1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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15 | // * use. Please see the license in the file LICENSE and URL above * |
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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: G4PolarizedBhabhaCrossSection.cc,v 1.5 2007/11/01 17:32:34 schaelic Exp $ |
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27 | // GEANT4 tag $Name: geant4-09-02 $ |
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28 | // ------------------------------------------------------------------- |
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29 | // |
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30 | // GEANT4 Class file |
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31 | // |
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32 | // |
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33 | // File name: G4PolarizedBhabhaCrossSection |
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34 | // |
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35 | // Author: Andreas Schaelicke |
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36 | // |
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37 | // Creation date: 12.01.2006 |
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38 | // |
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39 | // Modifications: |
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40 | // 16-01-06 included cross section as calculated by P.Starovoitov |
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41 | // 24-08-06 bugfix in total cross section (A. Schaelicke) |
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42 | // 07-11-06 modify reference system for polarisation vectors |
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43 | // (A. Schaelicke & P.Starovoitov) |
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44 | // |
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45 | // Class Description: |
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46 | // * calculates the differential cross section |
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47 | // incomming positron Kpl(along positive z direction) scatters at |
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48 | // an electron Kmn at rest |
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49 | // * phi denotes the angle between the scattering plane (defined by the |
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50 | // outgoing electron) and X-axis |
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51 | // * all stokes vectors refer to spins in the Global System (X,Y,Z) |
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52 | // |
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53 | |
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54 | #include "G4PolarizedBhabhaCrossSection.hh" |
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55 | |
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56 | G4PolarizedBhabhaCrossSection::G4PolarizedBhabhaCrossSection() |
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57 | { |
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58 | } |
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59 | G4PolarizedBhabhaCrossSection::~G4PolarizedBhabhaCrossSection() |
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60 | { |
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61 | } |
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62 | void G4PolarizedBhabhaCrossSection::Initialize( |
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63 | G4double e, |
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64 | G4double gamma, |
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65 | G4double /*phi*/, |
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66 | const G4StokesVector & pol0, |
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67 | const G4StokesVector & pol1, |
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68 | G4int flag) |
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69 | { |
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70 | SetXmax(1.); |
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71 | |
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72 | G4double re2 = classic_electr_radius * classic_electr_radius; |
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73 | G4double gamma2 = gamma*gamma; |
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74 | G4double gamma3 = gamma2*gamma; |
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75 | G4double gmo = (gamma - 1.); |
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76 | G4double gmo2 = (gamma - 1.)*(gamma - 1.); |
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77 | G4double gmo3 = gmo2*(gamma - 1.); |
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78 | G4double gpo = (gamma + 1.); |
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79 | G4double gpo2 = (gamma + 1.)*(gamma + 1.); |
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80 | G4double gpo3 = gpo2*(gamma + 1.); |
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81 | G4double gpo12 = std::sqrt(gpo); |
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82 | G4double gpo32 = gpo*gpo12; |
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83 | G4double gpo52 = gpo2*gpo12; |
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84 | |
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85 | G4double pref = re2/(gamma - 1.0); |
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86 | G4double sqrttwo=std::sqrt(2.); |
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87 | G4double d = std::sqrt(1./e - 1.); |
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88 | G4double e2 = e*e; |
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89 | G4double e3 = e2*e; |
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90 | |
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91 | // *** new *** |
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92 | G4double gmo12 = std::sqrt(gmo); |
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93 | G4double gmo32 = gmo*gmo12; |
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94 | G4double egmp32 = std::pow(e*(2 + e*gmo)*gpo,(3./2.)); |
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95 | G4double e32 = e*std::sqrt(e); |
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96 | |
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97 | G4bool polarized=(!pol0.IsZero())||(!pol1.IsZero()); |
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98 | |
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99 | if (flag==0) polarized=false; |
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100 | // Unpolarised part of XS |
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101 | // *AS* UnpME . OK |
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102 | phi0 = 0.; |
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103 | phi0+= e2*gmo3/gpo3; |
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104 | phi0+= -2.*e*gamma*gmo2/gpo3; |
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105 | phi0+= (3.*gamma2 + 6.*gamma + 4.)*gmo/gpo3; |
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106 | phi0+= -(2.*gamma2 + 4.*gamma + 1.)/(e*gpo2); |
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107 | phi0+= gamma2/(e2*(gamma2 - 1.)); |
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108 | phi0*=0.25; |
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109 | // Initial state polarisarion dependence |
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110 | if (polarized) { |
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111 | // G4cout<<"Polarized differential Bhabha cross section"<<G4endl; |
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112 | // G4cout<<"Initial state polarisation contributions"<<G4endl; |
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113 | // G4cout<<"Diagonal Matrix Elements"<<G4endl; |
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114 | // *** new *** |
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115 | G4double xx = -((e*gmo - gamma)*(-1 - gamma + e*(e*gmo - gamma)*(3 + gamma)))/(4*e*gpo3); |
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116 | G4double yy = (e3*gmo3 - 2*e2*gmo2*gamma - gpo*(1 + 2*gamma) + e*(-2 + gamma2 + gamma3))/(4*e*gpo3); |
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117 | G4double zz = ((e*gmo - gamma)*(e2*gmo*(3 + gamma) - e*gamma*(3 + gamma) + gpo*(1 + 2*gamma)))/(4*e*gpo3); |
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118 | // *** |
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119 | |
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120 | phi0 += xx*pol0.x()*pol1.x() + yy*pol0.y()*pol1.y() + zz*pol0.z()*pol1.z(); |
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121 | |
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122 | { |
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123 | G4double xy = 0; |
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124 | G4double xz = (d*(e*gmo - gamma)*(-1 + 2*e*gmo - gamma))/(2*sqrttwo*gpo52); |
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125 | G4double yx = 0; |
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126 | G4double yz = 0; |
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127 | G4double zx = xz; |
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128 | G4double zy = 0; |
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129 | // G4cout<<"Non-diagonal Matrix Elements"<<G4endl; |
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130 | phi0+=yx*pol0.y()*pol1.x() + xy*pol0.x()*pol1.y(); |
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131 | phi0+=zx*pol0.z()*pol1.x() + xz*pol0.x()*pol1.z(); |
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132 | phi0+=zy*pol0.z()*pol1.y() + yz*pol0.y()*pol1.z(); |
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133 | } |
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134 | } |
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135 | // Final state polarisarion dependence |
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136 | phi2=G4ThreeVector(); |
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137 | phi3=G4ThreeVector(); |
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138 | |
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139 | if (flag>=1) { |
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140 | // |
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141 | // Final Positron Ppl |
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142 | // |
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143 | // initial positron Kpl |
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144 | if (!pol0.IsZero()) { |
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145 | |
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146 | G4double xxPplKpl = -((-1 + e)*(e*gmo - gamma)*(-(gamma*gpo) + e*(-2 + gamma + gamma2)))/ |
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147 | (4*e2*gpo*std::sqrt(gmo*gpo*(-1 + e + gamma - e*gamma)* (1 + e + gamma - e*gamma))); |
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148 | G4double xyPplKpl = 0; |
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149 | G4double xzPplKpl = ((e*gmo - gamma)*(-1 - gamma + e*gmo*(1 + 2*gamma)))/ |
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150 | (2*sqrttwo*e32*gmo*gpo2*std::sqrt(1 + e + gamma - e*gamma)); |
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151 | G4double yxPplKpl = 0; |
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152 | G4double yyPplKpl = (gamma2*gpo + e2*gmo2*(3 + gamma) - |
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153 | e*gmo*(1 + 2*gamma*(2 + gamma)))/(4*e2*gmo*gpo2); |
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154 | G4double yzPplKpl = 0; |
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155 | G4double zxPplKpl = ((e*gmo - gamma)*(1 + e*(-1 + 2*e*gmo - 2*gamma)*gmo + gamma))/ |
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156 | (2*sqrttwo*e*gmo*gpo2*std::sqrt(e*(1 + e + gamma - e*gamma))); |
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157 | G4double zyPplKpl = 0; |
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158 | G4double zzPplKpl = -((e*gmo - gamma)*std::sqrt((1 - e)/(e - e*gamma2 + gpo2))* |
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159 | (2*e2*gmo2 + gamma + gamma2 - e*(-2 + gamma + gamma2)))/ |
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160 | (4*e2*(-1 + gamma2)); |
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161 | |
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162 | phi2[0] += xxPplKpl*pol0.x() + xyPplKpl*pol0.y() + xzPplKpl*pol0.z(); |
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163 | phi2[1] += yxPplKpl*pol0.x() + yyPplKpl*pol0.y() + yzPplKpl*pol0.z(); |
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164 | phi2[2] += zxPplKpl*pol0.x() + zyPplKpl*pol0.y() + zzPplKpl*pol0.z(); |
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165 | } |
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166 | // initial electron Kmn |
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167 | if (!pol1.IsZero()) { |
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168 | G4double xxPplKmn = ((-1 + e)*(e*(-2 + gamma)*gmo + gamma))/(4*e*gpo32*std::sqrt(1 + e2*gmo + gamma - 2*e*gamma)); |
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169 | G4double xyPplKmn = 0; |
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170 | G4double xzPplKmn = (-1 + e*gmo + gmo*gamma)/(2*sqrttwo*gpo2* std::sqrt(e*(1 + e + gamma - e*gamma))); |
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171 | G4double yxPplKmn = 0; |
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172 | G4double yyPplKmn = (-1 - 2*gamma + e*gmo*(3 + gamma))/(4*e*gpo2); |
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173 | G4double yzPplKmn = 0; |
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174 | G4double zxPplKmn = (1 + 2*e2*gmo2 + gamma + gamma2 + e*(1 + (3 - 4*gamma)*gamma))/ |
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175 | (2*sqrttwo*gpo2*std::sqrt(e*(1 + e + gamma - e*gamma))); |
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176 | G4double zyPplKmn = 0; |
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177 | G4double zzPplKmn = -(std::sqrt((1 - e)/(e - e*gamma2 + gpo2))* |
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178 | (2*e2*gmo2 + gamma + 2*gamma2 + e*(2 + gamma - 3*gamma2)))/(4*e*gpo); |
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179 | |
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180 | phi2[0] += xxPplKmn*pol1.x() + xyPplKmn*pol1.y() + xzPplKmn*pol1.z(); |
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181 | phi2[1] += yxPplKmn*pol1.x() + yyPplKmn*pol1.y() + yzPplKmn*pol1.z(); |
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182 | phi2[2] += zxPplKmn*pol1.x() + zyPplKmn*pol1.y() + zzPplKmn*pol1.z(); |
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183 | } |
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184 | // |
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185 | // Final Electron Pmn |
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186 | // |
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187 | // initial positron Kpl |
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188 | if (!pol0.IsZero()) { |
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189 | G4double xxPmnKpl = ((-1 + e*gmo)*(2 + gamma))/(4*gpo* std::sqrt(e*(2 + e*gmo)*gpo)); |
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190 | G4double xyPmnKpl = 0; |
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191 | G4double xzPmnKpl = (std::sqrt((-1 + e)/(-2 + e - e*gamma))* |
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192 | (e + gamma + e*gamma - 2*(-1 + e)*gamma2))/(2*sqrttwo*e*gpo2); |
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193 | G4double yxPmnKpl = 0; |
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194 | G4double yyPmnKpl = (-1 - 2*gamma + e*gmo*(3 + gamma))/(4*e*gpo2); |
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195 | G4double yzPmnKpl = 0; |
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196 | G4double zxPmnKpl = -((-1 + e)*(1 + 2*e*gmo)*(e*gmo - gamma))/ |
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197 | (2*sqrttwo*e*std::sqrt(-((-1 + e)*(2 + e*gmo)))*gpo2); |
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198 | G4double zyPmnKpl = 0; |
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199 | G4double zzPmnKpl = (-2 + 2*e2*gmo2 + gamma*(-1 + 2*gamma) + |
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200 | e*(-2 + (5 - 3*gamma)*gamma))/(4*std::sqrt(e*(2 + e*gmo))* gpo32); |
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201 | |
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202 | phi3[0] += xxPmnKpl*pol0.x() + xyPmnKpl*pol0.y() + xzPmnKpl*pol0.z(); |
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203 | phi3[1] += yxPmnKpl*pol0.x() + yyPmnKpl*pol0.y() + yzPmnKpl*pol0.z(); |
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204 | phi3[2] += zxPmnKpl*pol0.x() + zyPmnKpl*pol0.y() + zzPmnKpl*pol0.z(); |
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205 | } |
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206 | // initial electron Kmn |
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207 | if (!pol1.IsZero()) { |
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208 | G4double xxPmnKmn = -((2 + e*gmo)*(-1 + e*gmo - gamma)*(e*gmo - gamma)* |
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209 | (-2 + gamma))/(4*gmo*egmp32); |
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210 | G4double xyPmnKmn = 0; |
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211 | G4double xzPmnKmn = ((e*gmo - gamma)* |
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212 | std::sqrt((-1 + e + gamma - e*gamma)/(2 + e*gmo))* |
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213 | (e + gamma - e*gamma + gamma2))/ |
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214 | (2*sqrttwo*e2*gmo32*gpo2); |
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215 | G4double yxPmnKmn = 0; |
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216 | G4double yyPmnKmn = (gamma2*gpo + e2*gmo2*(3 + gamma) - |
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217 | e*gmo*(1 + 2*gamma*(2 + gamma)))/(4*e2*gmo*gpo2); |
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218 | G4double yzPmnKmn = 0; |
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219 | G4double zxPmnKmn = -((-1 + e)*(e*gmo - gamma)*(e*gmo + 2*e2*gmo2 - gamma*gpo))/ |
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220 | (2*sqrttwo*e2*std::sqrt(-((-1 + e)*(2 + e*gmo)))* gmo*gpo2); |
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221 | G4double zyPmnKmn = 0; |
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222 | G4double zzPmnKmn = ((e*gmo - gamma)*std::sqrt(e/((2 + e*gmo)*gpo))* |
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223 | (-(e*(-2 + gamma)*gmo) + 2*e2*gmo2 + (-2 + gamma)*gpo))/(4*e2*(-1 + gamma2)); |
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224 | |
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225 | phi3[0] += xxPmnKmn*pol1.x() + xyPmnKmn*pol1.y() + xzPmnKmn*pol1.z(); |
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226 | phi3[1] += yxPmnKmn*pol1.x() + yyPmnKmn*pol1.y() + yzPmnKmn*pol1.z(); |
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227 | phi3[2] += zxPmnKmn*pol1.x() + zyPmnKmn*pol1.y() + zzPmnKmn*pol1.z(); |
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228 | } |
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229 | } |
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230 | phi0 *= pref; |
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231 | phi2 *= pref; |
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232 | phi3 *= pref; |
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233 | |
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234 | } |
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235 | |
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236 | G4double G4PolarizedBhabhaCrossSection::XSection(const G4StokesVector & pol2, |
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237 | const G4StokesVector & pol3) |
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238 | { |
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239 | G4double xs=0.; |
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240 | xs+=phi0; |
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241 | |
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242 | G4bool polarized=(!pol2.IsZero())||(!pol3.IsZero()); |
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243 | if (polarized) { |
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244 | xs+=phi2*pol2 + phi3*pol3; |
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245 | } |
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246 | return xs; |
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247 | } |
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248 | |
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249 | G4double G4PolarizedBhabhaCrossSection::TotalXSection( |
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250 | G4double xmin, G4double xmax, G4double gamma, |
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251 | const G4StokesVector & pol0,const G4StokesVector & pol1) |
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252 | { |
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253 | G4double xs=0.; |
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254 | |
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255 | G4double x=xmin; |
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256 | |
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257 | if (xmax != 1.) G4cout<<" warning xmax expected to be 1 but is "<<xmax<< G4endl; |
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258 | |
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259 | // re -> electron radius^2; |
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260 | G4double re2 = classic_electr_radius * classic_electr_radius; |
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261 | G4double gamma2=gamma*gamma; |
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262 | G4double gmo2 = (gamma - 1.)*(gamma - 1.); |
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263 | G4double gpo2 = (gamma + 1.)*(gamma + 1.); |
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264 | G4double gpo3 = gpo2*(gamma + 1.); |
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265 | G4double logMEM = std::log(x); |
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266 | G4double pref = twopi*re2/(gamma - 1.0); |
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267 | // unpolarise XS |
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268 | G4double sigma0 = 0.; |
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269 | sigma0 += -gmo2*(gamma - 1.)*x*x*x/3. + gmo2*gamma*x*x; |
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270 | sigma0 += -(gamma - 1.)*(3.*gamma*(gamma + 2.) +4.)*x; |
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271 | sigma0 += (gamma*(gamma*(gamma*(4.*gamma - 1.) - 21.) - 7.)+13.)/(3.*(gamma - 1.)); |
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272 | sigma0 /= gpo3; |
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273 | sigma0 += logMEM*(2. - 1./gpo2); |
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274 | sigma0 += gamma2/((gamma2 - 1.)*x); |
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275 | // longitudinal part |
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276 | G4double sigma2=0.; |
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277 | sigma2 += logMEM*gamma*(gamma + 1.)*(2.*gamma + 1.); |
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278 | sigma2 += gamma*(7.*gamma*(gamma + 1.) - 2.)/3.; |
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279 | sigma2 += -(3.*gamma + 1.)*(gamma2 + gamma - 1.)*x; |
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280 | sigma2 += (gamma - 1.)*gamma*(gamma + 3.)*x*x; |
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281 | sigma2 += -gmo2*(gamma + 3.)*x*x*x/3.; |
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282 | sigma2 /= gpo3; |
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283 | // transverse part |
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284 | G4double sigma3=0.; |
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285 | sigma3 += 0.5*(gamma + 1.)*(3.*gamma + 1.)*logMEM; |
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286 | sigma3 += (gamma*(5.*gamma - 4.) - 13.)/6.; |
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287 | sigma3 += 0.5*(gamma2 + 3.)*x; |
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288 | sigma3 += - 2.*(gamma - 1.)*gamma*x*x; // *AS* changed sign |
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289 | sigma3 += 2.*gmo2*x*x*x/3.; |
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290 | sigma3 /= gpo3; |
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291 | // total cross section |
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292 | xs+=pref*(sigma0 + sigma2*pol0.z()*pol1.z() + sigma3*(pol0.x()*pol1.x()+pol0.y()*pol1.y())); |
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293 | |
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294 | return xs; |
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295 | } |
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296 | |
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297 | |
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298 | G4StokesVector G4PolarizedBhabhaCrossSection::GetPol2() |
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299 | { |
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300 | // Note, mean polarization can not contain correlation |
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301 | // effects. |
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302 | return 1./phi0 * phi2; |
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303 | } |
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304 | G4StokesVector G4PolarizedBhabhaCrossSection::GetPol3() |
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305 | { |
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306 | // Note, mean polarization can not contain correlation |
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307 | // effects. |
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308 | return 1./phi0 * phi3; |
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309 | } |
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