[819] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * By using, copying, modifying or distributing the software (or * |
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| 21 | // * any work based on the software) you agree to acknowledge its * |
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| 22 | // * use in resulting scientific publications, and indicate your * |
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| 23 | // * acceptance of all terms of the Geant4 Software license. * |
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| 24 | // ******************************************************************** |
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| 25 | // |
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| 26 | // $Id: G4PolarizedBhabhaCrossSection.cc,v 1.5 2007/11/01 17:32:34 schaelic Exp $ |
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[1228] | 27 | // GEANT4 tag $Name: geant4-09-03 $ |
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[819] | 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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