[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 | // ------------------------------------------------------------------- |
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| 27 | // $Id: G4PolarizedAnnihilationCrossSection.cc,v 1.6 2007/11/01 17:32:34 schaelic Exp $ |
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[961] | 28 | // GEANT4 tag $Name: geant4-09-02-ref-02 $ |
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[819] | 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: G4PolarizedAnnihilationCrossSection |
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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: 22.03.2006 |
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| 39 | // |
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| 40 | // Modifications: |
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| 41 | // 24-03-06 included cross section as given in W.McMaster, Nuovo Cimento 7, 1960, 395 |
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| 42 | // 27-07-06 new calculation by P.Starovoitov |
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| 43 | // 15.10.07 introduced a more general framework for cross sections (AS) |
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| 44 | // 16.10.07 some minor corrections in formula longPart |
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| 45 | // |
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| 46 | // Class Description: |
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| 47 | // * calculates the differential cross section in e+e- -> gamma gamma |
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| 48 | // |
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| 49 | |
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| 50 | #include "G4PolarizedAnnihilationCrossSection.hh" |
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| 51 | |
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| 52 | G4PolarizedAnnihilationCrossSection::G4PolarizedAnnihilationCrossSection() : |
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| 53 | polxx(0.), polyy(0.), polzz(0.), polxz(0.), polzx(0.), polxy(0.), |
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| 54 | polyx(0.), polyz(0.), polzy(0.), |
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| 55 | re2(1.), diffXSFactor(1.), totalXSFactor(1.), |
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| 56 | phi0(0.) |
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| 57 | { |
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| 58 | re2 = classic_electr_radius * classic_electr_radius; |
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| 59 | phi2 = G4ThreeVector(0., 0., 0.); |
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| 60 | phi3 = G4ThreeVector(0., 0., 0.); |
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| 61 | dice = 0.; |
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| 62 | polXS= 0.; |
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| 63 | unpXS = 0.; |
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| 64 | ISPxx=ISPyy=ISPzz=ISPnd=0.; |
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| 65 | } |
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| 66 | |
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| 67 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 68 | |
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| 69 | G4PolarizedAnnihilationCrossSection::~G4PolarizedAnnihilationCrossSection() |
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| 70 | { |
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| 71 | } |
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| 72 | |
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| 73 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 74 | |
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| 75 | void G4PolarizedAnnihilationCrossSection::TotalXS() |
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| 76 | { |
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| 77 | // total cross section is sum of |
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| 78 | // + unpol xsec "sigma0" |
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| 79 | // + longitudinal polarised cross section "sigma_zz" times pol_3(e-)*pol_3(e+) |
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| 80 | // + transverse contribution "(sigma_xx+sigma_yy)/2" times pol_T(e-)*pol_T(e+) |
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| 81 | // (Note: if both beams are transversely polarised, i.e. pol_T(e-)!=0 and |
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| 82 | // pol_T(e+)!=0, and sigma_xx!=sigma_yy, then the diff. cross section will |
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| 83 | // exhibit a azimuthal asymmetry even if pol_T(e-)*pol_T(e+)==0) |
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| 84 | |
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| 85 | |
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| 86 | } |
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| 87 | |
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| 88 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 89 | |
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| 90 | void G4PolarizedAnnihilationCrossSection::Initialize( |
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| 91 | G4double eps, |
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| 92 | G4double gam, |
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| 93 | G4double , // phi |
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| 94 | const G4StokesVector & pol0, // positron polarization |
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| 95 | const G4StokesVector & pol1, // electron polarization |
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| 96 | G4int flag) |
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| 97 | { |
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| 98 | |
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| 99 | diffXSFactor=re2/(gam - 1.); |
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| 100 | DefineCoefficients(pol0,pol1); |
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| 101 | // |
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| 102 | // prepare dicing |
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| 103 | // |
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| 104 | dice = 0.; |
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| 105 | G4double symmXS = 0.125*((-1./sqr(gam + 1.))/sqr(eps) + |
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| 106 | ((sqr(gam) + 4.*gam - 1.)/sqr(gam + 1.))/eps - 1.); |
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| 107 | // |
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| 108 | // |
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| 109 | // |
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| 110 | G4ThreeVector epsVector(1./sqr(eps), 1./eps, 1.); |
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| 111 | G4ThreeVector oneEpsVector(1./sqr(1. - eps), 1./(1.-eps), 1.); |
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| 112 | G4ThreeVector sumEpsVector(epsVector + oneEpsVector); |
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| 113 | G4ThreeVector difEpsVector(epsVector - oneEpsVector); |
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| 114 | G4ThreeVector calcVector(0., 0., 0.); |
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| 115 | // |
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| 116 | // temporary variables |
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| 117 | // |
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| 118 | G4double helpVar2 = 0., helpVar1 = 0.; |
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| 119 | // |
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| 120 | // unpolarised contribution |
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| 121 | // |
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| 122 | helpVar1 = (gam*gam + 4.*gam + 1.)/sqr(gam + 1.); |
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| 123 | helpVar2 = -1./sqr(gam + 1.); |
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| 124 | calcVector = G4ThreeVector(helpVar2, helpVar1, -1.); |
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| 125 | unpXS = 0.125 * calcVector * sumEpsVector; |
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| 126 | |
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| 127 | // initial particles polarised contribution |
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| 128 | helpVar2 = 1./sqr(gam + 1.); |
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| 129 | helpVar1 = -(gam*gam + 4.*gam + 1.)/sqr(gam + 1.); |
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| 130 | calcVector = G4ThreeVector(helpVar2, helpVar1, 0.5*(gam + 3.)); |
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| 131 | ISPxx = 0.25*(calcVector * sumEpsVector)/(gam - 1.); |
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| 132 | |
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| 133 | helpVar1 = 1./sqr(gam + 1.); |
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| 134 | calcVector = G4ThreeVector(-helpVar1, 2.*gam*helpVar1, -1.); |
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| 135 | ISPyy = 0.125 * calcVector * sumEpsVector; |
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| 136 | |
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| 137 | helpVar1 = 1./(gam - 1.); |
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| 138 | helpVar2 = 1./sqr(gam + 1.); |
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| 139 | calcVector = G4ThreeVector(-(gam*gam + 1.)*helpVar2,(gam*gam*(gam + 1.) + 7.*gam + 3.)*helpVar2, -(gam + 3.)); |
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| 140 | ISPzz = 0.125*helpVar1*(calcVector * sumEpsVector); |
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| 141 | |
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| 142 | helpVar1 = std::sqrt(std::fabs(eps*(1. - eps)*2.*(gam + 1.) - 1.)); |
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| 143 | calcVector = G4ThreeVector(-1./(gam*gam - 1.), 2./(gam - 1.), 0.); |
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| 144 | ISPnd = 0.125*(calcVector * difEpsVector) * helpVar1; |
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| 145 | |
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| 146 | polXS = 0.; |
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| 147 | polXS += ISPxx*polxx; |
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| 148 | polXS += ISPyy*polyy; |
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| 149 | polXS += ISPzz*polzz; |
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| 150 | polXS += ISPnd*(polzx + polxz); |
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| 151 | phi0 = unpXS + polXS; |
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| 152 | dice = symmXS; |
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| 153 | // if(polzz != 0.) dice *= (1. + std::fabs(polzz*ISPzz/unpXS)); |
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| 154 | if(polzz != 0.) { |
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| 155 | dice *= (1. + (polzz*ISPzz/unpXS)); |
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| 156 | if (dice<0.) dice=0.; |
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| 157 | } |
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| 158 | // prepare final state coefficients |
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| 159 | if (flag==2) { |
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| 160 | // |
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| 161 | // circular polarisation |
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| 162 | // |
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| 163 | G4double circ1 = 0., circ2 = 0., circ3 = 0.; |
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| 164 | helpVar1 = 8.*sqr(1. - eps)*sqr(eps)*(gam - 1.)*sqr(gam + 1.)/std::sqrt(gam*gam - 1.); |
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| 165 | helpVar2 = sqr(gam + 1.)*sqr(eps)*(-2.*eps + 3.) - (gam*gam + 3.*gam + 2.)*eps; |
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| 166 | circ1 = helpVar2 + gam; |
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| 167 | circ1 /= helpVar1; |
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| 168 | circ2 = helpVar2 + 1.; |
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| 169 | circ2 /= helpVar1; |
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| 170 | helpVar1 = std::sqrt(std::fabs(eps*(1. - eps)*2.*(gam + 1.) - 1.)); |
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| 171 | helpVar1 /= std::sqrt(gam*gam - 1.); |
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| 172 | calcVector = G4ThreeVector(1., -2.*gam, 0.); |
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| 173 | circ3 = 0.125*(calcVector * sumEpsVector)/(gam + 1.); |
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| 174 | circ3 *= helpVar1; |
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| 175 | |
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| 176 | phi2.setZ( circ2*pol1.z() + circ1*pol0.z() + circ3*(pol1.x() + pol0.x())); |
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| 177 | phi3.setZ(-circ1*pol1.z() - circ2*pol0.z() - circ3*(pol1.x() + pol0.x())); |
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| 178 | // |
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| 179 | // common to both linear polarisation |
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| 180 | // |
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| 181 | calcVector = G4ThreeVector(-1., 2.*gam, 0.); |
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| 182 | G4double linearZero = 0.125*(calcVector * sumEpsVector)/sqr(gam + 1.); |
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| 183 | // |
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| 184 | // Linear Polarisation #1 |
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| 185 | // |
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| 186 | helpVar1 = std::sqrt(std::fabs(2.*(gam + 1.)*(1. - eps)*eps - 1.))/((gam + 1.)*eps*(1. - eps)); |
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| 187 | helpVar2 = helpVar1*helpVar1; |
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| 188 | // |
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| 189 | // photon 1 |
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| 190 | // |
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| 191 | G4double diagContrib = 0.125*helpVar2*(polxx + polyy - polzz); |
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| 192 | G4double nonDiagContrib = 0.125*helpVar1*(-polxz/(1. - eps) + polzx/eps); |
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| 193 | |
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| 194 | phi2.setX(linearZero + diagContrib + nonDiagContrib); |
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| 195 | // |
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| 196 | // photon 2 |
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| 197 | // |
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| 198 | nonDiagContrib = 0.125*helpVar1*(polxz/eps - polzx/(1. - eps)); |
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| 199 | |
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| 200 | |
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| 201 | phi3.setX(linearZero + diagContrib + nonDiagContrib); |
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| 202 | // |
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| 203 | // Linear Polarisation #2 |
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| 204 | // |
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| 205 | helpVar1 = std::sqrt(gam*gam - 1.)*(2.*(gam + 1.)*eps*(1. - eps) - 1.); |
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| 206 | helpVar1 /= 8.*sqr(1. - eps)*sqr(eps)*sqr(gam + 1.)*(gam - 1.); |
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| 207 | helpVar2 = std::sqrt((gam*gam - 1.)*std::fabs(2.*(gam + 1.)*eps*(1. - eps) - 1.)); |
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| 208 | helpVar2 /= 8.*sqr(1. - eps)*sqr(eps)*sqr(gam + 1.)*(gam - 1.); |
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| 209 | |
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| 210 | G4double contrib21 = (-polxy + polyx)*helpVar1; |
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| 211 | G4double contrib32 = -(eps*(gam + 1.) - 1.)*polyz + (eps*(gam + 1.) - gam)*polzy; |
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| 212 | |
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| 213 | contrib32 *=helpVar2; |
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| 214 | phi2.setY(contrib21 + contrib32); |
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| 215 | |
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| 216 | contrib32 = -(eps*(gam + 1.) - gam)*polyz + (eps*(gam + 1.) - 1.)*polzy; |
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| 217 | contrib32 *=helpVar2; |
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| 218 | phi3.setY(contrib21 + contrib32); |
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| 219 | |
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| 220 | } |
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| 221 | phi0 *= diffXSFactor; |
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| 222 | phi2 *= diffXSFactor; |
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| 223 | phi3 *= diffXSFactor; |
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| 224 | } |
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| 225 | |
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| 226 | |
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| 227 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 228 | |
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| 229 | G4double G4PolarizedAnnihilationCrossSection::XSection(const G4StokesVector & pol2, |
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| 230 | const G4StokesVector & pol3) |
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| 231 | { |
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| 232 | G4double xs=phi0+pol2*phi2+pol3*phi3; |
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| 233 | return xs; |
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| 234 | } |
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| 235 | // |
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| 236 | // calculate total cross section |
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| 237 | // |
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| 238 | G4double G4PolarizedAnnihilationCrossSection::TotalXSection( |
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| 239 | G4double ,G4double ,G4double gam, |
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| 240 | const G4StokesVector & pol0,const G4StokesVector & pol1) |
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| 241 | { |
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| 242 | totalXSFactor =pi*re2/(gam + 1.); // atomic number ignored |
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| 243 | DefineCoefficients(pol0,pol1); |
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| 244 | |
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| 245 | G4double xs = 0.; |
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| 246 | |
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| 247 | |
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| 248 | G4double gam2 = gam*gam; |
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| 249 | G4double sqrtgam1 = std::sqrt(gam2 - 1.); |
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| 250 | G4double logMEM = std::log(gam+sqrtgam1); |
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| 251 | G4double unpME = (gam*(gam + 4.) + 1.)*logMEM; |
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| 252 | unpME += -(gam + 3.)*sqrtgam1; |
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| 253 | unpME /= 4.*(gam2 - 1.); |
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| 254 | // G4double longPart = - 2.*(gam*(gam + 4.) + 1.)*logMEM; |
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| 255 | // longPart += (gam*(gam + 4.) + 7.)*sqrtgam1; |
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| 256 | // longPart /= 4.*sqr(gam - 1.)*(gam + 1.); |
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| 257 | G4double longPart = (3+gam*(gam*(gam + 1.) + 7.))*logMEM; |
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| 258 | longPart += - (5.+ gam*(3*gam + 4.))*sqrtgam1; |
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| 259 | longPart /= 4.*sqr(gam - 1.)*(gam + 1.); |
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| 260 | G4double tranPart = -(5*gam + 1.)*logMEM; |
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| 261 | tranPart += (gam + 5.)*sqrtgam1; |
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| 262 | tranPart /= 4.*sqr(gam - 1.)*(gam + 1.); |
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| 263 | |
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| 264 | xs += unpME; |
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| 265 | xs += polzz*longPart; |
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| 266 | xs += (polxx + polyy)*tranPart; |
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| 267 | |
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| 268 | return xs*totalXSFactor; |
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| 269 | } |
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| 270 | |
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| 271 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 272 | G4StokesVector G4PolarizedAnnihilationCrossSection::GetPol2() |
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| 273 | { |
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| 274 | // Note, mean polarization can not contain correlation |
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| 275 | // effects. |
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| 276 | return 1./phi0 * phi2; |
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| 277 | } |
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| 278 | |
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| 279 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 280 | |
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| 281 | G4StokesVector G4PolarizedAnnihilationCrossSection::GetPol3() |
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| 282 | { |
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| 283 | // Note, mean polarization can not contain correlation |
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| 284 | // effects. |
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| 285 | return 1./phi0 * phi3; |
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| 286 | } |
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| 287 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 288 | void G4PolarizedAnnihilationCrossSection::DefineCoefficients(const G4StokesVector & pol0, |
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| 289 | const G4StokesVector & pol1) |
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| 290 | { |
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| 291 | polxx=pol0.x()*pol1.x(); |
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| 292 | polyy=pol0.y()*pol1.y(); |
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| 293 | polzz=pol0.z()*pol1.z(); |
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| 294 | |
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| 295 | polxz=pol0.x()*pol1.z(); |
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| 296 | polzx=pol0.z()*pol1.x(); |
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| 297 | |
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| 298 | polyz=pol0.y()*pol1.z(); |
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| 299 | polzy=pol0.z()*pol1.y(); |
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| 300 | |
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| 301 | polxy=pol0.x()*pol1.y(); |
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| 302 | polyx=pol0.y()*pol1.x(); |
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| 303 | } |
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| 304 | |
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| 305 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 306 | |
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| 307 | G4double G4PolarizedAnnihilationCrossSection::GetXmin(G4double y) |
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| 308 | { |
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| 309 | return 0.5*(1.-std::sqrt((y-1.)/(y+1.))); |
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| 310 | } |
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| 311 | G4double G4PolarizedAnnihilationCrossSection::GetXmax(G4double y) |
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| 312 | { |
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| 313 | return 0.5*(1.+std::sqrt((y-1.)/(y+1.))); |
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| 314 | } |
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| 315 | |
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| 316 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 317 | G4double G4PolarizedAnnihilationCrossSection::DiceEpsilon() |
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| 318 | { |
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| 319 | return dice; |
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| 320 | } |
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| 321 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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| 322 | G4double G4PolarizedAnnihilationCrossSection::getVar(G4int choice) |
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| 323 | { |
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| 324 | if (choice == -1) return polXS/unpXS; |
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| 325 | if (choice == 0) return unpXS; |
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| 326 | if (choice == 1) return ISPxx; |
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| 327 | if (choice == 2) return ISPyy; |
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| 328 | if (choice == 3) return ISPzz; |
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| 329 | if (choice == 4) return ISPnd; |
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| 330 | return 0; |
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| 331 | } |
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| 332 | //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo...... |
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