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2 | // ******************************************************************** |
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15 | // * use. Please see the license in the file LICENSE and URL above * |
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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: G4PolarizedMollerCrossSection.cc,v 1.5 2007/11/01 17:32:34 schaelic Exp $ |
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27 | // GEANT4 tag $Name: geant4-09-03 $ |
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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: G4PolarizedMollerCrossSection |
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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 | // |
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42 | // Class Description: |
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43 | // * calculates the differential cross section |
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44 | // incomming electron K1(along positive z direction) scatters at an electron K2 at rest |
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45 | // * phi denotes the angle between the scattering plane (defined by the |
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46 | // outgoing electron) and X-axis |
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47 | // * all stokes vectors refer to spins in the Global System (X,Y,Z) |
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48 | // |
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49 | |
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50 | #include "G4PolarizedMollerCrossSection.hh" |
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51 | |
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52 | G4PolarizedMollerCrossSection::G4PolarizedMollerCrossSection() |
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53 | { |
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54 | SetXmax(.5); |
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55 | } |
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56 | G4PolarizedMollerCrossSection::~G4PolarizedMollerCrossSection() {} |
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57 | void G4PolarizedMollerCrossSection::Initialize( |
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58 | G4double e, |
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59 | G4double gamma, |
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60 | G4double /*phi*/, |
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61 | const G4StokesVector & pol0, |
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62 | const G4StokesVector & pol1, |
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63 | G4int flag) |
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64 | { |
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65 | G4double re2 = classic_electr_radius * classic_electr_radius; |
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66 | G4double gamma2=gamma*gamma; |
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67 | G4double gmo = (gamma - 1.); |
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68 | G4double gmo2 = (gamma - 1.)*(gamma - 1.); |
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69 | G4double gpo = (gamma + 1.); |
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70 | G4double pref = gamma2*re2/(gmo2*(gamma + 1.0)); |
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71 | G4double sqrttwo=std::sqrt(2.); |
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72 | G4double f = (-1. + e); |
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73 | G4double e2 = e*e; |
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74 | G4double f2 = f*f; |
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75 | // G4double w = e*(1. - e); |
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76 | |
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77 | G4bool polarized=(!pol0.IsZero())||(!pol1.IsZero()); |
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78 | |
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79 | if (flag==0) polarized=false; |
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80 | // Unpolarised part of XS |
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81 | phi0 = 0.; |
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82 | phi0+= gmo2/gamma2; |
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83 | phi0+= ((1. - 2.*gamma)/gamma2)*(1./e + 1./(1.-e)); |
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84 | phi0+= 1./(e*e) + 1./((1. - e)*(1. - e)); |
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85 | phi0*=0.25; |
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86 | // Initial state polarisarion dependence |
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87 | if (polarized) { |
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88 | G4double usephi=1.; |
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89 | if (flag<=1) usephi=0.; |
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90 | // G4cout<<"Polarized differential moller cross section"<<G4endl; |
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91 | // G4cout<<"Initial state polarisation contributions"<<G4endl; |
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92 | // G4cout<<"Diagonal Matrix Elements"<<G4endl; |
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93 | G4double xx = (gamma - f*e*gmo*(3 + gamma))/(4*f*e*gamma2); |
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94 | G4double yy = (-1 + f*e*gmo2 + 2*gamma)/(4*f*e*gamma2); |
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95 | G4double zz = (-(e*gmo*(3 + gamma)) + e2*gmo*(3 + gamma) + |
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96 | gamma*(-1 + 2*gamma))/(4*f*e*gamma2); |
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97 | |
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98 | phi0 += xx*pol0.x()*pol1.x() + yy*pol0.y()*pol1.y() + zz*pol0.z()*pol1.z(); |
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99 | |
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100 | if (usephi==1.) { |
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101 | // G4cout<<"Non-diagonal Matrix Elements"<<G4endl; |
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102 | G4double xy = 0; |
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103 | G4double xz = -((-1 + 2*e)*gmo)/(2*sqrttwo*gamma2* |
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104 | std::sqrt(-((f*e)/gpo))); |
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105 | G4double yx = 0; |
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106 | G4double yz = 0; |
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107 | G4double zx = -((-1 + 2*e)*gmo)/(2*sqrttwo*gamma2* |
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108 | std::sqrt(-((f*e)/gpo))); |
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109 | G4double zy = 0; |
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110 | phi0+=yx*pol0.y()*pol1.x() + xy*pol0.x()*pol1.y(); |
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111 | phi0+=zx*pol0.z()*pol1.x() + xz*pol0.x()*pol1.z(); |
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112 | phi0+=zy*pol0.z()*pol1.y() + yz*pol0.y()*pol1.z(); |
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113 | } |
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114 | } |
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115 | // Final state polarisarion dependence |
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116 | phi2=G4ThreeVector(); |
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117 | phi3=G4ThreeVector(); |
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118 | |
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119 | if (flag>=1) { |
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120 | // |
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121 | // Final Electron P1 |
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122 | // |
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123 | |
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124 | // initial electron K1 |
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125 | if (!pol0.IsZero()) { |
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126 | G4double xxP1K1 = (std::sqrt(gpo/(1 + e2*gmo + gamma - 2*e*gamma))* |
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127 | (gamma - e*gpo))/(4*e2*gamma); |
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128 | G4double xyP1K1 = 0; |
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129 | G4double xzP1K1 = (-1 + 2*e*gamma)/(2*sqrttwo*f*gamma* |
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130 | std::sqrt(e*e2*(1 + e + gamma - e*gamma))); |
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131 | G4double yxP1K1 = 0; |
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132 | G4double yyP1K1 = (-gamma2 + e*(-1 + gamma*(2 + gamma)))/(4*f*e2*gamma2); |
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133 | G4double yzP1K1 = 0; |
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134 | G4double zxP1K1 = (1 + 2*e2*gmo - 2*e*gamma)/(2*sqrttwo*f*e*gamma* |
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135 | std::sqrt(e*(1 + e + gamma - e*gamma))); |
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136 | G4double zyP1K1 = 0; |
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137 | G4double zzP1K1 = (-gamma + e*(1 - 2*e*gmo + gamma))/(4*f*e2*gamma* |
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138 | std::sqrt(1 - (2*e)/(f*gpo))); |
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139 | phi2[0] += xxP1K1*pol0.x() + xyP1K1*pol0.y() + xzP1K1*pol0.z(); |
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140 | phi2[1] += yxP1K1*pol0.x() + yyP1K1*pol0.y() + yzP1K1*pol0.z(); |
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141 | phi2[2] += zxP1K1*pol0.x() + zyP1K1*pol0.y() + zzP1K1*pol0.z(); |
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142 | } |
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143 | // initial electron K2 |
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144 | if (!pol1.IsZero()) { |
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145 | G4double xxP1K2 = ((1 + e*(-3 + gamma))*std::sqrt(gpo/(1 + e2*gmo + gamma - |
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146 | 2*e*gamma)))/(4*f*e*gamma); |
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147 | G4double xyP1K2 = 0; |
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148 | G4double xzP1K2 = (-2 + 2*e + gamma)/(2*sqrttwo*f2*gamma* |
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149 | std::sqrt(e*(1 + e + gamma - e*gamma))); |
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150 | G4double yxP1K2 = 0; |
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151 | G4double yyP1K2 = (1 - 2*gamma + e*(-1 + gamma*(2 + gamma)))/(4*f2*e*gamma2); |
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152 | G4double yzP1K2 = 0; |
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153 | G4double zxP1K2 = (2*e*(1 + e*gmo - 2*gamma) + gamma)/(2*sqrttwo*f2*gamma* |
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154 | std::sqrt(e*(1 + e + gamma - e*gamma))); |
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155 | G4double zyP1K2 = 0; |
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156 | G4double zzP1K2 = (1 - 2*gamma + e*(-1 - 2*e*gmo + 3*gamma))/ |
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157 | (4*f2*e*gamma*std::sqrt(1 - (2*e)/(f*gpo))); |
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158 | phi2[0] += xxP1K2*pol1.x() + xyP1K2*pol1.y() + xzP1K2*pol1.z(); |
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159 | phi2[1] += yxP1K2*pol1.x() + yyP1K2*pol1.y() + yzP1K2*pol1.z(); |
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160 | phi2[2] += zxP1K2*pol1.x() + zyP1K2*pol1.y() + zzP1K2*pol1.z(); |
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161 | } |
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162 | // |
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163 | // Final Electron P2 |
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164 | // |
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165 | |
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166 | // initial electron K1 |
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167 | if (!pol0.IsZero()) { |
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168 | |
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169 | |
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170 | G4double xxP2K1 = (-1 + e + e*gamma)/(4*f2*gamma* |
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171 | std::sqrt((e*(2 + e*gmo))/gpo)); |
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172 | G4double xyP2K1 = 0; |
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173 | G4double xzP2K1 = -((1 + 2*f*gamma)*std::sqrt(f/(-2 + e - e*gamma)))/ |
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174 | (2*sqrttwo*f2*e*gamma); |
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175 | G4double yxP2K1 = 0; |
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176 | G4double yyP2K1 = (1 - 2*gamma + e*(-1 + gamma*(2 + gamma)))/(4*f2*e*gamma2); |
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177 | G4double yzP2K1 = 0; |
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178 | G4double zxP2K1 = (1 + 2*e*(-2 + e + gamma - e*gamma))/(2*sqrttwo*f*e* |
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179 | std::sqrt(-(f*(2 + e*gmo)))*gamma); |
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180 | G4double zyP2K1 = 0; |
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181 | G4double zzP2K1 = (std::sqrt((e*gpo)/(2 + e*gmo))* |
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182 | (-3 + e*(5 + 2*e*gmo - 3*gamma) + 2*gamma))/(4*f2*e*gamma); |
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183 | |
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184 | phi3[0] += xxP2K1*pol0.x() + xyP2K1*pol0.y() + xzP2K1*pol0.z(); |
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185 | phi3[1] += yxP2K1*pol0.x() + yyP2K1*pol0.y() + yzP2K1*pol0.z(); |
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186 | phi3[2] += zxP2K1*pol0.x() + zyP2K1*pol0.y() + zzP2K1*pol0.z(); |
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187 | } |
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188 | // initial electron K2 |
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189 | if (!pol1.IsZero()) { |
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190 | |
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191 | G4double xxP2K2 = (-2 - e*(-3 + gamma) + gamma)/ |
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192 | (4*f*e*gamma* std::sqrt((e*(2 + e*gmo))/gpo)); |
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193 | G4double xyP2K2 = 0; |
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194 | G4double xzP2K2 = ((-2*e + gamma)*std::sqrt(f/(-2 + e - e*gamma)))/ |
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195 | (2*sqrttwo*f*e2*gamma); |
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196 | G4double yxP2K2 = 0; |
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197 | G4double yyP2K2 = (-gamma2 + e*(-1 + gamma*(2 + gamma)))/(4*f*e2*gamma2); |
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198 | G4double yzP2K2 = 0; |
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199 | G4double zxP2K2 = (gamma + 2*e*(-1 + e - e*gamma))/ |
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200 | (2*sqrttwo*e2* std::sqrt(-(f*(2 + e*gmo)))*gamma); |
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201 | G4double zyP2K2 = 0; |
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202 | G4double zzP2K2 = (std::sqrt((e*gpo)/(2 + e*gmo))* |
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203 | (-2 + e*(3 + 2*e*gmo - gamma) + gamma))/(4*f*e2*gamma); |
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204 | phi3[0] += xxP2K2*pol1.x() + xyP2K2*pol1.y() + xzP2K2*pol1.z(); |
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205 | phi3[1] += yxP2K2*pol1.x() + yyP2K2*pol1.y() + yzP2K2*pol1.z(); |
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206 | phi3[2] += zxP2K2*pol1.x() + zyP2K2*pol1.y() + zzP2K2*pol1.z(); |
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207 | } |
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208 | } |
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209 | phi0 *= pref; |
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210 | phi2 *= pref; |
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211 | phi3 *= pref; |
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212 | } |
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213 | |
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214 | G4double G4PolarizedMollerCrossSection::XSection(const G4StokesVector & pol2, |
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215 | const G4StokesVector & pol3) |
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216 | { |
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217 | G4double xs=0.; |
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218 | xs+=phi0; |
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219 | |
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220 | G4bool polarized=(!pol2.IsZero())||(!pol3.IsZero()); |
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221 | if (polarized) { |
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222 | xs+=phi2*pol2 + phi3*pol3; |
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223 | } |
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224 | return xs; |
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225 | } |
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226 | |
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227 | G4double G4PolarizedMollerCrossSection::TotalXSection( |
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228 | G4double xmin, G4double xmax, G4double gamma, |
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229 | const G4StokesVector & pol0,const G4StokesVector & pol1) |
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230 | { |
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231 | G4double xs=0.; |
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232 | |
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233 | G4double x=xmin; |
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234 | |
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235 | if (xmax != 1./2.) G4cout<<" warning xmax expected to be 1/2 but is "<<xmax<< G4endl; |
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236 | |
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237 | // re -> electron radius^2; |
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238 | G4double re2 = classic_electr_radius * classic_electr_radius; |
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239 | G4double gamma2=gamma*gamma; |
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240 | G4double gmo2 = (gamma - 1.)*(gamma - 1.); |
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241 | G4double logMEM = std::log(1./x - 1.); |
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242 | G4double pref = twopi*gamma2*re2/(gmo2*(gamma + 1.0)); |
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243 | // unpolarise XS |
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244 | G4double sigma0 = 0.; |
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245 | sigma0 += (gmo2/gamma2)*(0.5 - x); |
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246 | sigma0 += ((1. - 2.*gamma)/gamma2)*logMEM; |
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247 | sigma0 += 1./x - 1./(1. - x); |
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248 | // longitudinal part |
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249 | G4double sigma2=0.; |
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250 | sigma2 += ((gamma2 + 2.*gamma - 3.)/gamma2)*(0.5 - x); |
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251 | sigma2 += (1./gamma - 2.)*logMEM; |
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252 | // transverse part |
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253 | G4double sigma3=0.; |
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254 | sigma3 += (2.*(1. - gamma)/gamma2)*(0.5 - x); |
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255 | sigma3 += (1. - 3.*gamma)/(2.*gamma2)*logMEM; |
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256 | // total cross section |
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257 | xs+=pref*(sigma0 + sigma2*pol0.z()*pol1.z() + sigma3*(pol0.x()*pol1.x()+pol0.y()*pol1.y())); |
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258 | |
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259 | return xs; |
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260 | } |
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261 | |
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262 | |
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263 | G4StokesVector G4PolarizedMollerCrossSection::GetPol2() |
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264 | { |
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265 | // Note, mean polarization can not contain correlation |
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266 | // effects. |
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267 | return 1./phi0 * phi2; |
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268 | } |
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269 | G4StokesVector G4PolarizedMollerCrossSection::GetPol3() |
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270 | { |
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271 | // Note, mean polarization can not contain correlation |
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272 | // effects. |
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273 | return 1./phi0 * phi3; |
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274 | } |
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