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24 | // ******************************************************************** |
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25 | // |
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26 | // $Id: G4PairProductionRelModel.cc,v 1.4 2010/10/26 09:06:04 vnivanch Exp $ |
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27 | // GEANT4 tag $Name: emstand-V09-03-24 $ |
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28 | // |
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29 | // ------------------------------------------------------------------- |
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30 | // |
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31 | // GEANT4 Class file |
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32 | // |
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33 | // |
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34 | // File name: G4PairProductionRelModel |
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35 | // |
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36 | // Author: Andreas Schaelicke |
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37 | // |
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38 | // Creation date: 02.04.2009 |
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39 | // |
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40 | // Modifications: |
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41 | // |
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42 | // Class Description: |
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43 | // |
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44 | // Main References: |
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45 | // J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 581. |
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46 | // S.Klein, Rev. Mod. Phys. 71 (1999) 1501. |
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47 | // T.Stanev et.al., Phys. Rev. D25 (1982) 1291. |
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48 | // M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media, Wiley, 1972. |
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49 | // |
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50 | // ------------------------------------------------------------------- |
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51 | // |
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52 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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53 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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54 | |
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55 | #include "G4PairProductionRelModel.hh" |
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56 | #include "G4Gamma.hh" |
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57 | #include "G4Electron.hh" |
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58 | #include "G4Positron.hh" |
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59 | |
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60 | #include "G4ParticleChangeForGamma.hh" |
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61 | #include "G4LossTableManager.hh" |
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62 | |
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63 | |
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64 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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65 | |
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66 | using namespace std; |
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67 | |
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68 | |
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69 | const G4double G4PairProductionRelModel::facFel = log(184.15); |
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70 | const G4double G4PairProductionRelModel::facFinel = log(1194.); // 1440. |
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71 | |
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72 | const G4double G4PairProductionRelModel::preS1 = 1./(184.15*184.15); |
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73 | const G4double G4PairProductionRelModel::logTwo = log(2.); |
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74 | |
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75 | const G4double G4PairProductionRelModel::xgi[]={ 0.0199, 0.1017, 0.2372, 0.4083, |
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76 | 0.5917, 0.7628, 0.8983, 0.9801 }; |
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77 | const G4double G4PairProductionRelModel::wgi[]={ 0.0506, 0.1112, 0.1569, 0.1813, |
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78 | 0.1813, 0.1569, 0.1112, 0.0506 }; |
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79 | const G4double G4PairProductionRelModel::Fel_light[] = {0., 5.31 , 4.79 , 4.74 , 4.71} ; |
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80 | const G4double G4PairProductionRelModel::Finel_light[] = {0., 6.144 , 5.621 , 5.805 , 5.924} ; |
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81 | |
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82 | |
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83 | |
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84 | G4PairProductionRelModel::G4PairProductionRelModel(const G4ParticleDefinition*, |
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85 | const G4String& nam) |
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86 | : G4VEmModel(nam), |
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87 | fLPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)*0.5), |
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88 | fLPMflag(true), |
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89 | lpmEnergy(0.), |
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90 | use_completescreening(false) |
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91 | { |
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92 | fParticleChange = 0; |
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93 | theGamma = G4Gamma::Gamma(); |
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94 | thePositron = G4Positron::Positron(); |
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95 | theElectron = G4Electron::Electron(); |
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96 | |
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97 | nist = G4NistManager::Instance(); |
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98 | |
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99 | currentZ = z13 = z23 = lnZ = Fel = Finel = fCoulomb = phiLPM = gLPM = xiLPM = 0; |
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100 | |
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101 | } |
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102 | |
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103 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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104 | |
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105 | G4PairProductionRelModel::~G4PairProductionRelModel() |
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106 | {} |
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107 | |
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108 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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109 | |
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110 | void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p, |
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111 | const G4DataVector& cuts) |
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112 | { |
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113 | if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); } |
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114 | InitialiseElementSelectors(p, cuts); |
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115 | } |
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116 | |
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117 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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118 | |
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119 | G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double totalEnergy, G4double Z) |
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120 | { |
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121 | G4double cross = 0.0; |
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122 | |
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123 | // number of intervals and integration step |
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124 | G4double vcut = electron_mass_c2/totalEnergy ; |
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125 | |
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126 | // limits by the screening variable |
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127 | G4double dmax = DeltaMax(); |
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128 | G4double dmin = min(DeltaMin(totalEnergy),dmax); |
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129 | G4double vcut1 = 0.5 - 0.5*sqrt(1. - dmin/dmax) ; |
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130 | vcut = max(vcut, vcut1); |
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131 | |
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132 | |
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133 | G4double vmax = 0.5; |
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134 | G4int n = 1; // needs optimisation |
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135 | |
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136 | G4double delta = (vmax - vcut)*totalEnergy/G4double(n); |
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137 | |
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138 | G4double e0 = vcut*totalEnergy; |
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139 | G4double xs; |
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140 | |
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141 | // simple integration |
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142 | for(G4int l=0; l<n; l++,e0 += delta) { |
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143 | for(G4int i=0; i<8; i++) { |
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144 | |
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145 | G4double eg = (e0 + xgi[i]*delta); |
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146 | if (fLPMflag && totalEnergy>100.*GeV) |
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147 | xs = ComputeRelDXSectionPerAtom(eg,totalEnergy,Z); |
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148 | else |
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149 | xs = ComputeDXSectionPerAtom(eg,totalEnergy,Z); |
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150 | cross += wgi[i]*xs; |
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151 | |
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152 | } |
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153 | } |
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154 | |
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155 | cross *= delta*2.; |
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156 | |
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157 | return cross; |
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158 | } |
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159 | |
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160 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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161 | |
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162 | G4double |
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163 | G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double eplusEnergy, |
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164 | G4double totalEnergy, |
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165 | G4double /*Z*/) |
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166 | { |
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167 | // most simple case - complete screening: |
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168 | |
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169 | // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k |
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170 | // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ] |
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171 | // y = E+/k |
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172 | G4double yp=eplusEnergy/totalEnergy; |
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173 | G4double ym=1.-yp; |
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174 | |
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175 | G4double cross = 0.; |
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176 | if (use_completescreening) |
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177 | cross = (yp*yp + ym*ym + 2./3.*ym*yp)*(Fel - fCoulomb) + 1./9.*yp*ym; |
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178 | else { |
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179 | G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym); |
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180 | cross = (yp*yp + ym*ym)*(0.25*Phi1(delta) - lnZ/3. - fCoulomb) |
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181 | + 2./3.*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb); |
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182 | } |
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183 | return cross/totalEnergy; |
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184 | |
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185 | } |
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186 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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187 | |
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188 | G4double |
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189 | G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double eplusEnergy, |
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190 | G4double totalEnergy, |
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191 | G4double /*Z*/) |
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192 | { |
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193 | // most simple case - complete screening: |
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194 | |
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195 | // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k |
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196 | // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ] |
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197 | // y = E+/k |
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198 | G4double yp=eplusEnergy/totalEnergy; |
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199 | G4double ym=1.-yp; |
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200 | |
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201 | CalcLPMFunctions(totalEnergy,eplusEnergy); // gamma |
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202 | |
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203 | G4double cross = 0.; |
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204 | if (use_completescreening) |
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205 | cross = xiLPM*(2./3.*phiLPM*(yp*yp + ym*ym) + gLPM)*(Fel - fCoulomb); |
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206 | else { |
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207 | G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym); |
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208 | cross = (1./3.*gLPM + 2./3.*phiLPM)*(yp*yp + ym*ym) |
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209 | *(0.25*Phi1(delta) - lnZ/3. - fCoulomb) |
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210 | + 2./3.*gLPM*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb); |
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211 | cross *= xiLPM; |
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212 | } |
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213 | return cross/totalEnergy; |
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214 | |
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215 | } |
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216 | |
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217 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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218 | |
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219 | void G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplus) |
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220 | { |
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221 | // *** calculate lpm variable s & sprime *** |
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222 | // Klein eqs. (78) & (79) |
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223 | G4double sprime = sqrt(0.125*k*lpmEnergy/(eplus*(k-eplus))); |
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224 | |
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225 | G4double s1 = preS1*z23; |
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226 | G4double logS1 = 2./3.*lnZ-2.*facFel; |
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227 | G4double logTS1 = logTwo+logS1; |
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228 | |
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229 | xiLPM = 2.; |
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230 | |
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231 | if (sprime>1) |
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232 | xiLPM = 1.; |
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233 | else if (sprime>sqrt(2.)*s1) { |
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234 | G4double h = log(sprime)/logTS1; |
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235 | xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1; |
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236 | } |
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237 | |
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238 | G4double s = sprime/sqrt(xiLPM); |
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239 | // G4cout<<"k="<<k<<" y="<<eplus/k<<G4endl; |
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240 | // G4cout<<"s="<<s<<G4endl; |
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241 | |
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242 | // *** calculate supression functions phi and G *** |
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243 | // Klein eqs. (77) |
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244 | G4double s2=s*s; |
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245 | G4double s3=s*s2; |
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246 | G4double s4=s2*s2; |
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247 | |
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248 | if (s<0.1) { |
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249 | // high suppression limit |
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250 | phiLPM = 6.*s - 18.84955592153876*s2 + 39.47841760435743*s3 |
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251 | - 57.69873135166053*s4; |
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252 | gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4; |
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253 | } |
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254 | else if (s<1.9516) { |
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255 | // intermediate suppression |
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256 | // using eq.77 approxim. valid s<2. |
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257 | phiLPM = 1.-exp(-6.*s*(1.+(3.-pi)*s) |
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258 | +s3/(0.623+0.795*s+0.658*s2)); |
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259 | if (s<0.415827397755) { |
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260 | // using eq.77 approxim. valid 0.07<s<2 |
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261 | G4double psiLPM = 1-exp(-4*s-8*s2/(1+3.936*s+4.97*s2-0.05*s3+7.50*s4)); |
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262 | gLPM = 3*psiLPM-2*phiLPM; |
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263 | } |
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264 | else { |
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265 | // using alternative parametrisiation |
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266 | G4double pre = -0.16072300849123999 + s*3.7550300067531581 + s2*-1.7981383069010097 |
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267 | + s3*0.67282686077812381 + s4*-0.1207722909879257; |
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268 | gLPM = tanh(pre); |
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269 | } |
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270 | } |
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271 | else { |
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272 | // low suppression limit valid s>2. |
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273 | phiLPM = 1. - 0.0119048/s4; |
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274 | gLPM = 1. - 0.0230655/s4; |
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275 | } |
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276 | |
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277 | // *** make sure suppression is smaller than 1 *** |
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278 | // *** caused by Migdal approximation in xi *** |
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279 | if (xiLPM*phiLPM>1. || s>0.57) xiLPM=1./phiLPM; |
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280 | } |
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281 | |
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282 | |
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283 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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284 | |
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285 | G4double |
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286 | G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*, |
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287 | G4double gammaEnergy, G4double Z, |
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288 | G4double, G4double, G4double) |
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289 | { |
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290 | // static const G4double gammaEnergyLimit = 1.5*MeV; |
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291 | G4double crossSection = 0.0 ; |
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292 | if ( Z < 0.9 ) return crossSection; |
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293 | if ( gammaEnergy <= 2.0*electron_mass_c2 ) return crossSection; |
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294 | |
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295 | SetCurrentElement(Z); |
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296 | // choose calculator according to parameters and switches |
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297 | // in the moment only one calculator: |
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298 | crossSection=ComputeXSectionPerAtom(gammaEnergy,Z); |
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299 | |
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300 | G4double xi = Finel/(Fel - fCoulomb); // inelastic contribution |
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301 | crossSection*=4.*Z*(Z+xi)*fine_structure_const*classic_electr_radius*classic_electr_radius; |
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302 | |
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303 | return crossSection; |
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304 | } |
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305 | |
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306 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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307 | |
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308 | void |
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309 | G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect, |
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310 | const G4MaterialCutsCouple* couple, |
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311 | const G4DynamicParticle* aDynamicGamma, |
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312 | G4double, |
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313 | G4double) |
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314 | // The secondaries e+e- energies are sampled using the Bethe - Heitler |
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315 | // cross sections with Coulomb correction. |
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316 | // A modified version of the random number techniques of Butcher & Messel |
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317 | // is used (Nuc Phys 20(1960),15). |
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318 | // |
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319 | // GEANT4 internal units. |
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320 | // |
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321 | // Note 1 : Effects due to the breakdown of the Born approximation at |
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322 | // low energy are ignored. |
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323 | // Note 2 : The differential cross section implicitly takes account of |
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324 | // pair creation in both nuclear and atomic electron fields. |
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325 | // However triplet prodution is not generated. |
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326 | { |
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327 | const G4Material* aMaterial = couple->GetMaterial(); |
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328 | |
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329 | G4double GammaEnergy = aDynamicGamma->GetKineticEnergy(); |
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330 | G4ParticleMomentum GammaDirection = aDynamicGamma->GetMomentumDirection(); |
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331 | |
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332 | G4double epsil ; |
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333 | G4double epsil0 = electron_mass_c2/GammaEnergy ; |
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334 | if(epsil0 > 1.0) return; |
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335 | |
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336 | // do it fast if GammaEnergy < 2. MeV |
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337 | static const G4double Egsmall=2.*MeV; |
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338 | |
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339 | // select randomly one element constituing the material |
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340 | const G4Element* anElement = SelectRandomAtom(aMaterial, theGamma, GammaEnergy); |
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341 | |
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342 | if (GammaEnergy < Egsmall) { |
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343 | |
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344 | epsil = epsil0 + (0.5-epsil0)*G4UniformRand(); |
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345 | |
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346 | } else { |
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347 | // now comes the case with GammaEnergy >= 2. MeV |
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348 | |
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349 | // Extract Coulomb factor for this Element |
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350 | G4double FZ = 8.*(anElement->GetIonisation()->GetlogZ3()); |
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351 | if (GammaEnergy > 50.*MeV) FZ += 8.*(anElement->GetfCoulomb()); |
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352 | |
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353 | // limits of the screening variable |
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354 | G4double screenfac = 136.*epsil0/(anElement->GetIonisation()->GetZ3()); |
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355 | G4double screenmax = exp ((42.24 - FZ)/8.368) - 0.952 ; |
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356 | G4double screenmin = min(4.*screenfac,screenmax); |
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357 | |
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358 | // limits of the energy sampling |
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359 | G4double epsil1 = 0.5 - 0.5*sqrt(1. - screenmin/screenmax) ; |
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360 | G4double epsilmin = max(epsil0,epsil1) , epsilrange = 0.5 - epsilmin; |
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361 | |
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362 | // |
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363 | // sample the energy rate of the created electron (or positron) |
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364 | // |
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365 | //G4double epsil, screenvar, greject ; |
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366 | G4double screenvar, greject ; |
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367 | |
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368 | G4double F10 = ScreenFunction1(screenmin) - FZ; |
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369 | G4double F20 = ScreenFunction2(screenmin) - FZ; |
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370 | G4double NormF1 = max(F10*epsilrange*epsilrange,0.); |
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371 | G4double NormF2 = max(1.5*F20,0.); |
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372 | |
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373 | do { |
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374 | if ( NormF1/(NormF1+NormF2) > G4UniformRand() ) { |
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375 | epsil = 0.5 - epsilrange*pow(G4UniformRand(), 0.333333); |
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376 | screenvar = screenfac/(epsil*(1-epsil)); |
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377 | if (fLPMflag && GammaEnergy>100.*GeV) { |
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378 | CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil); |
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379 | greject = xiLPM*((gLPM+2.*phiLPM)*Phi1(screenvar) - gLPM*Phi2(screenvar) - phiLPM*FZ)/F10; |
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380 | } |
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381 | else { |
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382 | greject = (ScreenFunction1(screenvar) - FZ)/F10; |
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383 | } |
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384 | |
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385 | } else { |
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386 | epsil = epsilmin + epsilrange*G4UniformRand(); |
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387 | screenvar = screenfac/(epsil*(1-epsil)); |
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388 | if (fLPMflag && GammaEnergy>100.*GeV) { |
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389 | CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil); |
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390 | greject = xiLPM*((0.5*gLPM+phiLPM)*Phi1(screenvar) + 0.5*gLPM*Phi2(screenvar) - 0.5*(gLPM+phiLPM)*FZ)/F20; |
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391 | } |
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392 | else { |
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393 | greject = (ScreenFunction2(screenvar) - FZ)/F20; |
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394 | } |
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395 | } |
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396 | |
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397 | } while( greject < G4UniformRand() ); |
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398 | |
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399 | } // end of epsil sampling |
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400 | |
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401 | // |
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402 | // fixe charges randomly |
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403 | // |
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404 | |
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405 | G4double ElectTotEnergy, PositTotEnergy; |
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406 | if (G4UniformRand() > 0.5) { |
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407 | |
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408 | ElectTotEnergy = (1.-epsil)*GammaEnergy; |
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409 | PositTotEnergy = epsil*GammaEnergy; |
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410 | |
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411 | } else { |
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412 | |
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413 | PositTotEnergy = (1.-epsil)*GammaEnergy; |
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414 | ElectTotEnergy = epsil*GammaEnergy; |
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415 | } |
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416 | |
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417 | // |
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418 | // scattered electron (positron) angles. ( Z - axis along the parent photon) |
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419 | // |
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420 | // universal distribution suggested by L. Urban |
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421 | // (Geant3 manual (1993) Phys211), |
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422 | // derived from Tsai distribution (Rev Mod Phys 49,421(1977)) |
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423 | |
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424 | G4double u; |
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425 | const G4double a1 = 0.625 , a2 = 3.*a1 , d = 27. ; |
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426 | |
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427 | if (9./(9.+d) >G4UniformRand()) u= - log(G4UniformRand()*G4UniformRand())/a1; |
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428 | else u= - log(G4UniformRand()*G4UniformRand())/a2; |
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429 | |
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430 | G4double TetEl = u*electron_mass_c2/ElectTotEnergy; |
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431 | G4double TetPo = u*electron_mass_c2/PositTotEnergy; |
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432 | G4double Phi = twopi * G4UniformRand(); |
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433 | G4double dxEl= sin(TetEl)*cos(Phi),dyEl= sin(TetEl)*sin(Phi),dzEl=cos(TetEl); |
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434 | G4double dxPo=-sin(TetPo)*cos(Phi),dyPo=-sin(TetPo)*sin(Phi),dzPo=cos(TetPo); |
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435 | |
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436 | // |
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437 | // kinematic of the created pair |
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438 | // |
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439 | // the electron and positron are assumed to have a symetric |
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440 | // angular distribution with respect to the Z axis along the parent photon. |
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441 | |
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442 | G4double ElectKineEnergy = max(0.,ElectTotEnergy - electron_mass_c2); |
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443 | |
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444 | G4ThreeVector ElectDirection (dxEl, dyEl, dzEl); |
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445 | ElectDirection.rotateUz(GammaDirection); |
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446 | |
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447 | // create G4DynamicParticle object for the particle1 |
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448 | G4DynamicParticle* aParticle1= new G4DynamicParticle( |
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449 | theElectron,ElectDirection,ElectKineEnergy); |
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450 | |
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451 | // the e+ is always created (even with Ekine=0) for further annihilation. |
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452 | |
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453 | G4double PositKineEnergy = max(0.,PositTotEnergy - electron_mass_c2); |
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454 | |
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455 | G4ThreeVector PositDirection (dxPo, dyPo, dzPo); |
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456 | PositDirection.rotateUz(GammaDirection); |
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457 | |
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458 | // create G4DynamicParticle object for the particle2 |
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459 | G4DynamicParticle* aParticle2= new G4DynamicParticle( |
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460 | thePositron,PositDirection,PositKineEnergy); |
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461 | |
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462 | // Fill output vector |
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463 | fvect->push_back(aParticle1); |
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464 | fvect->push_back(aParticle2); |
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465 | |
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466 | // kill incident photon |
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467 | fParticleChange->SetProposedKineticEnergy(0.); |
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468 | fParticleChange->ProposeTrackStatus(fStopAndKill); |
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469 | } |
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470 | |
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471 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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472 | |
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473 | |
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474 | void G4PairProductionRelModel::SetupForMaterial(const G4ParticleDefinition*, |
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475 | const G4Material* mat, G4double) |
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476 | { |
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477 | lpmEnergy = mat->GetRadlen()*fLPMconstant; |
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478 | // G4cout<<" lpmEnergy="<<lpmEnergy<<G4endl; |
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479 | } |
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480 | |
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481 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo.... |
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