[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: G4FinalStateIonisationBorn.cc,v 1.9 2007/11/26 17:27:09 pia Exp $ |
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| 28 | // GEANT4 tag $Name: $ |
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| 29 | // |
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| 30 | // Contact Author: Sebastien Incerti (incerti@cenbg.in2p3.fr) |
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| 31 | // Maria Grazia Pia (Maria.Grazia.Pia@cern.ch) |
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| 32 | // |
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| 33 | // Reference: TNS Geant4-DNA paper |
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| 34 | // Reference for implementation model: NIM. 155, pp. 145-156, 1978 |
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| 35 | |
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| 36 | // History: |
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| 37 | // ----------- |
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| 38 | // Date Name Modification |
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| 39 | // 28 Apr 2007 M.G. Pia Created in compliance with design described in TNS paper |
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| 40 | // Nov 2007 S. Incerti Implementation |
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| 41 | // 26 Nov 2007 MGP Cleaned up std:: |
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| 42 | // |
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| 43 | // ------------------------------------------------------------------- |
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| 44 | |
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| 45 | // Class description: |
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| 46 | // Reference: TNS Geant4-DNA paper |
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| 47 | // S. Chauvie et al., Geant4 physics processes for microdosimetry simulation: |
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| 48 | // design foundation and implementation of the first set of models, |
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| 49 | // IEEE Trans. Nucl. Sci., vol. 54, no. 6, Dec. 2007. |
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| 50 | // Further documentation available from http://www.ge.infn.it/geant4/dna |
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| 51 | |
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| 52 | // ------------------------------------------------------------------- |
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| 53 | |
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| 54 | |
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| 55 | #include "G4FinalStateIonisationBorn.hh" |
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| 56 | #include "G4Track.hh" |
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| 57 | #include "G4Step.hh" |
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| 58 | #include "G4DynamicParticle.hh" |
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| 59 | #include "Randomize.hh" |
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| 60 | |
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| 61 | #include "G4ParticleTypes.hh" |
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| 62 | #include "G4ParticleDefinition.hh" |
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| 63 | #include "G4Electron.hh" |
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| 64 | #include "G4Proton.hh" |
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| 65 | #include "G4SystemOfUnits.hh" |
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| 66 | #include "G4ParticleMomentum.hh" |
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| 67 | |
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| 68 | |
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| 69 | G4FinalStateIonisationBorn::G4FinalStateIonisationBorn() |
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| 70 | { |
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| 71 | |
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| 72 | name = "IonisationBorn"; |
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| 73 | |
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| 74 | // NEW |
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| 75 | // Factor to scale microscopic/macroscopic cross section data in water |
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| 76 | |
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| 77 | G4double scaleFactor = (1.e-22 / 3.343) * m*m; |
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| 78 | |
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| 79 | // Energy limits |
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| 80 | G4ParticleDefinition* electronDef = G4Electron::ElectronDefinition(); |
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| 81 | G4ParticleDefinition* protonDef = G4Proton::ProtonDefinition(); |
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| 82 | |
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| 83 | G4String electron; |
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| 84 | G4String proton; |
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| 85 | |
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| 86 | // Default energy limits (defined for protection against anomalous behaviour only) |
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| 87 | lowEnergyLimitDefault = 25 * eV; |
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| 88 | highEnergyLimitDefault = 10 * MeV; |
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| 89 | |
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| 90 | char *path = getenv("G4LEDATA"); |
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| 91 | |
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| 92 | if (!path) |
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| 93 | G4Exception("G4DNACrossSectionDataSet::FullFileName - G4LEDATA environment variable not set"); |
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| 94 | |
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| 95 | // Data members for electrons |
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| 96 | |
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| 97 | if (electronDef != 0) |
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| 98 | { |
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| 99 | electron = electronDef->GetParticleName(); |
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| 100 | lowEnergyLimit[electron] = 25. * eV; |
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| 101 | highEnergyLimit[electron] = 30. * keV; |
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| 102 | |
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| 103 | std::ostringstream eFullFileName; |
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| 104 | eFullFileName << path << "/dna/sigmadiff_ionisation_e_born.dat"; |
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| 105 | std::ifstream eDiffCrossSection(eFullFileName.str().c_str()); |
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| 106 | // eDiffCrossSection(eFullFileName.str().c_str()); |
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| 107 | if (!eDiffCrossSection) |
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| 108 | { |
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| 109 | // G4cout << "ERROR OPENING DATA FILE IN ELECTRON BORN IONIZATION !!! " << G4endl; |
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| 110 | G4Exception("G4FinalStateIonisationBorn::ERROR OPENING electron DATA FILE"); |
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| 111 | while(1); // ---- MGP ---- What is this? |
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| 112 | } |
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| 113 | |
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| 114 | eTdummyVec.push_back(0.); |
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| 115 | while(!eDiffCrossSection.eof()) |
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| 116 | { |
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| 117 | double tDummy; |
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| 118 | double eDummy; |
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| 119 | eDiffCrossSection>>tDummy>>eDummy; |
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| 120 | if (tDummy != eTdummyVec.back()) eTdummyVec.push_back(tDummy); |
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| 121 | for (int j=0; j<5; j++) |
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| 122 | { |
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| 123 | eDiffCrossSection>>eDiffCrossSectionData[j][tDummy][eDummy]; |
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| 124 | eDiffCrossSectionData[j][tDummy][eDummy]*=scaleFactor; |
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| 125 | eVecm[tDummy].push_back(eDummy); |
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| 126 | } |
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| 127 | } |
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| 128 | |
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| 129 | } |
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| 130 | else |
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| 131 | { |
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| 132 | G4Exception("G4FinalStateIonisationBorn Constructor: electron is not defined"); |
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| 133 | } |
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| 134 | |
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| 135 | // Data members for protons |
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| 136 | |
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| 137 | if (protonDef != 0) |
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| 138 | { |
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| 139 | proton = protonDef->GetParticleName(); |
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| 140 | lowEnergyLimit[proton] = 500. * keV; |
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| 141 | highEnergyLimit[proton] = 10. * MeV; |
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| 142 | |
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| 143 | std::ostringstream pFullFileName; |
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| 144 | pFullFileName << path << "/dna/sigmadiff_ionisation_p_born.dat"; |
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| 145 | std::ifstream pDiffCrossSection(pFullFileName.str().c_str()); |
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| 146 | // pDiffCrossSection(pFullFileName.str().c_str()); |
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| 147 | if (!pDiffCrossSection) |
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| 148 | { |
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| 149 | // G4cout<<"ERROR OPENING DATA FILE IN PROTON BORN IONIZATION !!! "<<G4endl; |
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| 150 | G4Exception("G4FinalStateIonisationBorn::ERROR OPENING proton DATA FILE"); |
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| 151 | while(1); // ---- MGP ---- What is this? |
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| 152 | } |
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| 153 | |
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| 154 | pTdummyVec.push_back(0.); |
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| 155 | while(!pDiffCrossSection.eof()) |
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| 156 | { |
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| 157 | double tDummy; |
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| 158 | double eDummy; |
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| 159 | pDiffCrossSection>>tDummy>>eDummy; |
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| 160 | if (tDummy != pTdummyVec.back()) pTdummyVec.push_back(tDummy); |
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| 161 | for (int j=0; j<5; j++) |
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| 162 | { |
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| 163 | pDiffCrossSection>>pDiffCrossSectionData[j][tDummy][eDummy]; |
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| 164 | pDiffCrossSectionData[j][tDummy][eDummy]*=scaleFactor; |
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| 165 | //G4cout << "j=" << j << " Tdum=" << tDummy << " Edum=" << eDummy << " pDiff=" << pDiffCrossSectionData[j][tDummy][eDummy] << G4endl; |
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| 166 | pVecm[tDummy].push_back(eDummy); |
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| 167 | } |
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| 168 | } |
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| 169 | } |
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| 170 | else |
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| 171 | { |
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| 172 | G4Exception("G4FinalStateIonisationBorn Constructor: proton is not defined"); |
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| 173 | } |
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| 174 | } |
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| 175 | |
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| 176 | |
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| 177 | G4FinalStateIonisationBorn::~G4FinalStateIonisationBorn() |
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| 178 | { |
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| 179 | eVecm.clear(); |
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| 180 | pVecm.clear(); |
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| 181 | } |
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| 182 | |
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| 183 | |
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| 184 | const G4FinalStateProduct& G4FinalStateIonisationBorn::GenerateFinalState(const G4Track& track, const G4Step& /* step */) |
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| 185 | { |
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| 186 | // Clear previous secondaries, energy deposit and particle kill status |
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| 187 | product.Clear(); |
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| 188 | |
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| 189 | const G4DynamicParticle* particle = track.GetDynamicParticle(); |
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| 190 | |
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| 191 | G4double lowLim = lowEnergyLimitDefault; |
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| 192 | G4double highLim = highEnergyLimitDefault; |
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| 193 | |
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| 194 | G4double k = particle->GetKineticEnergy(); |
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| 195 | |
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| 196 | const G4String& particleName = particle->GetDefinition()->GetParticleName(); |
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| 197 | |
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| 198 | // Retrieve energy limits for the current particle type |
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| 199 | |
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| 200 | std::map< G4String,G4double,std::less<G4String> >::iterator pos1; |
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| 201 | pos1 = lowEnergyLimit.find(particleName); |
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| 202 | |
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| 203 | // Lower limit |
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| 204 | if (pos1 != lowEnergyLimit.end()) |
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| 205 | { |
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| 206 | lowLim = pos1->second; |
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| 207 | } |
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| 208 | |
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| 209 | // Upper limit |
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| 210 | std::map< G4String,G4double,std::less<G4String> >::iterator pos2; |
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| 211 | pos2 = highEnergyLimit.find(particleName); |
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| 212 | |
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| 213 | if (pos2 != highEnergyLimit.end()) |
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| 214 | { |
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| 215 | highLim = pos2->second; |
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| 216 | } |
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| 217 | |
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| 218 | // Verify that the current track is within the energy limits of validity of the cross section model |
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| 219 | |
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| 220 | if (k >= lowLim && k <= highLim) |
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| 221 | { |
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| 222 | // Kinetic energy of primary particle |
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| 223 | |
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| 224 | G4ParticleMomentum primaryDirection = particle->GetMomentumDirection(); |
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| 225 | G4double particleMass = particle->GetDefinition()->GetPDGMass(); |
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| 226 | G4double totalEnergy = k + particleMass; |
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| 227 | G4double pSquare = k * (totalEnergy + particleMass); |
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| 228 | G4double totalMomentum = std::sqrt(pSquare); |
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| 229 | |
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| 230 | const G4String& particleName = particle->GetDefinition()->GetParticleName(); |
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| 231 | |
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| 232 | G4int ionizationShell = cross.RandomSelect(k,particleName); |
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| 233 | |
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| 234 | G4double secondaryKinetic = RandomizeEjectedElectronEnergy(particle->GetDefinition(),k,ionizationShell); |
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| 235 | |
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| 236 | G4double bindingEnergy = waterStructure.IonisationEnergy(ionizationShell); |
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| 237 | |
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| 238 | G4double cosTheta = 0.; |
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| 239 | G4double phi = 0.; |
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| 240 | RandomizeEjectedElectronDirection(track.GetDefinition(), k,secondaryKinetic, cosTheta, phi); |
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| 241 | |
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| 242 | G4double sinTheta = std::sqrt(1.-cosTheta*cosTheta); |
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| 243 | G4double dirX = sinTheta*std::cos(phi); |
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| 244 | G4double dirY = sinTheta*std::sin(phi); |
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| 245 | G4double dirZ = cosTheta; |
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| 246 | G4ThreeVector deltaDirection(dirX,dirY,dirZ); |
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| 247 | deltaDirection.rotateUz(primaryDirection); |
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| 248 | |
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| 249 | G4double deltaTotalMomentum = std::sqrt(secondaryKinetic*(secondaryKinetic + 2.*electron_mass_c2 )); |
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| 250 | |
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| 251 | //Primary Particle Direction |
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| 252 | G4double finalPx = totalMomentum*primaryDirection.x() - deltaTotalMomentum*deltaDirection.x(); |
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| 253 | G4double finalPy = totalMomentum*primaryDirection.y() - deltaTotalMomentum*deltaDirection.y(); |
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| 254 | G4double finalPz = totalMomentum*primaryDirection.z() - deltaTotalMomentum*deltaDirection.z(); |
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| 255 | G4double finalMomentum = std::sqrt(finalPx*finalPx + finalPy*finalPy + finalPz*finalPz); |
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| 256 | finalPx /= finalMomentum; |
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| 257 | finalPy /= finalMomentum; |
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| 258 | finalPz /= finalMomentum; |
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| 259 | |
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| 260 | product.ModifyPrimaryParticle(finalPx,finalPy,finalPz,k-bindingEnergy-secondaryKinetic); |
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| 261 | product.AddEnergyDeposit(bindingEnergy); |
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| 262 | |
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| 263 | G4DynamicParticle* aElectron = new G4DynamicParticle(G4Electron::Electron(),deltaDirection,secondaryKinetic); |
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| 264 | product.AddSecondary(aElectron); |
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| 265 | } |
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| 266 | |
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| 267 | return product; |
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| 268 | } |
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| 269 | |
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| 270 | |
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| 271 | G4double G4FinalStateIonisationBorn::RandomizeEjectedElectronEnergy(G4ParticleDefinition* particleDefinition, |
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| 272 | G4double k, |
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| 273 | G4int shell) |
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| 274 | { |
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| 275 | |
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| 276 | if (particleDefinition == G4Electron::ElectronDefinition()) |
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| 277 | { |
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| 278 | |
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| 279 | G4double maximumEnergyTransfer=0.; |
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| 280 | if ((k+waterStructure.IonisationEnergy(shell))/2. > k) maximumEnergyTransfer=k; |
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| 281 | else maximumEnergyTransfer = (k+waterStructure.IonisationEnergy(shell))/2.; |
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| 282 | |
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| 283 | G4double crossSectionMaximum = 0.; |
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| 284 | for(G4double value=waterStructure.IonisationEnergy(shell); value<=maximumEnergyTransfer; value+=0.1*eV) |
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| 285 | { |
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| 286 | G4double differentialCrossSection = DifferentialCrossSection(particleDefinition, k/eV, value/eV, shell); |
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| 287 | if(differentialCrossSection >= crossSectionMaximum) crossSectionMaximum = differentialCrossSection; |
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| 288 | } |
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| 289 | |
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| 290 | G4double secondaryElectronKineticEnergy=0.; |
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| 291 | do |
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| 292 | { |
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| 293 | secondaryElectronKineticEnergy = G4UniformRand() * (maximumEnergyTransfer-waterStructure.IonisationEnergy(shell)); |
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| 294 | } while(G4UniformRand()*crossSectionMaximum > |
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| 295 | DifferentialCrossSection(particleDefinition, k/eV,(secondaryElectronKineticEnergy+waterStructure.IonisationEnergy(shell))/eV,shell)); |
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| 296 | |
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| 297 | return secondaryElectronKineticEnergy; |
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| 298 | |
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| 299 | } |
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| 300 | |
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| 301 | if (particleDefinition == G4Proton::ProtonDefinition()) |
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| 302 | { |
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| 303 | G4double maximumKineticEnergyTransfer = 4.* (electron_mass_c2 / proton_mass_c2) * k - (waterStructure.IonisationEnergy(shell)); |
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| 304 | |
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| 305 | G4double crossSectionMaximum = 0.; |
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| 306 | for (G4double value = waterStructure.IonisationEnergy(shell); |
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| 307 | value<=4.*waterStructure.IonisationEnergy(shell) ; |
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| 308 | value+=0.1*eV) |
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| 309 | { |
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| 310 | G4double differentialCrossSection = DifferentialCrossSection(particleDefinition, k/eV, value/eV, shell); |
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| 311 | if (differentialCrossSection >= crossSectionMaximum) crossSectionMaximum = differentialCrossSection; |
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| 312 | } |
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| 313 | |
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| 314 | G4double secondaryElectronKineticEnergy = 0.; |
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| 315 | do |
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| 316 | { |
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| 317 | secondaryElectronKineticEnergy = G4UniformRand() * maximumKineticEnergyTransfer; |
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| 318 | } while(G4UniformRand()*crossSectionMaximum >= |
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| 319 | DifferentialCrossSection(particleDefinition, k/eV,(secondaryElectronKineticEnergy+waterStructure.IonisationEnergy(shell))/eV,shell)); |
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| 320 | |
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| 321 | return secondaryElectronKineticEnergy; |
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| 322 | } |
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| 323 | |
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| 324 | return 0; |
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| 325 | } |
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| 326 | |
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| 327 | |
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| 328 | void G4FinalStateIonisationBorn::RandomizeEjectedElectronDirection(G4ParticleDefinition* particleDefinition, |
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| 329 | G4double k, |
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| 330 | G4double secKinetic, |
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| 331 | G4double & cosTheta, |
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| 332 | G4double & phi ) |
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| 333 | { |
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| 334 | if (particleDefinition == G4Electron::ElectronDefinition()) |
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| 335 | { |
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| 336 | |
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| 337 | phi = twopi * G4UniformRand(); |
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| 338 | if (secKinetic < 50.*eV) cosTheta = (2.*G4UniformRand())-1.; |
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| 339 | else if (secKinetic <= 200.*eV) |
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| 340 | { |
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| 341 | if (G4UniformRand() <= 0.1) cosTheta = (2.*G4UniformRand())-1.; |
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| 342 | else cosTheta = G4UniformRand()*(std::sqrt(2.)/2); |
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| 343 | } |
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| 344 | else |
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| 345 | { |
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| 346 | G4double sin2O = (1.-secKinetic/k) / (1.+secKinetic/(2.*electron_mass_c2)); |
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| 347 | cosTheta = std::sqrt(1.-sin2O); |
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| 348 | } |
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| 349 | } |
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| 350 | |
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| 351 | if (particleDefinition == G4Proton::ProtonDefinition()) |
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| 352 | { |
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| 353 | G4double maxSecKinetic = 4.* (electron_mass_c2 / proton_mass_c2) * k; |
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| 354 | phi = twopi * G4UniformRand(); |
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| 355 | cosTheta = std::sqrt(secKinetic / maxSecKinetic); |
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| 356 | } |
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| 357 | } |
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| 358 | |
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| 359 | |
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| 360 | double G4FinalStateIonisationBorn::DifferentialCrossSection(G4ParticleDefinition * particleDefinition, |
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| 361 | G4double k, |
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| 362 | G4double energyTransfer, |
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| 363 | G4int ionizationLevelIndex) |
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| 364 | { |
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| 365 | G4double sigma = 0.; |
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| 366 | |
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| 367 | if (energyTransfer >= waterStructure.IonisationEnergy(ionizationLevelIndex)) |
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| 368 | { |
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| 369 | G4double valueT1 = 0; |
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| 370 | G4double valueT2 = 0; |
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| 371 | G4double valueE21 = 0; |
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| 372 | G4double valueE22 = 0; |
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| 373 | G4double valueE12 = 0; |
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| 374 | G4double valueE11 = 0; |
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| 375 | |
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| 376 | G4double xs11 = 0; |
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| 377 | G4double xs12 = 0; |
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| 378 | G4double xs21 = 0; |
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| 379 | G4double xs22 = 0; |
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| 380 | |
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| 381 | |
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| 382 | if (particleDefinition == G4Electron::ElectronDefinition()) |
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| 383 | { |
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| 384 | // k should be in eV and energy transfer eV also |
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| 385 | std::vector<double>::iterator t2 = std::upper_bound(eTdummyVec.begin(),eTdummyVec.end(), k); |
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| 386 | std::vector<double>::iterator t1 = t2-1; |
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| 387 | std::vector<double>::iterator e12 = std::upper_bound(eVecm[(*t1)].begin(),eVecm[(*t1)].end(), energyTransfer); |
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| 388 | std::vector<double>::iterator e11 = e12-1; |
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| 389 | |
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| 390 | std::vector<double>::iterator e22 = std::upper_bound(eVecm[(*t2)].begin(),eVecm[(*t2)].end(), energyTransfer); |
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| 391 | std::vector<double>::iterator e21 = e22-1; |
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| 392 | |
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| 393 | valueT1 =*t1; |
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| 394 | valueT2 =*t2; |
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| 395 | valueE21 =*e21; |
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| 396 | valueE22 =*e22; |
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| 397 | valueE12 =*e12; |
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| 398 | valueE11 =*e11; |
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| 399 | |
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| 400 | xs11 = eDiffCrossSectionData[ionizationLevelIndex][valueT1][valueE11]; |
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| 401 | xs12 = eDiffCrossSectionData[ionizationLevelIndex][valueT1][valueE12]; |
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| 402 | xs21 = eDiffCrossSectionData[ionizationLevelIndex][valueT2][valueE21]; |
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| 403 | xs22 = eDiffCrossSectionData[ionizationLevelIndex][valueT2][valueE22]; |
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| 404 | |
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| 405 | } |
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| 406 | |
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| 407 | if (particleDefinition == G4Proton::ProtonDefinition()) |
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| 408 | { |
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| 409 | // k should be in eV and energy transfer eV also |
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| 410 | std::vector<double>::iterator t2 = std::upper_bound(pTdummyVec.begin(),pTdummyVec.end(), k); |
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| 411 | std::vector<double>::iterator t1 = t2-1; |
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| 412 | std::vector<double>::iterator e12 = std::upper_bound(pVecm[(*t1)].begin(),pVecm[(*t1)].end(), energyTransfer); |
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| 413 | std::vector<double>::iterator e11 = e12-1; |
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| 414 | |
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| 415 | std::vector<double>::iterator e22 = std::upper_bound(pVecm[(*t2)].begin(),pVecm[(*t2)].end(), energyTransfer); |
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| 416 | std::vector<double>::iterator e21 = e22-1; |
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| 417 | |
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| 418 | valueT1 =*t1; |
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| 419 | valueT2 =*t2; |
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| 420 | valueE21 =*e21; |
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| 421 | valueE22 =*e22; |
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| 422 | valueE12 =*e12; |
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| 423 | valueE11 =*e11; |
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| 424 | |
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| 425 | xs11 = pDiffCrossSectionData[ionizationLevelIndex][valueT1][valueE11]; |
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| 426 | xs12 = pDiffCrossSectionData[ionizationLevelIndex][valueT1][valueE12]; |
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| 427 | xs21 = pDiffCrossSectionData[ionizationLevelIndex][valueT2][valueE21]; |
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| 428 | xs22 = pDiffCrossSectionData[ionizationLevelIndex][valueT2][valueE22]; |
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| 429 | } |
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| 430 | |
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| 431 | G4double xsProduct = xs11 * xs12 * xs21 * xs22; |
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| 432 | // if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.); |
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| 433 | if (xsProduct != 0.) |
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| 434 | { |
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| 435 | sigma = QuadInterpolator(valueE11, valueE12, |
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| 436 | valueE21, valueE22, |
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| 437 | xs11, xs12, |
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| 438 | xs21, xs22, |
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| 439 | valueT1, valueT2, |
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| 440 | k, energyTransfer); |
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| 441 | } |
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| 442 | } |
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| 443 | return sigma; |
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| 444 | } |
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| 445 | |
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| 446 | |
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| 447 | G4double G4FinalStateIonisationBorn::LogLogInterpolate(G4double e1, |
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| 448 | G4double e2, |
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| 449 | G4double e, |
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| 450 | G4double xs1, |
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| 451 | G4double xs2) |
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| 452 | { |
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| 453 | G4double a = (std::log10(xs2)-std::log10(xs1)) / (std::log10(e2)-std::log10(e1)); |
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| 454 | G4double b = std::log10(xs2) - a*std::log10(e2); |
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| 455 | G4double sigma = a*std::log10(e) + b; |
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| 456 | G4double value = (std::pow(10.,sigma)); |
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| 457 | return value; |
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| 458 | } |
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| 459 | |
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| 460 | |
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| 461 | G4double G4FinalStateIonisationBorn::QuadInterpolator(G4double e11, G4double e12, |
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| 462 | G4double e21, G4double e22, |
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| 463 | G4double xs11, G4double xs12, |
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| 464 | G4double xs21, G4double xs22, |
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| 465 | G4double t1, G4double t2, |
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| 466 | G4double t, G4double e) |
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| 467 | { |
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| 468 | G4double interpolatedvalue1 = LogLogInterpolate(e11, e12, e, xs11, xs12); |
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| 469 | G4double interpolatedvalue2 = LogLogInterpolate(e21, e22, e, xs21, xs22); |
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| 470 | G4double value = LogLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2); |
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| 471 | return value; |
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| 472 | } |
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| 473 | |
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| 474 | |
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