| 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: G4PolarizedMollerCrossSection.cc,v 1.5 2007/11/01 17:32:34 schaelic Exp $ |
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| 27 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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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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