Gabriele Cosmo
712 lines
32 KiB
C++
712 lines
32 KiB
C++
//
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// ********************************************************************
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// * License and Disclaimer *
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// * *
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// * The Geant4 software is copyright of the Copyright Holders of *
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// * the Geant4 Collaboration. It is provided under the terms and *
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// * conditions of the Geant4 Software License, included in the file *
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// * LICENSE and available at http://cern.ch/geant4/license . These *
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// * include a list of copyright holders. *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. Please see the license in the file LICENSE and URL above *
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// * for the full disclaimer and the limitation of liability. *
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// * *
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// * This code implementation is the result of the scientific and *
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// * technical work of the GEANT4 collaboration. *
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// * By using, copying, modifying or distributing the software (or *
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// * any work based on the software) you agree to acknowledge its *
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// * use in resulting scientific publications, and indicate your *
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// * acceptance of all terms of the Geant4 Software license. *
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// ********************************************************************
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//
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//
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// -------------------------------------------------------------------
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//
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// GEANT4 Class file
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//
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//
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// File name: G4PairProductionRelModel
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//
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// Author: Andreas Schaelicke
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//
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// Creation date: 02.04.2009
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//
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// Modifications:
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// 20.03.17 Change LPMconstant such that it gives suppression variable 's'
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// that consistent to Migdal's one; fix a small bug in 'logTS1'
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// computation; suppression is consistent now with the one in the
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// brem. model (F.Hariri)
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// 28-05-18 New version with improved screening function approximation, improved
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// LPM function approximation, efficiency, documentation and cleanup.
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// Corrected call to selecting target atom in the final state sampling.
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// (M. Novak)
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//
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// Class Description:
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//
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// Main References:
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// J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 581.
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// S.Klein, Rev. Mod. Phys. 71 (1999) 1501.
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// T.Stanev et.al., Phys. Rev. D25 (1982) 1291.
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// M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media,
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// Wiley, 1972.
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//
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// -------------------------------------------------------------------
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#include "G4PairProductionRelModel.hh"
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#include "G4PhysicalConstants.hh"
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#include "G4SystemOfUnits.hh"
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#include "G4Gamma.hh"
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#include "G4Electron.hh"
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#include "G4Positron.hh"
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#include "G4ParticleChangeForGamma.hh"
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#include "G4LossTableManager.hh"
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#include "G4ModifiedTsai.hh"
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#include "G4Exp.hh"
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#include "G4Pow.hh"
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#include "G4AutoLock.hh"
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const G4int G4PairProductionRelModel::gMaxZet = 120;
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// LPM constant: \alpha(mc^2)^2/(4\pi*\hbar c)
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const G4double G4PairProductionRelModel::gLPMconstant =
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CLHEP::fine_structure_const*CLHEP::electron_mass_c2*CLHEP::electron_mass_c2
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/(4.*CLHEP::pi*CLHEP::hbarc);
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// abscissas and weights of an 8 point Gauss-Legendre quadrature
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// for numerical integration on [0,1]
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const G4double G4PairProductionRelModel::gXGL[] = {
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1.98550718e-02, 1.01666761e-01, 2.37233795e-01, 4.08282679e-01,
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5.91717321e-01, 7.62766205e-01, 8.98333239e-01, 9.80144928e-01
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};
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const G4double G4PairProductionRelModel::gWGL[] = {
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5.06142681e-02, 1.11190517e-01, 1.56853323e-01, 1.81341892e-01,
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1.81341892e-01, 1.56853323e-01, 1.11190517e-01, 5.06142681e-02
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};
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// elastic and inelatic radiation logarithms for light elements (where the
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// Thomas-Fermi model doesn't work): computed by using Dirac-Fock model of atom.
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const G4double G4PairProductionRelModel::gFelLowZet [] = {
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0.0, 5.3104, 4.7935, 4.7402, 4.7112, 4.6694, 4.6134, 4.5520
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};
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const G4double G4PairProductionRelModel::gFinelLowZet[] = {
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0.0, 5.9173, 5.6125, 5.5377, 5.4728, 5.4174, 5.3688, 5.3236
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};
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// constant cross section factor
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const G4double G4PairProductionRelModel::gXSecFactor =
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4.*CLHEP::fine_structure_const*CLHEP::classic_electr_radius
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*CLHEP::classic_electr_radius;
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// gamma energy limit above which LPM suppression will be applied (if the
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// fIsUseLPMCorrection flag is true)
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const G4double G4PairProductionRelModel::gEgLPMActivation = 100.*CLHEP::GeV;
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// special data structure per element i.e. per Z
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std::vector<G4PairProductionRelModel::ElementData*> G4PairProductionRelModel::gElementData;
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// LPM supression functions evaluated at initialisation time
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G4PairProductionRelModel::LPMFuncs G4PairProductionRelModel::gLPMFuncs;
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namespace
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{
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G4Mutex thePairProdRelMutex = G4MUTEX_INITIALIZER;
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}
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// CTR
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G4PairProductionRelModel::G4PairProductionRelModel(const G4ParticleDefinition*,
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const G4String& nam)
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: G4VEmModel(nam), fIsUseLPMCorrection(true), fIsUseCompleteScreening(false),
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fLPMEnergy(0.), fG4Calc(G4Pow::GetInstance()), fTheGamma(G4Gamma::Gamma()),
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fTheElectron(G4Electron::Electron()), fThePositron(G4Positron::Positron()),
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fParticleChange(nullptr)
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{
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// gamma energy below which the parametrized atomic x-section is used (30 GeV)
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fParametrizedXSectionThreshold = 30.0*CLHEP::GeV;
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// gamma energy below the Coulomb correction is turned off (50 MeV)
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fCoulombCorrectionThreshold = 50.0*CLHEP::MeV;
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// set angular generator used in the final state kinematics computation
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SetAngularDistribution(new G4ModifiedTsai());
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}
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// DTR
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G4PairProductionRelModel::~G4PairProductionRelModel()
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{
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if (isFirstInstance) {
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// clear ElementData container
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for (auto const & ptr : gElementData) { delete ptr; }
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gElementData.clear();
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// clear LPMFunctions (if any)
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if (fIsUseLPMCorrection) {
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gLPMFuncs.fLPMFuncG.clear();
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gLPMFuncs.fLPMFuncPhi.clear();
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gLPMFuncs.fIsInitialized = false;
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}
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}
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}
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void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p,
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const G4DataVector& cuts)
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{
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if(nullptr == fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
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if (isFirstInstance || gElementData.empty()) {
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// init element data and LPM funcs
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G4AutoLock l(&thePairProdRelMutex);
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if (gElementData.empty()) {
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isFirstInstance = true;
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gElementData.resize(gMaxZet+1, nullptr);
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}
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// static data should be initialised only in the one instance
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InitialiseElementData();
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if (fIsUseLPMCorrection) {
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InitLPMFunctions();
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}
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l.unlock();
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}
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// element selectors should be initialised in the master thread
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if (IsMaster()) {
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InitialiseElementSelectors(p, cuts);
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}
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}
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void G4PairProductionRelModel::InitialiseLocal(const G4ParticleDefinition*,
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G4VEmModel* masterModel)
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{
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SetElementSelectors(masterModel->GetElementSelectors());
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}
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G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double gammaEnergy,
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G4double Z)
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{
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G4double xSection = 0.0;
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// check if LPM suppression needs to be used
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const G4bool isLPM = (fIsUseLPMCorrection && gammaEnergy>gEgLPMActivation);
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// determine the kinematical limits (taken into account the correction due to
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// the way in which the Coulomb correction is applied i.e. avoid negative DCS)
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const G4int iz = std::min(gMaxZet, G4lrint(Z));
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const G4double eps0 = CLHEP::electron_mass_c2/gammaEnergy;
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// Coulomb correction is always included in the DCS even below 50 MeV (note:
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// that this DCS is only used to get the integrated x-section)
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const G4double dmax = gElementData[iz]->fDeltaMaxHigh;
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const G4double dmin = 4.*eps0*gElementData[iz]->fDeltaFactor;
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const G4double eps1 = 0.5 - 0.5*std::sqrt(1.-dmin/dmax);
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const G4double epsMin = std::max(eps0, eps1);
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const G4double epsMax = 0.5; // DCS is symmetric around eps=0.5
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// let Et be the total energy transferred to the e- or to the e+
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// the [Et-min, Et-max] interval will be divided into i=1,2,..,n subintervals
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// with width of dInterv = (Et-max - Et-min)/n and numerical integration will
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// be done in each sub-inteval using the xi = (Et - Et_i-min)/dInterv variable
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// that is in [0,1]. The 8-point GL q. is used for the integration on [0,1].
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const G4int numSub = 2;
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const G4double dInterv= (epsMax - epsMin)*gammaEnergy/G4double(numSub);
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G4double minEti = epsMin*gammaEnergy; // Et-min i.e. Et_0-min
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for (G4int i = 0; i < numSub; ++i) {
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for (G4int ngl = 0; ngl < 8; ++ngl) {
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const G4double Et = (minEti + gXGL[ngl]*dInterv);
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const G4double xs = isLPM ? ComputeRelDXSectionPerAtom(Et, gammaEnergy, Z)
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: ComputeDXSectionPerAtom(Et, gammaEnergy, Z);
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xSection += gWGL[ngl]*xs;
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}
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// update minimum Et of the sub-inteval
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minEti += dInterv;
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}
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// apply corrections of variable transformation and half interval integration
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xSection = std::max(2.*xSection*dInterv, 0.);
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return xSection;
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}
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// DCS WITHOUT LPM SUPPRESSION
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// Computes DCS value for a given target element (Z), initial gamma energy (Eg),
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// total energy transferred to one of the e-/e+ pair(Et) WITHOUT LPM suppression
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// The constant factor 4 \alpha r_0^2 Z (Z +\eta(Z)) is not included here and
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// the returned value will be differential in total energy transfer instead of
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// the eps=Et/Eg. The computed part of the DCS
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// NORMAL CASE: DEFAULT STTING (i.e. fIsUseCompleteScreening = FALSE)
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// ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = (eps^2+(1-eps)^2)*[phi1(d)/4-ln(Z)/3-fc]
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// + 2*eps(1-eps)*[phi2(d)/4-ln(Z)/3-fc]/3 where the universal (in the TF model)
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// screening variable d=d(eps)=136Z^(-1/3)eps0/[eps*(1-eps)] with eps0=mc^2/Eg.
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// COMPLETE SCREENING (when d(eps) approx-equal-to 0) : NEED TO BE SET BY USER
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// ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = (eps^2+(1-eps)^2+eps*(1-eps)/3)*[Lel-fc]
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// -eps(1-eps)/9 where Lel=phi1(0)/4-ln(Z)/3 is the elastic(coherent) radiation
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// logarithm, fc is the Coulomb correction and the relation phi2(0)/4-ln(Z)/3 =
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// phi1(0)/4-1/6-ln(Z)/3 = Lel-1/6 (due to phi2(0)=phi1(0)-2/3) was used.
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G4double G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double pEnergy,
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G4double gammaEnergy,
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G4double Z)
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{
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G4double xSection = 0.;
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const G4int iz = std::min(gMaxZet, G4lrint(Z));
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const G4double eps = pEnergy/gammaEnergy;
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const G4double epsm = 1.-eps;
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const G4double dum = eps*epsm;
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if (fIsUseCompleteScreening) {
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// complete screening:
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const G4double Lel = gElementData[iz]->fLradEl;
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const G4double fc = gElementData[iz]->fCoulomb;
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xSection = (eps*eps + epsm*epsm + 2.*dum/3.)*(Lel-fc) - dum/9.;
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} else {
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// normal case:
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const G4double eps0 = CLHEP::electron_mass_c2/gammaEnergy;
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const G4double fc = gElementData[iz]->fCoulomb;
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const G4double lnZ13 = gElementData[iz]->fLogZ13;
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const G4double delta = gElementData[iz]->fDeltaFactor*eps0/dum;
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G4double phi1, phi2;
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ComputePhi12(delta, phi1, phi2);
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xSection = (eps*eps + epsm*epsm)*(0.25*phi1-lnZ13-fc)
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+ 2.*dum*(0.25*phi2-lnZ13-fc)/3.;
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}
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// non-const. part of the DCS differential in total energy transfer not in eps
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// ds/dEt=ds/deps deps/dEt with deps/dEt=1/Eg
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return std::max(xSection, 0.0)/gammaEnergy;
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}
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// DCS WITH POSSIBLE LPM SUPPRESSION
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// Computes DCS value for a given target element (Z), initial gamma energy (Eg),
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// total energy transferred to one of the e-/e+ pair(Et) WITH LPM suppression.
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// For a given Z, the LPM suppression will depend on the material through the
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// LMP-Energy. This will determine the suppression variable s and the LPM sup-
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// pression functions xi(s), fi(s) and G(s).
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// The constant factor 4 \alpha r_0^2 Z (Z +\eta(Z)) is not included here and
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// the returned value will be differential in total energy transfer instead of
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// the eps=Et/Eg. The computed part of the DCS
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// NORMAL CASE: DEFAULT STTING (i.e. fIsUseCompleteScreening = FALSE)
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// ds/deps(Et,Eg,Z)=ds/deps(eps,Z) = xi(s)*{ (eps^2+(1-eps)^2)*[2fi(s)/3+G(s)/3]
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// *[phi1(d)/4-ln(Z)/3-fc] + 2*eps(1-eps)*G(s)*[phi2(d)/4-ln(Z)/3-fc]/3 } where
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// the universal (in the TF model) screening variable d=d(eps)=136Z^(-1/3)eps0
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// /[eps*(1-eps)] with eps0=mc^2/Eg.
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// COMPLETE SCREENING (when d(eps) approx-equal-to 0) : NEED TO BE SET BY USER
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// ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = xi(s)*{ [Lel-fc]*[ (eps^2+(1-eps)^2+eps
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// *(1-eps)/3)*2fi(s)/3 + G(s)/3] - eps(1-eps)*G(s)/9 }
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// Note, that when the LPM suppression is absent i.e. xi(s)=fi(s)=G(s)=1, both
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// the normal and the complete screening DCS give back the NO-LMP case above.
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G4double G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double pEnergy,
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G4double gammaEnergy,
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G4double Z)
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{
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G4double xSection = 0.;
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const G4int iz = std::min(gMaxZet, G4lrint(Z));
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const G4double eps = pEnergy/gammaEnergy;
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const G4double epsm = 1.-eps;
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const G4double dum = eps*epsm;
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// evaluate LPM suppression functions
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G4double fXiS, fGS, fPhiS;
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ComputeLPMfunctions(fXiS, fGS, fPhiS, eps, gammaEnergy, iz);
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if (fIsUseCompleteScreening) {
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// complete screening:
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const G4double Lel = gElementData[iz]->fLradEl;
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const G4double fc = gElementData[iz]->fCoulomb;
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xSection = (Lel-fc)*((eps*eps+epsm*epsm)*2.*fPhiS + fGS)/3. - dum*fGS/9.;
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} else {
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// normal case:
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const G4double eps0 = CLHEP::electron_mass_c2/gammaEnergy;
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const G4double fc = gElementData[iz]->fCoulomb;
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const G4double lnZ13 = gElementData[iz]->fLogZ13;
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const G4double delta = gElementData[iz]->fDeltaFactor*eps0/dum;
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G4double phi1, phi2;
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ComputePhi12(delta, phi1, phi2);
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xSection = (eps*eps + epsm*epsm)*(2.*fPhiS+fGS)*(0.25*phi1-lnZ13-fc)/3.
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+ 2.*dum*fGS*(0.25*phi2-lnZ13-fc)/3.;
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}
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// non-const. part of the DCS differential in total energy transfer not in eps
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// ds/dEt=ds/deps deps/dEt with deps/dEt=1/Eg
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return std::max(fXiS*xSection, 0.0)/gammaEnergy;
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}
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G4double
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G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
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G4double gammaEnergy, G4double Z, G4double, G4double, G4double)
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{
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G4double crossSection = 0.0 ;
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// check kinematical limit
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if ( gammaEnergy <= 2.0*electron_mass_c2 ) { return crossSection; }
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// compute the atomic cross section either by using x-section parametrization
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// or by numerically integrationg the DCS (with or without LPM)
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if ( gammaEnergy < fParametrizedXSectionThreshold) {
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// using the parametrized cross sections (max up to 80 GeV)
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crossSection = ComputeParametrizedXSectionPerAtom(gammaEnergy, Z);
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} else {
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// by numerical integration of the DCS:
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// Computes the cross section with or without LPM suppression depending on
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// settings (by default with if the gamma energy is above a given threshold)
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// and using or not using complete sreening approximation (by default not).
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// Only the dependent part is computed in the numerical integration of the DCS
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// i.e. the result must be multiplied here with 4 \alpha r_0^2 Z(Z+\eta(Z))
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crossSection = ComputeXSectionPerAtom(gammaEnergy, Z);
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// apply the constant factors:
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// - eta(Z) is a correction to account interaction in the field of e-
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// - gXSecFactor = 4 \alpha r_0^2
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const G4int iz = std::min(gMaxZet, G4lrint(Z));
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const G4double eta = gElementData[iz]->fEtaValue;
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crossSection *= gXSecFactor*Z*(Z+eta);
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}
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// final protection
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return std::max(crossSection, 0.);
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}
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void G4PairProductionRelModel::SetupForMaterial(const G4ParticleDefinition*,
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const G4Material* mat, G4double)
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{
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fLPMEnergy = mat->GetRadlen()*gLPMconstant;
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}
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void
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G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
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const G4MaterialCutsCouple* couple,
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const G4DynamicParticle* aDynamicGamma,
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G4double,
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G4double)
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// The secondaries e+e- energies are sampled using the Bethe - Heitler
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// cross sections with Coulomb correction.
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// A modified version of the random number techniques of Butcher & Messel
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// is used (Nuc Phys 20(1960),15).
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//
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// GEANT4 internal units.
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//
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// Note 1 : Effects due to the breakdown of the Born approximation at
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// low energy are ignored.
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// Note 2 : The differential cross section implicitly takes account of
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// pair creation in both nuclear and atomic electron fields.
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// However triplet prodution is not generated.
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{
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const G4Material* mat = couple->GetMaterial();
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const G4double gammaEnergy = aDynamicGamma->GetKineticEnergy();
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const G4double eps0 = CLHEP::electron_mass_c2/gammaEnergy ;
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//
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// check kinematical limit: gamma energy(Eg) must be at least 2 e- rest mass
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// (but the model should be used at higher energies above 100 MeV)
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if (eps0 > 0.5) { return; }
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//
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// select target atom of the material
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const G4Element* anElement = SelectTargetAtom(couple, fTheGamma, gammaEnergy,
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aDynamicGamma->GetLogKineticEnergy());
|
||
CLHEP::HepRandomEngine* rndmEngine = G4Random::getTheEngine();
|
||
//
|
||
// 'eps' is the total energy transferred to one of the e-/e+ pair in initial
|
||
// gamma energy units Eg. Since the corresponding DCS is symmetric on eps=0.5,
|
||
// the kinematical limits for eps0=mc^2/Eg <= eps <= 0.5
|
||
// 1. 'eps' is sampled uniformly on the [eps0, 0.5] inteval if Eg<Egsmall
|
||
// 2. otherwise, on the [eps_min, 0.5] interval according to the DCS (case 2.)
|
||
G4double eps;
|
||
// case 1.
|
||
static const G4double Egsmall = 2.*CLHEP::MeV;
|
||
if (gammaEnergy < Egsmall) {
|
||
eps = eps0 + (0.5-eps0)*rndmEngine->flat();
|
||
} else {
|
||
// case 2.
|
||
// get the Coulomb factor for the target element (Z) and gamma energy (Eg)
|
||
// F(Z) = 8*ln(Z)/3 if Eg <= 50 [MeV] => no Coulomb correction
|
||
// F(Z) = 8*ln(Z)/3 + 8*fc(Z) if Eg > 50 [MeV] => fc(Z) is the Coulomb cor.
|
||
//
|
||
// The screening variable 'delta(eps)' = 136*Z^{-1/3}*eps0/[eps(1-eps)]
|
||
// Due to the Coulomb correction, the DCS can go below zero even at
|
||
// kinematicaly allowed eps > eps0 values. In order to exclude this eps
|
||
// range with negative DCS, the minimum eps value will be set to eps_min =
|
||
// max[eps0, epsp] with epsp is the solution of SF(delta(epsp)) - F(Z)/2 = 0
|
||
// with SF being the screening function (SF1=SF2 at high value of delta).
|
||
// The solution is epsp = 0.5 - 0.5*sqrt[ 1 - 4*136*Z^{-1/3}eps0/deltap]
|
||
// with deltap = Exp[(42.038-F(Z))/8.29]-0.958. So the limits are:
|
||
// - when eps=eps_max = 0.5 => delta_min = 136*Z^{-1/3}*eps0/4
|
||
// - epsp = 0.5 - 0.5*sqrt[ 1 - delta_min/deltap]
|
||
// - and eps_min = max[eps0, epsp]
|
||
const G4int iZet = std::min(gMaxZet, anElement->GetZasInt());
|
||
const G4double deltaFactor = gElementData[iZet]->fDeltaFactor*eps0;
|
||
const G4double deltaMin = 4.*deltaFactor;
|
||
G4double deltaMax = gElementData[iZet]->fDeltaMaxLow;
|
||
G4double FZ = 8.*gElementData[iZet]->fLogZ13;
|
||
if ( gammaEnergy > fCoulombCorrectionThreshold ) { // Eg > 50 MeV ?
|
||
FZ += 8.*gElementData[iZet]->fCoulomb;
|
||
deltaMax = gElementData[iZet]->fDeltaMaxHigh;
|
||
}
|
||
// compute the limits of eps
|
||
const G4double epsp = 0.5 - 0.5*std::sqrt(1. - deltaMin/deltaMax) ;
|
||
const G4double epsMin = std::max(eps0,epsp);
|
||
const G4double epsRange = 0.5 - epsMin;
|
||
//
|
||
// sample the energy rate (eps) of the created electron (or positron)
|
||
G4double F10, F20;
|
||
ScreenFunction12(deltaMin, F10, F20);
|
||
F10 -= FZ;
|
||
F20 -= FZ;
|
||
const G4double NormF1 = std::max(F10 * epsRange * epsRange, 0.);
|
||
const G4double NormF2 = std::max(1.5 * F20 , 0.);
|
||
const G4double NormCond = NormF1/(NormF1 + NormF2);
|
||
// check if LPM correction is active
|
||
const G4bool isLPM = (fIsUseLPMCorrection && gammaEnergy>gEgLPMActivation);
|
||
fLPMEnergy = mat->GetRadlen()*gLPMconstant;
|
||
// we will need 3 uniform random number for each trial of sampling
|
||
G4double rndmv[3];
|
||
G4double greject = 0.;
|
||
do {
|
||
rndmEngine->flatArray(3, rndmv);
|
||
if (NormCond > rndmv[0]) {
|
||
eps = 0.5 - epsRange * fG4Calc->A13(rndmv[1]);
|
||
const G4double delta = deltaFactor/(eps*(1.-eps));
|
||
if (isLPM) {
|
||
G4double lpmXiS, lpmGS, lpmPhiS, phi1, phi2;
|
||
ComputePhi12(delta, phi1, phi2);
|
||
ComputeLPMfunctions(lpmXiS, lpmGS, lpmPhiS, eps, gammaEnergy, iZet);
|
||
greject = lpmXiS*((2.*lpmPhiS+lpmGS)*phi1-lpmGS*phi2-lpmPhiS*FZ)/F10;
|
||
} else {
|
||
greject = (ScreenFunction1(delta)-FZ)/F10;
|
||
}
|
||
} else {
|
||
eps = epsMin + epsRange*rndmv[1];
|
||
const G4double delta = deltaFactor/(eps*(1.-eps));
|
||
if (isLPM) {
|
||
G4double lpmXiS, lpmGS, lpmPhiS, phi1, phi2;
|
||
ComputePhi12(delta, phi1, phi2);
|
||
ComputeLPMfunctions(lpmXiS, lpmGS, lpmPhiS, eps, gammaEnergy, iZet);
|
||
greject = lpmXiS*( (lpmPhiS+0.5*lpmGS)*phi1 + 0.5*lpmGS*phi2
|
||
-0.5*(lpmGS+lpmPhiS)*FZ )/F20;
|
||
} else {
|
||
greject = (ScreenFunction2(delta)-FZ)/F20;
|
||
}
|
||
}
|
||
// Loop checking, 03-Aug-2015, Vladimir Ivanchenko
|
||
} while (greject < rndmv[2]);
|
||
// end of eps sampling
|
||
}
|
||
//
|
||
// select charges randomly
|
||
G4double eTotEnergy, pTotEnergy;
|
||
if (rndmEngine->flat() > 0.5) {
|
||
eTotEnergy = (1.-eps)*gammaEnergy;
|
||
pTotEnergy = eps*gammaEnergy;
|
||
} else {
|
||
pTotEnergy = (1.-eps)*gammaEnergy;
|
||
eTotEnergy = eps*gammaEnergy;
|
||
}
|
||
//
|
||
// sample pair kinematics
|
||
//
|
||
const G4double eKinEnergy = std::max(0.,eTotEnergy - CLHEP::electron_mass_c2);
|
||
const G4double pKinEnergy = std::max(0.,pTotEnergy - CLHEP::electron_mass_c2);
|
||
//
|
||
G4ThreeVector eDirection, pDirection;
|
||
//
|
||
GetAngularDistribution()->SamplePairDirections(aDynamicGamma,
|
||
eKinEnergy, pKinEnergy, eDirection, pDirection);
|
||
// create G4DynamicParticle object for the particle1
|
||
auto aParticle1 = new G4DynamicParticle(fTheElectron,eDirection,eKinEnergy);
|
||
|
||
// create G4DynamicParticle object for the particle2
|
||
auto aParticle2 = new G4DynamicParticle(fThePositron,pDirection,pKinEnergy);
|
||
// Fill output vector
|
||
fvect->push_back(aParticle1);
|
||
fvect->push_back(aParticle2);
|
||
// kill incident photon
|
||
fParticleChange->SetProposedKineticEnergy(0.);
|
||
fParticleChange->ProposeTrackStatus(fStopAndKill);
|
||
}
|
||
|
||
// should be called only by the master and at initialisation
|
||
void G4PairProductionRelModel::InitialiseElementData()
|
||
{
|
||
// create for all elements that are in the detector
|
||
auto elemTable = G4Element::GetElementTable();
|
||
for (auto const & elem : *elemTable) {
|
||
const G4int iz = std::min(gMaxZet, elem->GetZasInt());
|
||
if (nullptr == gElementData[iz]) { // create it if doesn't exist yet
|
||
const G4double logZ13 = elem->GetIonisation()->GetlogZ3();
|
||
const G4double Z13 = elem->GetIonisation()->GetZ3();
|
||
const G4double fc = elem->GetfCoulomb();
|
||
const G4double FZLow = 8.*logZ13;
|
||
const G4double FZHigh = 8.*(logZ13 + fc);
|
||
G4double Fel;
|
||
G4double Finel;
|
||
if (iz<5) { // use data from Dirac-Fock atomic model
|
||
Fel = gFelLowZet[iz];
|
||
Finel = gFinelLowZet[iz];
|
||
} else { // use the results of the Thomas-Fermi-Moliere model
|
||
Fel = G4Log(184.) - logZ13;
|
||
Finel = G4Log(1194.) - 2.*logZ13;
|
||
}
|
||
auto elD = new ElementData();
|
||
elD->fLogZ13 = logZ13;
|
||
elD->fCoulomb = fc;
|
||
elD->fLradEl = Fel;
|
||
elD->fDeltaFactor = 136./Z13;
|
||
elD->fDeltaMaxLow = G4Exp((42.038 - FZLow)/8.29) - 0.958;
|
||
elD->fDeltaMaxHigh = G4Exp((42.038 - FZHigh)/8.29) - 0.958;
|
||
elD->fEtaValue = Finel/(Fel-fc);
|
||
elD->fLPMVarS1Cond = std::sqrt(2.)*Z13*Z13/(184.*184.);
|
||
elD->fLPMILVarS1Cond = 1./G4Log(elD->fLPMVarS1Cond);
|
||
gElementData[iz] = elD;
|
||
}
|
||
}
|
||
}
|
||
|
||
// s goes up to 2 with ds = 0.01 be default
|
||
void G4PairProductionRelModel::InitLPMFunctions() {
|
||
if (!gLPMFuncs.fIsInitialized) {
|
||
const G4int num = gLPMFuncs.fSLimit*gLPMFuncs.fISDelta+1;
|
||
gLPMFuncs.fLPMFuncG.resize(num);
|
||
gLPMFuncs.fLPMFuncPhi.resize(num);
|
||
for (G4int i=0; i<num; ++i) {
|
||
const G4double sval = i/gLPMFuncs.fISDelta;
|
||
ComputeLPMGsPhis(gLPMFuncs.fLPMFuncG[i],gLPMFuncs.fLPMFuncPhi[i],sval);
|
||
}
|
||
gLPMFuncs.fIsInitialized = true;
|
||
}
|
||
}
|
||
|
||
// used only at initialisation time
|
||
void G4PairProductionRelModel::ComputeLPMGsPhis(G4double &funcGS, G4double &funcPhiS, const G4double varShat) {
|
||
if (varShat < 0.01) {
|
||
funcPhiS = 6.0*varShat*(1.0-CLHEP::pi*varShat);
|
||
funcGS = 12.0*varShat-2.0*funcPhiS;
|
||
} else {
|
||
const G4double varShat2 = varShat*varShat;
|
||
const G4double varShat3 = varShat*varShat2;
|
||
const G4double varShat4 = varShat2*varShat2;
|
||
if (varShat < 0.415827397755) { // Stanev ap.: for \psi(s) and compute G(s)
|
||
funcPhiS = 1.0-G4Exp( -6.0*varShat*(1.0+varShat*(3.0-CLHEP::pi))
|
||
+ varShat3/(0.623+0.796*varShat+0.658*varShat2));
|
||
// 1-\exp \left\{-4s-\frac{8s^2}{1+3.936s+4.97s^2-0.05s^3+7.5s^4} \right\}
|
||
const G4double funcPsiS = 1.0-G4Exp( -4.0*varShat - 8.0*varShat2/(1.0
|
||
+ 3.936*varShat+4.97*varShat2-0.05*varShat3+7.5*varShat4));
|
||
// G(s) = 3 \psi(s) - 2 \phi(s)
|
||
funcGS = 3.0*funcPsiS - 2.0*funcPhiS;
|
||
} else if (varShat < 1.55) {
|
||
funcPhiS = 1.0-G4Exp( -6.0*varShat*(1.0+varShat*(3.0-CLHEP::pi))
|
||
+ varShat3/(0.623+0.796*varShat+0.658*varShat2));
|
||
const G4double dum0 = -0.16072300849123999+3.7550300067531581*varShat
|
||
-1.7981383069010097 *varShat2
|
||
+0.67282686077812381*varShat3
|
||
-0.1207722909879257 *varShat4;
|
||
funcGS = std::tanh(dum0);
|
||
} else {
|
||
funcPhiS = 1.0-0.01190476/varShat4;
|
||
if (varShat < 1.9156) {
|
||
const G4double dum0 = -0.16072300849123999+3.7550300067531581*varShat
|
||
-1.7981383069010097 *varShat2
|
||
+0.67282686077812381*varShat3
|
||
-0.1207722909879257 *varShat4;
|
||
funcGS = std::tanh(dum0);
|
||
} else {
|
||
funcGS = 1.0-0.0230655/varShat4;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
// used at run-time to get some pre-computed LPM function values
|
||
void G4PairProductionRelModel::GetLPMFunctions(G4double &lpmGs,
|
||
G4double &lpmPhis,
|
||
const G4double sval) {
|
||
if (sval < gLPMFuncs.fSLimit) {
|
||
G4double val = sval*gLPMFuncs.fISDelta;
|
||
const G4int ilow = (G4int)val;
|
||
val -= ilow;
|
||
lpmGs = (gLPMFuncs.fLPMFuncG[ilow+1]-gLPMFuncs.fLPMFuncG[ilow])*val
|
||
+ gLPMFuncs.fLPMFuncG[ilow];
|
||
lpmPhis = (gLPMFuncs.fLPMFuncPhi[ilow+1]-gLPMFuncs.fLPMFuncPhi[ilow])*val
|
||
+ gLPMFuncs.fLPMFuncPhi[ilow];
|
||
} else {
|
||
G4double ss = sval*sval;
|
||
ss *= ss;
|
||
lpmPhis = 1.0-0.01190476/ss;
|
||
lpmGs = 1.0-0.0230655/ss;
|
||
}
|
||
}
|
||
|
||
void G4PairProductionRelModel::ComputeLPMfunctions(G4double &funcXiS,
|
||
G4double &funcGS, G4double &funcPhiS, const G4double eps,
|
||
const G4double egamma, const G4int izet)
|
||
{
|
||
// 1. y = E_+/E_{\gamma} with E_+ being the total energy transfered
|
||
// to one of the e-/e+ pair
|
||
// s' = \sqrt{ \frac{1}{8} \frac{1}{y(1-y)} \frac{E^{KL}_{LPM}}{E_{\gamma}} }
|
||
const G4double varSprime = std::sqrt(0.125*fLPMEnergy/(eps*egamma*(1.0-eps)));
|
||
const G4double condition = gElementData[izet]->fLPMVarS1Cond;
|
||
funcXiS = 2.0;
|
||
if (varSprime > 1.0) {
|
||
funcXiS = 1.0;
|
||
} else if (varSprime > condition) {
|
||
const G4double dum = gElementData[izet]->fLPMILVarS1Cond;
|
||
const G4double funcHSprime = G4Log(varSprime)*dum;
|
||
funcXiS = 1.0 + funcHSprime
|
||
- 0.08*(1.0-funcHSprime)*funcHSprime*(2.0-funcHSprime)*dum;
|
||
}
|
||
// 2. s=\frac{s'}{\sqrt{\xi(s')}}
|
||
const G4double varShat = varSprime / std::sqrt(funcXiS);
|
||
GetLPMFunctions(funcGS, funcPhiS, varShat);
|
||
// MAKE SURE SUPPRESSION IS SMALLER THAN 1: due to Migdal's approximation on xi
|
||
if (funcXiS * funcPhiS > 1. || varShat > 0.57) {
|
||
funcXiS = 1. / funcPhiS;
|
||
}
|
||
}
|
||
|
||
// Calculates the microscopic cross section in GEANT4 internal units. Same as in
|
||
// G4BetheHeitlerModel and should be used below 80 GeV since it start to deverge
|
||
// from the cross section data above 80-90 GeV:
|
||
// Parametrized formula (L. Urban) is used to estimate the atomic cross sections
|
||
// given numerically in the table of [Hubbell, J. H., Heinz Albert Gimm, and I.
|
||
// Overbo: "Pair, Triplet, and Total Atomic Cross Sections (and Mass Attenuation
|
||
// Coefficients) for 1 MeV‐100 GeV Photons in Elements Z= 1 to 100." Journal of
|
||
// physical and chemical reference data 9.4 (1980): 1023-1148.]
|
||
//
|
||
// The formula gives a good approximation of the data from 1.5 MeV to 100 GeV.
|
||
// below 1.5 MeV: sigma=sigma(1.5MeV)*(GammaEnergy-2electronmass)
|
||
// *(GammaEnergy-2electronmass)
|
||
G4double
|
||
G4PairProductionRelModel::ComputeParametrizedXSectionPerAtom(G4double gammaE,
|
||
G4double Z)
|
||
{
|
||
G4double xSection = 0.0 ;
|
||
// short versions
|
||
static const G4double kMC2 = CLHEP::electron_mass_c2;
|
||
// zero cross section below the kinematical limit: Eg<2mc^2
|
||
if (Z < 0.9 || gammaE <= 2.0*kMC2) { return xSection; }
|
||
//
|
||
static const G4double gammaEnergyLimit = 1.5*CLHEP::MeV;
|
||
// set coefficients a, b c
|
||
static const G4double a0 = 8.7842e+2*CLHEP::microbarn;
|
||
static const G4double a1 = -1.9625e+3*CLHEP::microbarn;
|
||
static const G4double a2 = 1.2949e+3*CLHEP::microbarn;
|
||
static const G4double a3 = -2.0028e+2*CLHEP::microbarn;
|
||
static const G4double a4 = 1.2575e+1*CLHEP::microbarn;
|
||
static const G4double a5 = -2.8333e-1*CLHEP::microbarn;
|
||
|
||
static const G4double b0 = -1.0342e+1*CLHEP::microbarn;
|
||
static const G4double b1 = 1.7692e+1*CLHEP::microbarn;
|
||
static const G4double b2 = -8.2381 *CLHEP::microbarn;
|
||
static const G4double b3 = 1.3063 *CLHEP::microbarn;
|
||
static const G4double b4 = -9.0815e-2*CLHEP::microbarn;
|
||
static const G4double b5 = 2.3586e-3*CLHEP::microbarn;
|
||
|
||
static const G4double c0 = -4.5263e+2*CLHEP::microbarn;
|
||
static const G4double c1 = 1.1161e+3*CLHEP::microbarn;
|
||
static const G4double c2 = -8.6749e+2*CLHEP::microbarn;
|
||
static const G4double c3 = 2.1773e+2*CLHEP::microbarn;
|
||
static const G4double c4 = -2.0467e+1*CLHEP::microbarn;
|
||
static const G4double c5 = 6.5372e-1*CLHEP::microbarn;
|
||
// check low energy limit of the approximation (1.5 MeV)
|
||
G4double gammaEnergyOrg = gammaE;
|
||
if (gammaE < gammaEnergyLimit) { gammaE = gammaEnergyLimit; }
|
||
// compute gamma energy variables
|
||
const G4double x = G4Log(gammaE/kMC2);
|
||
const G4double x2 = x *x;
|
||
const G4double x3 = x2*x;
|
||
const G4double x4 = x3*x;
|
||
const G4double x5 = x4*x;
|
||
//
|
||
const G4double F1 = a0 + a1*x + a2*x2 + a3*x3 + a4*x4 + a5*x5;
|
||
const G4double F2 = b0 + b1*x + b2*x2 + b3*x3 + b4*x4 + b5*x5;
|
||
const G4double F3 = c0 + c1*x + c2*x2 + c3*x3 + c4*x4 + c5*x5;
|
||
// compute the approximated cross section
|
||
xSection = (Z + 1.)*(F1*Z + F2*Z*Z + F3);
|
||
// check if we are below the limit of the approximation and apply correction
|
||
if (gammaEnergyOrg < gammaEnergyLimit) {
|
||
const G4double dum = (gammaEnergyOrg-2.*kMC2)/(gammaEnergyLimit-2.*kMC2);
|
||
xSection *= dum*dum;
|
||
}
|
||
return xSection;
|
||
}
|
||
|
||
|