecpssrCrossSection::G4ecpssrCrossSection() |
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53 | { } |
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54 | |
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55 | G4ecpssrCrossSection::~G4ecpssrCrossSection() |
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56 | { } |
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57 | |
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58 | //---------------------------------this "ExpIntFunction" function allows fast evaluation of the n order exponential integral function En(x)------ |
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59 | |
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60 | G4double G4ecpssrCrossSection::ExpIntFunction(G4int n,G4double x) |
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61 | |
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62 | { |
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63 | G4int i; |
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64 | G4int ii; |
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65 | G4int nm1; |
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66 | G4double a; |
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67 | G4double b; |
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68 | G4double c; |
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69 | G4double d; |
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70 | G4double del; |
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71 | G4double fact; |
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72 | G4double h; |
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73 | G4double psi; |
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74 | G4double ans = 0; |
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75 | const G4double euler= 0.5772156649; |
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76 | const G4int maxit= 100; |
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77 | const G4double fpmin = 1.0e-30; |
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78 | const G4double eps = 1.0e-7; |
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79 | nm1=n-1; |
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80 | if (n<0 || x<0.0 || (x==0.0 && (n==0 || n==1))) |
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81 | G4cout << "bad arguments in ExpIntFunction" << G4endl; |
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82 | else { |
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83 | if (n==0) ans=std::exp(-x)/x; |
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84 | else { |
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85 | if (x==0.0) ans=1.0/nm1; |
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86 | else { |
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87 | if (x > 1.0) { |
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88 | b=x+n; |
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89 | c=1.0/fpmin; |
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90 | d=1.0/b; |
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91 | h=d; |
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92 | for (i=1;i<=maxit;i++) { |
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93 | a=-i*(nm1+i); |
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94 | b +=2.0; |
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95 | d=1.0/(a*d+b); |
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96 | c=b+a/c; |
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97 | del=c*d; |
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98 | h *=del; |
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99 | if (std::fabs(del-1.0) < eps) { |
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100 | ans=h*std::exp(-x); |
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101 | return ans; |
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102 | } |
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103 | } |
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104 | } else { |
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105 | ans = (nm1!=0 ? 1.0/nm1 : -std::log(x)-euler); |
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106 | fact=1.0; |
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107 | for (i=1;i<=maxit;i++) { |
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108 | fact *=-x/i; |
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109 | if (i !=nm1) del = -fact/(i-nm1); |
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110 | else { |
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111 | psi = -euler; |
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112 | for (ii=1;ii<=nm1;ii++) psi +=1.0/ii; |
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113 | del=fact*(-std::log(x)+psi); |
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114 | } |
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115 | ans += del; |
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116 | if (std::fabs(del) < std::fabs(ans)*eps) return ans; |
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117 | } |
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118 | } |
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119 | } |
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120 | } |
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121 | } |
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122 | return ans; |
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123 | } |
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124 | //----------------------------------------------------------------------------------------------------------- |
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125 | |
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126 | |
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127 | G4double G4ecpssrCrossSection::CalculateCrossSection(G4int zTarget,G4int zIncident, G4double energyIncident) |
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128 | |
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129 | //this K-CrossSection calculation method is done according to W.Brandt and G.Lapicki, Phys.Rev.A23(1981)// |
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130 | |
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131 | { |
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132 | |
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133 | G4NistManager* massManager = G4NistManager::Instance(); |
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134 | |
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135 | G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance(); |
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136 | |
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137 | G4double massIncident; |
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138 | |
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139 | if (zIncident == 1) |
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140 | { |
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141 | G4Proton* aProtone = G4Proton::Proton(); |
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142 | |
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143 | massIncident = aProtone->GetPDGMass(); |
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144 | } |
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145 | else |
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146 | { |
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147 | if (zIncident == 2) |
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148 | { |
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149 | G4Alpha* aAlpha = G4Alpha::Alpha(); |
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150 | |
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151 | massIncident = aAlpha->GetPDGMass(); |
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152 | } |
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153 | else |
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154 | { |
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155 | G4cout << "we can treat only Proton or Alpha incident particles " << G4endl; |
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156 | massIncident =0.; |
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157 | } |
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158 | } |
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159 | |
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160 | G4double kBindingEnergy = transitionManager->Shell(zTarget,0)->BindingEnergy(); |
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161 | |
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162 | G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2; |
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163 | |
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164 | G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2;//the mass of the system (projectile, target) |
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165 | |
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166 | const G4double zkshell= 0.3; |
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167 | |
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168 | G4double screenedzTarget = zTarget-zkshell; // screenedzTarget is the screened nuclear charge of the target |
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169 | |
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170 | const G4double rydbergMeV= 13.6e-6; |
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171 | |
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172 | G4double tetaK = kBindingEnergy/((screenedzTarget*screenedzTarget)*rydbergMeV); //tetaK denotes the reduced binding energy of the electron |
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173 | |
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174 | const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; |
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175 | |
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176 | G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.); //sigma0 is the initial cross section of K shell at stable state |
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177 | |
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178 | //--------------------------------------------------------------------------------------------------------------------- |
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179 | |
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180 | G4double velocity = CalculateVelocity( zTarget, zIncident, energyIncident); //is the scaled velocity parameter of the system |
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181 | |
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182 | //--------------------------------------------------------------------------------------------------------------------- |
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183 | |
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184 | const G4double kAnalyticalApproximation= 1.5; |
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185 | |
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186 | G4double x = kAnalyticalApproximation/velocity; |
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187 | |
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188 | G4double electrIonizationEnergy; |
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189 | |
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190 | if ( x<0.035) |
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191 | { |
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192 | electrIonizationEnergy= 0.75*pi*(std::log(1./(x*x))-1.); |
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193 | } |
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194 | else |
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195 | { |
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196 | if ( x<3.) |
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197 | { |
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198 | electrIonizationEnergy =std::exp(-2.*x)/(0.031+(0.213*std::pow(x,0.5))+(0.005*x)-(0.069*std::pow(x,3./2.))+(0.324*x*x)); |
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199 | } |
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200 | |
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201 | else |
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202 | { |
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203 | electrIonizationEnergy =2.*std::exp(-2.*x)/std::pow(x,1.6); } |
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204 | } |
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205 | |
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206 | G4double hFunction =(electrIonizationEnergy*2.)/(tetaK*std::pow(velocity,3)); //hFunction represents the correction for polarization effet |
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207 | |
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208 | G4double gFunction = (1.+(9.*velocity)+(31.*velocity*velocity)+(98.*std::pow(velocity,3.))+(12.*std::pow(velocity,4.))+(25.*std::pow(velocity,5.)) |
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209 | +(4.2*std::pow(velocity,6.))+(0.515*std::pow(velocity,7.)))/std::pow(1.+velocity,9.); //gFunction represents the correction for binding effet |
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210 | |
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211 | //----------------------------------------------------------------------------------------------------------------------------- |
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212 | |
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213 | G4double sigmaPSS = 1.+(((2.*zIncident)/(screenedzTarget*tetaK))*(gFunction-hFunction)); //describes the perturbed stationnairy state of the affected atomic electon |
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214 | |
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215 | //---------------------------------------------------------------------------------------------------------------------------- |
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216 | |
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217 | const G4double cNaturalUnit= 1/fine_structure_const; // it's the speed of light according to Atomic-Unit-System |
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218 | |
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219 | G4double ykFormula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocity/sigmaPSS); |
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220 | |
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221 | G4double relativityCorrection = std::pow((1.+(1.1*ykFormula*ykFormula)),0.5)+ykFormula;// the relativistic correction parameter |
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222 | |
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223 | G4double reducedVelocity = velocity*std::pow(relativityCorrection,0.5); // presents the reduced collision velocity parameter |
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224 | |
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225 | G4double universalFunction = (std::pow(2.,9.)/45.)*std::pow(reducedVelocity/sigmaPSS,8.)*std::pow((1.+(1.72*(reducedVelocity/sigmaPSS)*(reducedVelocity/sigmaPSS))),-4.);// is the reduced universal cross section |
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226 | |
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227 | //---------------------------------------------------------------------------------------------------------------------- |
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228 | |
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229 | G4double sigmaPSSR = (sigma0/(sigmaPSS*tetaK))*universalFunction; //sigmaPSSR is the straight-line K-shell ionization cross section |
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230 | |
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231 | //----------------------------------------------------------------------------------------------------------------------- |
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232 | |
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233 | G4double pssDeltaK = (4./(systemMass*sigmaPSS*tetaK))*(sigmaPSS/velocity)*(sigmaPSS/velocity); |
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234 | |
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235 | G4double energyLoss = std::pow(1-pssDeltaK,0.5); //energyLoss incorporates the straight-line energy-loss |
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236 | |
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237 | G4double energyLossFunction = (std::pow(2.,-9)/8.)*((((9.*energyLoss)-1.)*std::pow(1.+energyLoss,9.))+(((9.*energyLoss)+1.)*std::pow(1.-energyLoss,9.)));//energy loss function |
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238 | |
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239 | //---------------------------------------------------------------------------------------------------------------------------------------------- |
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240 | |
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241 | G4double coulombDeflection = (4.*pi*zIncident/systemMass)*std::pow(tetaK*sigmaPSS,-2.)*std::pow(velocity/sigmaPSS,-3.)*(zTarget/screenedzTarget); //incorporates Coulomb deflection parameter |
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242 | |
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243 | G4double cParameter = 2.*coulombDeflection/(energyLoss*(energyLoss+1.)); |
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244 | |
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245 | |
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246 | G4double coulombDeflectionFunction = 9.*ExpIntFunction(10,cParameter); //this function describes Coulomb-deflection effect |
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247 | |
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248 | //-------------------------------------------------------------------------------------------------------------------------------------------------- |
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249 | |
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250 | |
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251 | G4double crossSection = energyLossFunction* coulombDeflectionFunction*sigmaPSSR; //this ECPSSR cross section is estimated at perturbed-stationnairy-state(PSS) |
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252 | //and it's reduced by the energy-loss(E),the Coulomb deflection(C), |
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253 | //and the relativity(R) effects |
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254 | |
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255 | //-------------------------------------------------------------------------------------------------------------------------------------------------- |
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256 | |
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257 | return crossSection; |
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258 | } |
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259 | |
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260 | G4double G4ecpssrCrossSection::CalculateVelocity(G4int zTarget, G4int zIncident, G4double energyIncident) |
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261 | |
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262 | { |
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263 | |
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264 | G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance(); |
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265 | |
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266 | G4double kBindingEnergy = (transitionManager->Shell(zTarget,0)->BindingEnergy())/MeV; |
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267 | |
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268 | G4double massIncident; |
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269 | |
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270 | if (zIncident == 1) |
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271 | { |
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272 | G4Proton* aProtone = G4Proton::Proton(); |
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273 | |
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274 | massIncident = aProtone->GetPDGMass(); |
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275 | } |
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276 | else |
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277 | { |
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278 | if (zIncident == 2) |
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279 | { |
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280 | G4Alpha* aAlpha = G4Alpha::Alpha(); |
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281 | |
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282 | massIncident = aAlpha->GetPDGMass(); |
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283 | } |
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284 | else |
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285 | { |
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286 | G4cout << "we can treat only Proton or Alpha incident particles " << G4endl; |
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287 | massIncident =0.; |
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288 | } |
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289 | } |
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290 | |
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291 | const G4double zkshell= 0.3; |
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292 | |
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293 | G4double screenedzTarget = zTarget- zkshell; |
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294 | |
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295 | const G4double rydbergMeV= 13.6e-6; |
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296 | |
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297 | G4double tetaK = kBindingEnergy/(screenedzTarget*screenedzTarget*rydbergMeV); |
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298 | |
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299 | G4double velocity =(2./(tetaK*screenedzTarget))*std::pow(((energyIncident*electron_mass_c2)/(massIncident*rydbergMeV)),0.5); |
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300 | |
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301 | return velocity; |
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302 | } |
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303 | |
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