[968] | 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: G4ecpssrCrossSection.cc,v 1.5 2008/12/18 13:01:32 gunter Exp $ |
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| 27 | // GEANT4 tag $Name: geant4-09-02-ref-02 $ |
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| 28 | // |
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| 29 | // Author: Haifa Ben Abdelouahed |
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| 30 | // |
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| 31 | // |
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| 32 | // History: |
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| 33 | // ----------- |
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| 34 | // 21 Apr 2008 H. Ben Abdelouahed 1st implementation |
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| 35 | // 21 Apr 2008 MGP Major revision according to a design iteration |
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| 36 | // |
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| 37 | // ------------------------------------------------------------------- |
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| 38 | // Class description: |
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| 39 | // Low Energy Electromagnetic Physics, Cross section, p ionisation, K shell |
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| 40 | // Further documentation available from http://www.ge.infn.it/geant4/lowE |
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| 41 | // ------------------------------------------------------------------- |
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| 42 | |
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| 43 | |
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| 44 | #include "globals.hh" |
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| 45 | #include "G4ecpssrCrossSection.hh" |
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| 46 | #include "G4AtomicTransitionManager.hh" |
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| 47 | #include "G4NistManager.hh" |
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| 48 | #include "G4Proton.hh" |
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| 49 | #include "G4Alpha.hh" |
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| 50 | #include <math.h> |
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| 51 | |
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| 52 | G4ecpssrCrossSection::G4ecpssrCrossSection() |
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| 53 | { } |
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| 54 | |
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| 55 | G4ecpssrCrossSection::~G4ecpssrCrossSection() |
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| 56 | { } |
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| 57 | |
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| 58 | //---------------------------------this "ExpIntFunction" function allows fast evaluation of the n order exponential integral function En(x)------ |
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| 59 | |
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| 60 | G4double G4ecpssrCrossSection::ExpIntFunction(G4int n,G4double x) |
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| 61 | |
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| 62 | { |
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| 63 | G4int i; |
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| 64 | G4int ii; |
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| 65 | G4int nm1; |
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| 66 | G4double a; |
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| 67 | G4double b; |
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| 68 | G4double c; |
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| 69 | G4double d; |
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| 70 | G4double del; |
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| 71 | G4double fact; |
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| 72 | G4double h; |
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| 73 | G4double psi; |
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| 74 | G4double ans = 0; |
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| 75 | const G4double euler= 0.5772156649; |
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| 76 | const G4int maxit= 100; |
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| 77 | const G4double fpmin = 1.0e-30; |
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| 78 | const G4double eps = 1.0e-7; |
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| 79 | nm1=n-1; |
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| 80 | if (n<0 || x<0.0 || (x==0.0 && (n==0 || n==1))) |
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| 81 | G4cout << "bad arguments in ExpIntFunction" << G4endl; |
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| 82 | else { |
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| 83 | if (n==0) ans=std::exp(-x)/x; |
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| 84 | else { |
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| 85 | if (x==0.0) ans=1.0/nm1; |
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| 86 | else { |
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| 87 | if (x > 1.0) { |
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| 88 | b=x+n; |
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| 89 | c=1.0/fpmin; |
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| 90 | d=1.0/b; |
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| 91 | h=d; |
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| 92 | for (i=1;i<=maxit;i++) { |
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| 93 | a=-i*(nm1+i); |
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| 94 | b +=2.0; |
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| 95 | d=1.0/(a*d+b); |
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| 96 | c=b+a/c; |
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| 97 | del=c*d; |
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| 98 | h *=del; |
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| 99 | if (std::fabs(del-1.0) < eps) { |
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| 100 | ans=h*std::exp(-x); |
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| 101 | return ans; |
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| 102 | } |
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| 103 | } |
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| 104 | } else { |
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| 105 | ans = (nm1!=0 ? 1.0/nm1 : -std::log(x)-euler); |
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| 106 | fact=1.0; |
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| 107 | for (i=1;i<=maxit;i++) { |
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| 108 | fact *=-x/i; |
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| 109 | if (i !=nm1) del = -fact/(i-nm1); |
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| 110 | else { |
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| 111 | psi = -euler; |
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| 112 | for (ii=1;ii<=nm1;ii++) psi +=1.0/ii; |
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| 113 | del=fact*(-std::log(x)+psi); |
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| 114 | } |
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| 115 | ans += del; |
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| 116 | if (std::fabs(del) < std::fabs(ans)*eps) return ans; |
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| 117 | } |
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| 118 | } |
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| 119 | } |
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| 120 | } |
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| 121 | } |
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| 122 | return ans; |
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| 123 | } |
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| 124 | //----------------------------------------------------------------------------------------------------------- |
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| 125 | |
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| 126 | |
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| 127 | G4double G4ecpssrCrossSection::CalculateCrossSection(G4int zTarget,G4int zIncident, G4double energyIncident) |
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| 128 | |
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| 129 | //this K-CrossSection calculation method is done according to W.Brandt and G.Lapicki, Phys.Rev.A23(1981)// |
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| 130 | |
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| 131 | { |
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| 132 | |
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| 133 | G4NistManager* massManager = G4NistManager::Instance(); |
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| 134 | |
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| 135 | G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance(); |
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| 136 | |
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| 137 | G4double massIncident; |
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| 138 | |
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| 139 | if (zIncident == 1) |
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| 140 | { |
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| 141 | G4Proton* aProtone = G4Proton::Proton(); |
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| 142 | |
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| 143 | massIncident = aProtone->GetPDGMass(); |
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| 144 | } |
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| 145 | else |
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| 146 | { |
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| 147 | if (zIncident == 2) |
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| 148 | { |
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| 149 | G4Alpha* aAlpha = G4Alpha::Alpha(); |
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| 150 | |
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| 151 | massIncident = aAlpha->GetPDGMass(); |
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| 152 | } |
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| 153 | else |
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| 154 | { |
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| 155 | G4cout << "we can treat only Proton or Alpha incident particles " << G4endl; |
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| 156 | massIncident =0.; |
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| 157 | } |
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| 158 | } |
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| 159 | |
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| 160 | G4double kBindingEnergy = transitionManager->Shell(zTarget,0)->BindingEnergy(); |
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| 161 | |
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| 162 | G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2; |
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| 163 | |
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| 164 | G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2;//the mass of the system (projectile, target) |
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| 165 | |
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| 166 | const G4double zkshell= 0.3; |
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| 167 | |
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| 168 | G4double screenedzTarget = zTarget-zkshell; // screenedzTarget is the screened nuclear charge of the target |
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| 169 | |
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| 170 | const G4double rydbergMeV= 13.6e-6; |
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| 171 | |
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| 172 | G4double tetaK = kBindingEnergy/((screenedzTarget*screenedzTarget)*rydbergMeV); //tetaK denotes the reduced binding energy of the electron |
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| 173 | |
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| 174 | const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; |
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| 175 | |
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| 176 | G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.); //sigma0 is the initial cross section of K shell at stable state |
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| 177 | |
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| 178 | //--------------------------------------------------------------------------------------------------------------------- |
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| 179 | |
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| 180 | G4double velocity = CalculateVelocity( zTarget, zIncident, energyIncident); //is the scaled velocity parameter of the system |
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| 181 | |
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| 182 | //--------------------------------------------------------------------------------------------------------------------- |
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| 183 | |
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| 184 | const G4double kAnalyticalApproximation= 1.5; |
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| 185 | |
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| 186 | G4double x = kAnalyticalApproximation/velocity; |
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| 187 | |
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| 188 | G4double electrIonizationEnergy; |
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| 189 | |
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| 190 | if ( x<0.035) |
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| 191 | { |
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| 192 | electrIonizationEnergy= 0.75*pi*(std::log(1./(x*x))-1.); |
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| 193 | } |
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| 194 | else |
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| 195 | { |
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| 196 | if ( x<3.) |
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| 197 | { |
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| 198 | electrIonizationEnergy =std::exp(-2.*x)/(0.031+(0.213*std::pow(x,0.5))+(0.005*x)-(0.069*std::pow(x,3./2.))+(0.324*x*x)); |
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| 199 | } |
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| 200 | |
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| 201 | else |
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| 202 | { |
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| 203 | electrIonizationEnergy =2.*std::exp(-2.*x)/std::pow(x,1.6); } |
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| 204 | } |
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| 205 | |
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| 206 | G4double hFunction =(electrIonizationEnergy*2.)/(tetaK*std::pow(velocity,3)); //hFunction represents the correction for polarization effet |
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| 207 | |
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| 208 | G4double gFunction = (1.+(9.*velocity)+(31.*velocity*velocity)+(98.*std::pow(velocity,3.))+(12.*std::pow(velocity,4.))+(25.*std::pow(velocity,5.)) |
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| 209 | +(4.2*std::pow(velocity,6.))+(0.515*std::pow(velocity,7.)))/std::pow(1.+velocity,9.); //gFunction represents the correction for binding effet |
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| 210 | |
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| 211 | //----------------------------------------------------------------------------------------------------------------------------- |
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| 212 | |
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| 213 | G4double sigmaPSS = 1.+(((2.*zIncident)/(screenedzTarget*tetaK))*(gFunction-hFunction)); //describes the perturbed stationnairy state of the affected atomic electon |
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| 214 | |
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| 215 | //---------------------------------------------------------------------------------------------------------------------------- |
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| 216 | |
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| 217 | const G4double cNaturalUnit= 1/fine_structure_const; // it's the speed of light according to Atomic-Unit-System |
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| 218 | |
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| 219 | G4double ykFormula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocity/sigmaPSS); |
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| 220 | |
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| 221 | G4double relativityCorrection = std::pow((1.+(1.1*ykFormula*ykFormula)),0.5)+ykFormula;// the relativistic correction parameter |
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| 222 | |
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| 223 | G4double reducedVelocity = velocity*std::pow(relativityCorrection,0.5); // presents the reduced collision velocity parameter |
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| 224 | |
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| 225 | G4double universalFunction = (std::pow(2.,9.)/45.)*std::pow(reducedVelocity/sigmaPSS,8.)*std::pow((1.+(1.72*(reducedVelocity/sigmaPSS)*(reducedVelocity/sigmaPSS))),-4.);// is the reduced universal cross section |
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| 226 | |
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| 227 | //---------------------------------------------------------------------------------------------------------------------- |
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| 228 | |
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| 229 | G4double sigmaPSSR = (sigma0/(sigmaPSS*tetaK))*universalFunction; //sigmaPSSR is the straight-line K-shell ionization cross section |
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| 230 | |
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| 231 | //----------------------------------------------------------------------------------------------------------------------- |
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| 232 | |
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| 233 | G4double pssDeltaK = (4./(systemMass*sigmaPSS*tetaK))*(sigmaPSS/velocity)*(sigmaPSS/velocity); |
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| 234 | |
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| 235 | G4double energyLoss = std::pow(1-pssDeltaK,0.5); //energyLoss incorporates the straight-line energy-loss |
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| 236 | |
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| 237 | G4double energyLossFunction = (std::pow(2.,-9)/8.)*((((9.*energyLoss)-1.)*std::pow(1.+energyLoss,9.))+(((9.*energyLoss)+1.)*std::pow(1.-energyLoss,9.)));//energy loss function |
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| 238 | |
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| 239 | //---------------------------------------------------------------------------------------------------------------------------------------------- |
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| 240 | |
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| 241 | G4double coulombDeflection = (4.*pi*zIncident/systemMass)*std::pow(tetaK*sigmaPSS,-2.)*std::pow(velocity/sigmaPSS,-3.)*(zTarget/screenedzTarget); //incorporates Coulomb deflection parameter |
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| 242 | |
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| 243 | G4double cParameter = 2.*coulombDeflection/(energyLoss*(energyLoss+1.)); |
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| 244 | |
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| 245 | |
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| 246 | G4double coulombDeflectionFunction = 9.*ExpIntFunction(10,cParameter); //this function describes Coulomb-deflection effect |
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| 247 | |
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| 248 | //-------------------------------------------------------------------------------------------------------------------------------------------------- |
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| 249 | |
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| 250 | |
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| 251 | G4double crossSection = energyLossFunction* coulombDeflectionFunction*sigmaPSSR; //this ECPSSR cross section is estimated at perturbed-stationnairy-state(PSS) |
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| 252 | //and it's reduced by the energy-loss(E),the Coulomb deflection(C), |
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| 253 | //and the relativity(R) effects |
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| 254 | |
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| 255 | //-------------------------------------------------------------------------------------------------------------------------------------------------- |
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| 256 | |
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| 257 | return crossSection; |
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| 258 | } |
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| 259 | |
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| 260 | G4double G4ecpssrCrossSection::CalculateVelocity(G4int zTarget, G4int zIncident, G4double energyIncident) |
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| 261 | |
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| 262 | { |
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| 263 | |
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| 264 | G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance(); |
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| 265 | |
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| 266 | G4double kBindingEnergy = (transitionManager->Shell(zTarget,0)->BindingEnergy())/MeV; |
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| 267 | |
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| 268 | G4double massIncident; |
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| 269 | |
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| 270 | if (zIncident == 1) |
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| 271 | { |
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| 272 | G4Proton* aProtone = G4Proton::Proton(); |
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| 273 | |
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| 274 | massIncident = aProtone->GetPDGMass(); |
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| 275 | } |
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| 276 | else |
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| 277 | { |
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| 278 | if (zIncident == 2) |
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| 279 | { |
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| 280 | G4Alpha* aAlpha = G4Alpha::Alpha(); |
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| 281 | |
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| 282 | massIncident = aAlpha->GetPDGMass(); |
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| 283 | } |
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| 284 | else |
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| 285 | { |
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| 286 | G4cout << "we can treat only Proton or Alpha incident particles " << G4endl; |
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| 287 | massIncident =0.; |
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| 288 | } |
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| 289 | } |
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| 290 | |
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| 291 | const G4double zkshell= 0.3; |
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| 292 | |
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| 293 | G4double screenedzTarget = zTarget- zkshell; |
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| 294 | |
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| 295 | const G4double rydbergMeV= 13.6e-6; |
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| 296 | |
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| 297 | G4double tetaK = kBindingEnergy/(screenedzTarget*screenedzTarget*rydbergMeV); |
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| 298 | |
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| 299 | G4double velocity =(2./(tetaK*screenedzTarget))*std::pow(((energyIncident*electron_mass_c2)/(massIncident*rydbergMeV)),0.5); |
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| 300 | |
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| 301 | return velocity; |
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| 302 | } |
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| 303 | |
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