| Geant4 Cross Reference |
1 // 1 //
2 // ******************************************* 2 // ********************************************************************
3 // * License and Disclaimer 3 // * License and Disclaimer *
4 // * 4 // * *
5 // * The Geant4 software is copyright of th 5 // * The Geant4 software is copyright of the Copyright Holders of *
6 // * the Geant4 Collaboration. It is provided 6 // * the Geant4 Collaboration. It is provided under the terms and *
7 // * conditions of the Geant4 Software License 7 // * conditions of the Geant4 Software License, included in the file *
8 // * LICENSE and available at http://cern.ch/ 8 // * LICENSE and available at http://cern.ch/geant4/license . These *
9 // * include a list of copyright holders. 9 // * include a list of copyright holders. *
10 // * 10 // * *
11 // * Neither the authors of this software syst 11 // * Neither the authors of this software system, nor their employing *
12 // * institutes,nor the agencies providing fin 12 // * institutes,nor the agencies providing financial support for this *
13 // * work make any representation or warran 13 // * work make any representation or warranty, express or implied, *
14 // * regarding this software system or assum 14 // * regarding this software system or assume any liability for its *
15 // * use. Please see the license in the file 15 // * use. Please see the license in the file LICENSE and URL above *
16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. *
17 // * 17 // * *
18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and *
19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. *
20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or *
21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its *
22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your *
23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. *
24 // ******************************************* 24 // ********************************************************************
25 // 25 //
>> 26 // $Id: G4PairProductionRelModel.cc 108504 2018-02-15 15:46:37Z gcosmo $
26 // 27 //
27 // ------------------------------------------- 28 // -------------------------------------------------------------------
28 // 29 //
29 // GEANT4 Class file 30 // GEANT4 Class file
30 // 31 //
31 // 32 //
32 // File name: G4PairProductionRelModel 33 // File name: G4PairProductionRelModel
33 // 34 //
34 // Author: Andreas Schaelicke 35 // Author: Andreas Schaelicke
35 // 36 //
36 // Creation date: 02.04.2009 37 // Creation date: 02.04.2009
37 // 38 //
38 // Modifications: 39 // Modifications:
39 // 20.03.17 Change LPMconstant such that it gi << 40 //
40 // that consistent to Migdal's one; f << 41 // 20.03.17 change LPMconstant such that it gives suppression variable 's'
41 // computation; suppression is consis << 42 // that consistent to Migdal's one; fix a small bug in 'logTS1'
42 // brem. model (F.Hariri) << 43 // computation; suppression is consistent now with the one in the
43 // 28-05-18 New version with improved screenin << 44 // brem. model (F.Hariri)
44 // LPM function approximation, effici <<
45 // Corrected call to selecting target <<
46 // (M. Novak) <<
47 // 45 //
48 // Class Description: 46 // Class Description:
49 // 47 //
50 // Main References: 48 // Main References:
51 // J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 49 // J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 581.
52 // S.Klein, Rev. Mod. Phys. 71 (1999) 1501. 50 // S.Klein, Rev. Mod. Phys. 71 (1999) 1501.
53 // T.Stanev et.al., Phys. Rev. D25 (1982) 129 51 // T.Stanev et.al., Phys. Rev. D25 (1982) 1291.
54 // M.L.Ter-Mikaelian, High-energy Electromagn 52 // M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media,
55 // Wiley, 1972. 53 // Wiley, 1972.
56 // 54 //
57 // ------------------------------------------- 55 // -------------------------------------------------------------------
>> 56 //
>> 57 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 58 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
58 59
59 #include "G4PairProductionRelModel.hh" 60 #include "G4PairProductionRelModel.hh"
60 #include "G4PhysicalConstants.hh" 61 #include "G4PhysicalConstants.hh"
61 #include "G4SystemOfUnits.hh" 62 #include "G4SystemOfUnits.hh"
62 #include "G4Gamma.hh" 63 #include "G4Gamma.hh"
63 #include "G4Electron.hh" 64 #include "G4Electron.hh"
64 #include "G4Positron.hh" 65 #include "G4Positron.hh"
65 #include "G4ParticleChangeForGamma.hh" 66 #include "G4ParticleChangeForGamma.hh"
66 #include "G4LossTableManager.hh" 67 #include "G4LossTableManager.hh"
67 #include "G4ModifiedTsai.hh" <<
68 #include "G4Exp.hh" <<
69 #include "G4Pow.hh" <<
70 #include "G4AutoLock.hh" <<
71 <<
72 const G4int G4PairProductionRelModel::gMaxZet <<
73 <<
74 // LPM constant: \alpha(mc^2)^2/(4\pi*\hbar c) <<
75 const G4double G4PairProductionRelModel::gLPMc <<
76 CLHEP::fine_structure_const*CLHEP::electron_ <<
77 /(4.*CLHEP::pi*CLHEP::hbarc); <<
78 <<
79 // abscissas and weights of an 8 point Gauss-L <<
80 // for numerical integration on [0,1] <<
81 const G4double G4PairProductionRelModel::gXGL[ <<
82 1.98550718e-02, 1.01666761e-01, 2.37233795e- <<
83 5.91717321e-01, 7.62766205e-01, 8.98333239e- <<
84 }; <<
85 const G4double G4PairProductionRelModel::gWGL[ <<
86 5.06142681e-02, 1.11190517e-01, 1.56853323e- <<
87 1.81341892e-01, 1.56853323e-01, 1.11190517e- <<
88 }; <<
89 <<
90 // elastic and inelatic radiation logarithms f <<
91 // Thomas-Fermi model doesn't work): computed <<
92 const G4double G4PairProductionRelModel::gFelL <<
93 0.0, 5.3104, 4.7935, 4.7402, 4.7112, 4.6694, <<
94 }; <<
95 const G4double G4PairProductionRelModel::gFine <<
96 0.0, 5.9173, 5.6125, 5.5377, 5.4728, 5.4174, <<
97 }; <<
98 <<
99 // constant cross section factor <<
100 const G4double G4PairProductionRelModel::gXSec <<
101 4.*CLHEP::fine_structure_const*CLHEP::classi <<
102 *CLHEP::classic_electr_radius; <<
103 <<
104 // gamma energy limit above which LPM suppress <<
105 // fIsUseLPMCorrection flag is true) <<
106 const G4double G4PairProductionRelModel::gEgLP <<
107 68
108 // special data structure per element i.e. per << 69 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
109 std::vector<G4PairProductionRelModel::ElementD <<
110 70
111 // LPM supression functions evaluated at initi << 71 using namespace std;
112 G4PairProductionRelModel::LPMFuncs G4PairProdu <<
113 72
114 namespace << 73 const G4double G4PairProductionRelModel::facFel = G4Log(184.15);
115 { << 74 const G4double G4PairProductionRelModel::facFinel = G4Log(1194.); // 1440.
116 G4Mutex thePairProdRelMutex = G4MUTEX_INITIA << 75
117 } << 76 const G4double G4PairProductionRelModel::preS1 = 1./(184.15*184.15);
>> 77 const G4double G4PairProductionRelModel::logTwo = G4Log(2.);
>> 78
>> 79 const G4double G4PairProductionRelModel::xgi[]={ 0.0199, 0.1017, 0.2372, 0.4083,
>> 80 0.5917, 0.7628, 0.8983, 0.9801 };
>> 81 const G4double G4PairProductionRelModel::wgi[]={ 0.0506, 0.1112, 0.1569, 0.1813,
>> 82 0.1813, 0.1569, 0.1112, 0.0506 };
>> 83 const G4double G4PairProductionRelModel::Fel_light[] = {0., 5.31 , 4.79 , 4.74 , 4.71};
>> 84 const G4double G4PairProductionRelModel::Finel_light[] = {0., 6.144 , 5.621 , 5.805 , 5.924};
>> 85
>> 86 const G4double G4PairProductionRelModel::xsfactor =
>> 87 4*CLHEP::fine_structure_const*CLHEP::classic_electr_radius*CLHEP::classic_electr_radius;
>> 88 const G4double G4PairProductionRelModel::Egsmall = 2.*CLHEP::MeV;
>> 89 const G4double G4PairProductionRelModel::Eghigh = 100.*CLHEP::GeV;
118 90
119 // CTR <<
120 G4PairProductionRelModel::G4PairProductionRelM 91 G4PairProductionRelModel::G4PairProductionRelModel(const G4ParticleDefinition*,
121 << 92 const G4String& nam)
122 : G4VEmModel(nam), fIsUseLPMCorrection(true) << 93 : G4VEmModel(nam),
123 fLPMEnergy(0.), fG4Calc(G4Pow::GetInstance() << 94 fLPMconstant(CLHEP::fine_structure_const*CLHEP::electron_mass_c2*CLHEP::electron_mass_c2/
124 fTheElectron(G4Electron::Electron()), fThePo << 95 (4.*CLHEP::pi*CLHEP::hbarc)),
125 fParticleChange(nullptr) << 96 fLPMflag(true),
>> 97 lpmEnergy(0.),
>> 98 use_completescreening(false)
126 { 99 {
127 // gamma energy below which the parametrized << 100 fParticleChange = nullptr;
128 fParametrizedXSectionThreshold = 30.0*CLHEP: << 101 theGamma = G4Gamma::Gamma();
129 // gamma energy below the Coulomb correction << 102 thePositron = G4Positron::Positron();
130 fCoulombCorrectionThreshold = 50.0*CLHEP: << 103 theElectron = G4Electron::Electron();
131 // set angular generator used in the final s << 104
132 SetAngularDistribution(new G4ModifiedTsai()) << 105 g4calc = G4Pow::GetInstance();
>> 106
>> 107 currentZ = z13 = z23 = lnZ = Fel = Finel = fCoulomb = phiLPM = gLPM = xiLPM = 0;
133 } 108 }
134 109
135 // DTR << 110 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 111
136 G4PairProductionRelModel::~G4PairProductionRel 112 G4PairProductionRelModel::~G4PairProductionRelModel()
137 { << 113 {}
138 if (isFirstInstance) { << 114
139 // clear ElementData container << 115 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
140 for (auto const & ptr : gElementData) { de <<
141 gElementData.clear(); <<
142 // clear LPMFunctions (if any) <<
143 if (fIsUseLPMCorrection) { <<
144 gLPMFuncs.fLPMFuncG.clear(); <<
145 gLPMFuncs.fLPMFuncPhi.clear(); <<
146 gLPMFuncs.fIsInitialized = false; <<
147 } <<
148 } <<
149 } <<
150 116
151 void G4PairProductionRelModel::Initialise(cons 117 void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p,
152 cons << 118 const G4DataVector& cuts)
153 { 119 {
154 if(nullptr == fParticleChange) { fParticleCh << 120 if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
155 << 121 if(IsMaster() && LowEnergyLimit() < HighEnergyLimit()) {
156 if (isFirstInstance || gElementData.empty()) <<
157 // init element data and LPM funcs <<
158 G4AutoLock l(&thePairProdRelMutex); <<
159 if (gElementData.empty()) { <<
160 isFirstInstance = true; <<
161 gElementData.resize(gMaxZet+1, nullptr); <<
162 } <<
163 // static data should be initialised only <<
164 InitialiseElementData(); <<
165 if (fIsUseLPMCorrection) { <<
166 InitLPMFunctions(); <<
167 } <<
168 l.unlock(); <<
169 } <<
170 // element selectors should be initialised i <<
171 if (IsMaster()) { <<
172 InitialiseElementSelectors(p, cuts); 122 InitialiseElementSelectors(p, cuts);
173 } 123 }
174 } 124 }
175 125
>> 126 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 127
176 void G4PairProductionRelModel::InitialiseLocal 128 void G4PairProductionRelModel::InitialiseLocal(const G4ParticleDefinition*,
177 << 129 G4VEmModel* masterModel)
178 { 130 {
179 SetElementSelectors(masterModel->GetElementS << 131 if(LowEnergyLimit() < HighEnergyLimit()) {
>> 132 SetElementSelectors(masterModel->GetElementSelectors());
>> 133 }
180 } 134 }
181 135
182 G4double G4PairProductionRelModel::ComputeXSec << 136 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
183 << 137
>> 138 G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double totalEnergy, G4double Z)
184 { 139 {
185 G4double xSection = 0.0; << 140 G4double cross = 0.0;
186 // check if LPM suppression needs to be used << 141
187 const G4bool isLPM = (fIsUseLPMCorrection << 142 // number of intervals and integration step
188 // determine the kinematical limits (taken i << 143 G4double vcut = electron_mass_c2/totalEnergy ;
189 // the way in which the Coulomb correction i << 144
190 const G4int iz = std::min(gMaxZet, G4 << 145 // limits by the screening variable
191 const G4double eps0 = CLHEP::electron_mass << 146 G4double dmax = DeltaMax();
192 // Coulomb correction is always included in << 147 G4double dmin = std::min(DeltaMin(totalEnergy),dmax);
193 // that this DCS is only used to get the int << 148 G4double vcut1 = 0.5 - 0.5*sqrt(1. - dmin/dmax);
194 const G4double dmax = gElementData[iz]->fD << 149 vcut = max(vcut, vcut1);
195 const G4double dmin = 4.*eps0*gElementData << 150
196 const G4double eps1 = 0.5 - 0.5*std::sqrt( << 151 G4double vmax = 0.5;
197 const G4double epsMin = std::max(eps0, eps1) << 152 G4int n = 1; // needs optimisation
198 const G4double epsMax = 0.5; // DCS is symme << 153
199 // let Et be the total energy transferred to << 154 G4double delta = (vmax - vcut)*totalEnergy/G4double(n);
200 // the [Et-min, Et-max] interval will be div << 155
201 // with width of dInterv = (Et-max - Et-min) << 156 G4double e0 = vcut*totalEnergy;
202 // be done in each sub-inteval using the xi << 157
203 // that is in [0,1]. The 8-point GL q. is us << 158 // simple integration
204 const G4int numSub = 2; << 159 for(G4int l=0; l<n; ++l) {
205 const G4double dInterv= (epsMax - epsMin)*ga << 160 e0 += delta;
206 G4double minEti = epsMin*gammaEnergy; << 161 for(G4int i=0; i<8; ++i) {
207 for (G4int i = 0; i < numSub; ++i) { << 162
208 for (G4int ngl = 0; ngl < 8; ++ngl) { << 163 G4double eg = (e0 + xgi[i]*delta);
209 const G4double Et = (minEti + gXGL[ngl]* << 164 G4double xs = (fLPMflag && totalEnergy > Eghigh)
210 const G4double xs = isLPM ? ComputeRelDX << 165 ? ComputeRelDXSectionPerAtom(eg,totalEnergy,Z)
211 : ComputeDXSec << 166 : ComputeDXSectionPerAtom(eg,totalEnergy,Z);
212 xSection += gWGL[ngl]*xs; << 167 cross += wgi[i]*xs;
213 } 168 }
214 // update minimum Et of the sub-inteval <<
215 minEti += dInterv; <<
216 } 169 }
217 // apply corrections of variable transformat << 170
218 xSection = std::max(2.*xSection*dInterv, 0.) << 171 cross *= delta*2.;
219 return xSection; << 172 return cross;
220 } 173 }
221 174
222 // DCS WITHOUT LPM SUPPRESSION << 175 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
223 // Computes DCS value for a given target eleme << 176
224 // total energy transferred to one of the e-/e << 177 G4double
225 // The constant factor 4 \alpha r_0^2 Z (Z +\e << 178 G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double eplusEnergy,
226 // the returned value will be differential in << 179 G4double totalEnergy,
227 // the eps=Et/Eg. The computed part of the DCS << 180 G4double /*Z*/)
228 // NORMAL CASE: DEFAULT STTING (i.e. fIsUseCom << 181 {
229 // ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = (eps^2+ << 182 // most simple case - complete screening:
230 // + 2*eps(1-eps)*[phi2(d)/4-ln(Z)/3-fc]/3 whe << 183
231 // screening variable d=d(eps)=136Z^(-1/3)eps0 << 184 // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
232 // COMPLETE SCREENING (when d(eps) approx-equa << 185 // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
233 // ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = (eps^2+ << 186 // y = E+/k
234 // -eps(1-eps)/9 where Lel=phi1(0)/4-ln(Z)/3 i << 187 G4double yp=eplusEnergy/totalEnergy;
235 // logarithm, fc is the Coulomb correction and << 188 G4double ym=1.-yp;
236 // phi1(0)/4-1/6-ln(Z)/3 = Lel-1/6 (due to phi << 189
237 G4double G4PairProductionRelModel::ComputeDXSe << 190 G4double cross = 0.;
238 << 191 if (use_completescreening)
239 << 192 cross = (yp*yp + ym*ym + 2./3.*ym*yp)*(Fel - fCoulomb) + yp*ym/9.;
>> 193 else {
>> 194 G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
>> 195 cross = (yp*yp + ym*ym)*(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
>> 196 + 2./3.*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
>> 197 }
>> 198 return cross/totalEnergy;
>> 199 }
>> 200
>> 201 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 202
>> 203 G4double
>> 204 G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double eplusEnergy,
>> 205 G4double totalEnergy,
>> 206 G4double /*Z*/)
240 { 207 {
241 G4double xSection = 0.; << 208 // most simple case - complete screening:
242 const G4int iz = std::min(gMaxZet, G4lr << 209
243 const G4double eps = pEnergy/gammaEnergy; << 210 // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
244 const G4double epsm = 1.-eps; << 211 // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
245 const G4double dum = eps*epsm; << 212 // y = E+/k
246 if (fIsUseCompleteScreening) { << 213 G4double yp=eplusEnergy/totalEnergy;
247 // complete screening: << 214 G4double ym=1.-yp;
248 const G4double Lel = gElementData[iz]->f << 215
249 const G4double fc = gElementData[iz]->f << 216 CalcLPMFunctions(totalEnergy,eplusEnergy); // gamma
250 xSection = (eps*eps + epsm*epsm + 2.*dum/3 << 217
251 } else { << 218 G4double cross = 0.;
252 // normal case: << 219 if (use_completescreening)
253 const G4double eps0 = CLHEP::electron_mas << 220 cross = xiLPM*(2./3.*phiLPM*(yp*yp + ym*ym) + gLPM)*(Fel - fCoulomb);
254 const G4double fc = gElementData[iz]->f << 221 else {
255 const G4double lnZ13 = gElementData[iz]->f << 222 G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
256 const G4double delta = gElementData[iz]->f << 223 cross = (1./3.*gLPM + 2./3.*phiLPM)*(yp*yp + ym*ym)
257 G4double phi1, phi2; << 224 *(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
258 ComputePhi12(delta, phi1, phi2); << 225 + 2./3.*gLPM*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
259 xSection = (eps*eps + epsm*epsm)*(0.25*ph << 226 cross *= xiLPM;
260 + 2.*dum*(0.25*phi2-lnZ13-fc)/3 <<
261 } 227 }
262 // non-const. part of the DCS differential i << 228 return cross/totalEnergy;
263 // ds/dEt=ds/deps deps/dEt with deps/dEt=1/E << 229
264 return std::max(xSection, 0.0)/gammaEnergy; <<
265 } 230 }
266 231
267 // DCS WITH POSSIBLE LPM SUPPRESSION << 232 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
268 // Computes DCS value for a given target eleme << 233
269 // total energy transferred to one of the e-/e << 234 void
270 // For a given Z, the LPM suppression will dep << 235 G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplusEnergy)
271 // LMP-Energy. This will determine the suppres <<
272 // pression functions xi(s), fi(s) and G(s). <<
273 // The constant factor 4 \alpha r_0^2 Z (Z +\e <<
274 // the returned value will be differential in <<
275 // the eps=Et/Eg. The computed part of the DCS <<
276 // NORMAL CASE: DEFAULT STTING (i.e. fIsUseCom <<
277 // ds/deps(Et,Eg,Z)=ds/deps(eps,Z) = xi(s)*{ ( <<
278 // *[phi1(d)/4-ln(Z)/3-fc] + 2*eps(1-eps)*G(s) <<
279 // the universal (in the TF model) screening v <<
280 // /[eps*(1-eps)] with eps0=mc^2/Eg. <<
281 // COMPLETE SCREENING (when d(eps) approx-equa <<
282 // ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = xi(s)*{ <<
283 // *(1-eps)/3)*2fi(s)/3 + G(s)/3] - eps(1-eps) <<
284 // Note, that when the LPM suppression is abse <<
285 // the normal and the complete screening DCS g <<
286 G4double G4PairProductionRelModel::ComputeRelD <<
287 <<
288 <<
289 { 236 {
290 G4double xSection = 0.; << 237 // *** calculate lpm variable s & sprime ***
291 const G4int iz = std::min(gMaxZet, G4lr << 238 // Klein eqs. (78) & (79)
292 const G4double eps = pEnergy/gammaEnergy; << 239 G4double sprime = sqrt(0.125*k*lpmEnergy/(eplusEnergy*(k-eplusEnergy)));
293 const G4double epsm = 1.-eps; << 240
294 const G4double dum = eps*epsm; << 241 G4double s1 = preS1*z23;
295 // evaluate LPM suppression functions << 242 G4double logS1 = 2./3.*lnZ-2.*facFel;
296 G4double fXiS, fGS, fPhiS; << 243 G4double logTS1 = 0.5*logTwo+logS1;
297 ComputeLPMfunctions(fXiS, fGS, fPhiS, eps, g << 244
298 if (fIsUseCompleteScreening) { << 245 xiLPM = 2.;
299 // complete screening: << 246
300 const G4double Lel = gElementData[iz]->f << 247 if (sprime>1)
301 const G4double fc = gElementData[iz]->f << 248 xiLPM = 1.;
302 xSection = (Lel-fc)*((eps*eps+epsm*epsm)*2 << 249 else if (sprime>sqrt(2.)*s1) {
303 } else { << 250 G4double h = G4Log(sprime)/logTS1;
304 // normal case: << 251 xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1;
305 const G4double eps0 = CLHEP::electron_mas << 252 }
306 const G4double fc = gElementData[iz]->f << 253
307 const G4double lnZ13 = gElementData[iz]->f << 254 G4double s0 = sprime/sqrt(xiLPM);
308 const G4double delta = gElementData[iz]->f << 255 // G4cout<<"k="<<k<<" y="<<eplusEnergy/k<<G4endl;
309 G4double phi1, phi2; << 256 // G4cout<<"s0="<<s0<<G4endl;
310 ComputePhi12(delta, phi1, phi2); << 257
311 xSection = (eps*eps + epsm*epsm)*(2.*fPhi << 258 // *** calculate supression functions phi and G ***
312 + 2.*dum*fGS*(0.25*phi2-lnZ13-f << 259 // Klein eqs. (77)
>> 260 G4double s2=s0*s0;
>> 261 G4double s3=s0*s2;
>> 262 G4double s4=s2*s2;
>> 263
>> 264 if (s0<0.1) {
>> 265 // high suppression limit
>> 266 phiLPM = 6.*s0 - 18.84955592153876*s2 + 39.47841760435743*s3
>> 267 - 57.69873135166053*s4;
>> 268 gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4;
>> 269 }
>> 270 else if (s0<1.9516) {
>> 271 // intermediate suppression
>> 272 // using eq.77 approxim. valid s0<2.
>> 273 phiLPM = 1.-G4Exp(-6.*s0*(1.+(3.-pi)*s0)
>> 274 +s3/(0.623+0.795*s0+0.658*s2));
>> 275 if (s0<0.415827397755) {
>> 276 // using eq.77 approxim. valid 0.07<s<2
>> 277 G4double psiLPM = 1-G4Exp(-4*s0-8*s2/(1+3.936*s0+4.97*s2-0.05*s3+7.50*s4));
>> 278 gLPM = 3*psiLPM-2*phiLPM;
>> 279 }
>> 280 else {
>> 281 // using alternative parametrisiation
>> 282 G4double pre = -0.16072300849123999 + s0*3.7550300067531581 + s2*-1.7981383069010097
>> 283 + s3*0.67282686077812381 + s4*-0.1207722909879257;
>> 284 gLPM = std::tanh(pre);
>> 285 }
313 } 286 }
314 // non-const. part of the DCS differential i << 287 else {
315 // ds/dEt=ds/deps deps/dEt with deps/dEt=1/E << 288 // low suppression limit valid s>2.
316 return std::max(fXiS*xSection, 0.0)/gammaEne << 289 phiLPM = 1. - 0.0119048/s4;
>> 290 gLPM = 1. - 0.0230655/s4;
>> 291 }
>> 292
>> 293 // *** make sure suppression is smaller than 1 ***
>> 294 // *** caused by Migdal approximation in xi ***
>> 295 if (xiLPM*phiLPM>1. || s0>0.57) { xiLPM=1./phiLPM; }
317 } 296 }
318 297
>> 298 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 299
319 G4double 300 G4double
320 G4PairProductionRelModel::ComputeCrossSectionP 301 G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
321 G4double gammaEnergy, G4double Z, G4doub 302 G4double gammaEnergy, G4double Z, G4double, G4double, G4double)
322 { 303 {
323 G4double crossSection = 0.0 ; 304 G4double crossSection = 0.0 ;
324 // check kinematical limit <<
325 if ( gammaEnergy <= 2.0*electron_mass_c2 ) { 305 if ( gammaEnergy <= 2.0*electron_mass_c2 ) { return crossSection; }
326 // compute the atomic cross section either b <<
327 // or by numerically integrationg the DCS (w <<
328 if ( gammaEnergy < fParametrizedXSectionThre <<
329 // using the parametrized cross sections ( <<
330 crossSection = ComputeParametrizedXSection <<
331 } else { <<
332 // by numerical integration of the DCS: <<
333 // Computes the cross section with or with <<
334 // settings (by default with if the gamma <<
335 // and using or not using complete sreenin <<
336 // Only the dependent part is computed in <<
337 // i.e. the result must be multiplied here <<
338 crossSection = ComputeXSectionPerAtom(gamm <<
339 // apply the constant factors: <<
340 // - eta(Z) is a correction to account int <<
341 // - gXSecFactor = 4 \alpha r_0^2 <<
342 const G4int iz = std::min(gMaxZet, G4l <<
343 const G4double eta = gElementData[iz]->fEt <<
344 crossSection *= gXSecFactor*Z*(Z+eta) <<
345 } <<
346 // final protection <<
347 return std::max(crossSection, 0.); <<
348 } <<
349 306
350 void G4PairProductionRelModel::SetupForMateria << 307 SetCurrentElement(Z);
351 << 308 // choose calculator according to parameters and switches
352 { << 309 // in the moment only one calculator:
353 fLPMEnergy = mat->GetRadlen()*gLPMconstant; << 310 crossSection=ComputeXSectionPerAtom(gammaEnergy,Z);
>> 311
>> 312 G4double xi = Finel/(Fel - fCoulomb); // inelastic contribution
>> 313 crossSection *= xsfactor*Z*(Z+xi);
>> 314
>> 315 return crossSection;
354 } 316 }
355 317
>> 318 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 319
356 void 320 void
357 G4PairProductionRelModel::SampleSecondaries(st 321 G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
358 co << 322 const G4MaterialCutsCouple* couple,
359 co << 323 const G4DynamicParticle* aDynamicGamma,
360 G4 << 324 G4double,
361 G4 << 325 G4double)
362 // The secondaries e+e- energies are sampled u 326 // The secondaries e+e- energies are sampled using the Bethe - Heitler
363 // cross sections with Coulomb correction. 327 // cross sections with Coulomb correction.
364 // A modified version of the random number tec 328 // A modified version of the random number techniques of Butcher & Messel
365 // is used (Nuc Phys 20(1960),15). 329 // is used (Nuc Phys 20(1960),15).
366 // 330 //
367 // GEANT4 internal units. 331 // GEANT4 internal units.
368 // 332 //
369 // Note 1 : Effects due to the breakdown of th 333 // Note 1 : Effects due to the breakdown of the Born approximation at
370 // low energy are ignored. 334 // low energy are ignored.
371 // Note 2 : The differential cross section imp 335 // Note 2 : The differential cross section implicitly takes account of
372 // pair creation in both nuclear and 336 // pair creation in both nuclear and atomic electron fields.
373 // However triplet prodution is not g 337 // However triplet prodution is not generated.
374 { 338 {
375 const G4Material* mat = couple->GetM << 339 const G4Material* aMaterial = couple->GetMaterial();
376 const G4double gammaEnergy = aDynamicGamm << 340
377 const G4double eps0 = CLHEP::elect << 341 G4double GammaEnergy = aDynamicGamma->GetKineticEnergy();
378 // << 342 G4ParticleMomentum GammaDirection = aDynamicGamma->GetMomentumDirection();
379 // check kinematical limit: gamma energy(Eg) << 343
380 // (but the model should be used at higher e << 344 G4double epsil ;
381 if (eps0 > 0.5) { return; } << 345 G4double epsil0 = electron_mass_c2/GammaEnergy ;
382 // << 346 if(epsil0 > 1.0) { return; }
383 // select target atom of the material << 347
384 const G4Element* anElement = SelectTargetAto << 348 SetupForMaterial(theGamma, aMaterial, GammaEnergy);
385 aDyna << 349
>> 350 // select randomly one element constituing the material
>> 351 const G4Element* anElement =
>> 352 SelectRandomAtom(aMaterial, theGamma, GammaEnergy);
>> 353 SetCurrentElement(anElement->GetZasInt());
>> 354
386 CLHEP::HepRandomEngine* rndmEngine = G4Rando 355 CLHEP::HepRandomEngine* rndmEngine = G4Random::getTheEngine();
387 // << 356
388 // 'eps' is the total energy transferred to << 357 // do it fast if GammaEnergy < 2. MeV
389 // gamma energy units Eg. Since the correspo << 358 if (GammaEnergy < Egsmall) {
390 // the kinematical limits for eps0=mc^2/Eg < << 359 epsil = epsil0 + (0.5-epsil0)*rndmEngine->flat();
391 // 1. 'eps' is sampled uniformly on the [eps << 360
392 // 2. otherwise, on the [eps_min, 0.5] inter <<
393 G4double eps; <<
394 // case 1. <<
395 static const G4double Egsmall = 2.*CLHEP::Me <<
396 if (gammaEnergy < Egsmall) { <<
397 eps = eps0 + (0.5-eps0)*rndmEngine->flat() <<
398 } else { 361 } else {
399 // case 2. << 362 // now comes the case with GammaEnergy >= 2. MeV
400 // get the Coulomb factor for the target e << 363 // Extract Coulomb factor for this Element
401 // F(Z) = 8*ln(Z)/3 if Eg <= 50 << 364 G4double FZ = 8.*(anElement->GetIonisation()->GetlogZ3());
402 // F(Z) = 8*ln(Z)/3 + 8*fc(Z) if Eg > 50 << 365 static const G4double midEnergy = 50.*CLHEP::MeV;
>> 366 if (GammaEnergy > midEnergy) { FZ += 8.*(anElement->GetfCoulomb()); }
>> 367
>> 368 // limits of the screening variable
>> 369 G4double screenfac = 136.*epsil0/(anElement->GetIonisation()->GetZ3());
>> 370 //F.Hariri : correct sign of last term
>> 371 G4double screenmax = G4Exp ((42.24 - FZ)/8.368) + 0.952 ;
>> 372 G4double screenmin = std::min(4.*screenfac, screenmax);
>> 373
>> 374 // limits of the energy sampling
>> 375 G4double epsil1 = 0.5 - 0.5*sqrt(1. - screenmin/screenmax) ;
>> 376 G4double epsilmin = std::max(epsil0, epsil1);
>> 377 G4double epsilrange = 0.5 - epsilmin;
>> 378
403 // 379 //
404 // The screening variable 'delta(eps)' = 1 << 380 // sample the energy rate of the created electron (or positron)
405 // Due to the Coulomb correction, the DCS <<
406 // kinematicaly allowed eps > eps0 values. <<
407 // range with negative DCS, the minimum ep <<
408 // max[eps0, epsp] with epsp is the soluti <<
409 // with SF being the screening function (S <<
410 // The solution is epsp = 0.5 - 0.5*sqrt[ <<
411 // with deltap = Exp[(42.038-F(Z))/8.29]-0 <<
412 // - when eps=eps_max = 0.5 => <<
413 // - epsp = 0.5 - 0.5*sqrt[ 1 - delta_min/ <<
414 // - and eps_min = max[eps0, epsp] <<
415 const G4int iZet = std::min(gMax <<
416 const G4double deltaFactor = gElementData[ <<
417 const G4double deltaMin = 4.*deltaFacto <<
418 G4double deltaMax = gElementData[ <<
419 G4double FZ = 8.*gElementDa <<
420 if ( gammaEnergy > fCoulombCorrectionThres <<
421 FZ += 8.*gElementData[iZet]->fCoulo <<
422 deltaMax = gElementData[iZet]->fDeltaMax <<
423 } <<
424 // compute the limits of eps <<
425 const G4double epsp = 0.5 - 0.5*std <<
426 const G4double epsMin = std::max(eps0 <<
427 const G4double epsRange = 0.5 - epsMin; <<
428 // 381 //
429 // sample the energy rate (eps) of the cre << 382 //G4double epsil, screenvar, greject ;
430 G4double F10, F20; << 383 G4double screenvar, greject ;
431 ScreenFunction12(deltaMin, F10, F20); << 384
432 F10 -= FZ; << 385 G4double F10 = ScreenFunction1(screenmin) - FZ;
433 F20 -= FZ; << 386 G4double F20 = ScreenFunction2(screenmin) - FZ;
434 const G4double NormF1 = std::max(F10 * e << 387 G4double NormF1 = std::max(F10*epsilrange*epsilrange,0.);
435 const G4double NormF2 = std::max(1.5 * F << 388 G4double NormF2 = std::max(1.5*F20,0.);
436 const G4double NormCond = NormF1/(NormF1 + << 389
437 // check if LPM correction is active <<
438 const G4bool isLPM = (fIsUseLPMCorrection <<
439 fLPMEnergy = mat->GetRadlen()*gLPMconstant <<
440 // we will need 3 uniform random number fo <<
441 G4double rndmv[3]; <<
442 G4double greject = 0.; <<
443 do { 390 do {
444 rndmEngine->flatArray(3, rndmv); << 391 if ( NormF1/(NormF1+NormF2) > rndmEngine->flat() ) {
445 if (NormCond > rndmv[0]) { << 392 epsil = 0.5 - epsilrange*g4calc->A13(rndmEngine->flat());
446 eps = 0.5 - epsRange * fG4Calc->A13(rn << 393 screenvar = screenfac/(epsil*(1-epsil));
447 const G4double delta = deltaFactor/(ep << 394 if (fLPMflag && GammaEnergy > Eghigh) {
448 if (isLPM) { << 395 CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
449 G4double lpmXiS, lpmGS, lpmPhiS, phi << 396 greject = xiLPM*((gLPM+2.*phiLPM)*Phi1(screenvar) -
450 ComputePhi12(delta, phi1, phi2); << 397 gLPM*Phi2(screenvar) - phiLPM*FZ)/F10;
451 ComputeLPMfunctions(lpmXiS, lpmGS, l << 398 }
452 greject = lpmXiS*((2.*lpmPhiS+lpmGS) << 399 else {
453 } else { << 400 greject = (ScreenFunction1(screenvar) - FZ)/F10;
454 greject = (ScreenFunction1(delta)-FZ << 401 }
455 } << 402
456 } else { 403 } else {
457 eps = epsMin + epsRange*rndmv[1]; << 404 epsil = epsilmin + epsilrange*rndmEngine->flat();
458 const G4double delta = deltaFactor/(ep << 405 screenvar = screenfac/(epsil*(1-epsil));
459 if (isLPM) { << 406 if (fLPMflag && GammaEnergy > Eghigh) {
460 G4double lpmXiS, lpmGS, lpmPhiS, phi << 407 CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
461 ComputePhi12(delta, phi1, phi2); << 408 greject = xiLPM*((0.5*gLPM+phiLPM)*Phi1(screenvar) +
462 ComputeLPMfunctions(lpmXiS, lpmGS, l << 409 0.5*gLPM*Phi2(screenvar) - 0.5*(gLPM+phiLPM)*FZ)/F20;
463 greject = lpmXiS*( (lpmPhiS+0.5*lpmG << 410 }
464 -0.5*(lpmGS+lpmPh << 411 else {
465 } else { << 412 greject = (ScreenFunction2(screenvar) - FZ)/F20;
466 greject = (ScreenFunction2(delta)-FZ << 413 }
467 } <<
468 } 414 }
>> 415
469 // Loop checking, 03-Aug-2015, Vladimir 416 // Loop checking, 03-Aug-2015, Vladimir Ivanchenko
470 } while (greject < rndmv[2]); << 417 } while( greject < rndmEngine->flat());
471 // end of eps sampling << 418
472 } << 419 } // end of epsil sampling
>> 420
>> 421 //
>> 422 // fixe charges randomly
473 // 423 //
474 // select charges randomly << 424
475 G4double eTotEnergy, pTotEnergy; << 425 G4double ElectTotEnergy, PositTotEnergy;
476 if (rndmEngine->flat() > 0.5) { 426 if (rndmEngine->flat() > 0.5) {
477 eTotEnergy = (1.-eps)*gammaEnergy; << 427 ElectTotEnergy = (1.-epsil)*GammaEnergy;
478 pTotEnergy = eps*gammaEnergy; << 428 PositTotEnergy = epsil*GammaEnergy;
>> 429
479 } else { 430 } else {
480 pTotEnergy = (1.-eps)*gammaEnergy; << 431 PositTotEnergy = (1.-epsil)*GammaEnergy;
481 eTotEnergy = eps*gammaEnergy; << 432 ElectTotEnergy = epsil*GammaEnergy;
482 } 433 }
>> 434
483 // 435 //
484 // sample pair kinematics << 436 // scattered electron (positron) angles. ( Z - axis along the parent photon)
485 // <<
486 const G4double eKinEnergy = std::max(0.,eTot <<
487 const G4double pKinEnergy = std::max(0.,pTot <<
488 // 437 //
489 G4ThreeVector eDirection, pDirection; << 438 // universal distribution suggested by L. Urban
>> 439 // (Geant3 manual (1993) Phys211),
>> 440 // derived from Tsai distribution (Rev Mod Phys 49,421(1977))
>> 441
>> 442 static const G4double a1 = 1.6;
>> 443 static const G4double a2 = a1/3.;
>> 444 G4double uu = -G4Log(rndmEngine->flat()*rndmEngine->flat());
>> 445 G4double u = (0.25 > rndmEngine->flat()) ? uu*a1 : uu*a2;
>> 446
>> 447 G4double thetaEle = u*electron_mass_c2/ElectTotEnergy;
>> 448 G4double sinte = std::sin(thetaEle);
>> 449 G4double coste = std::cos(thetaEle);
>> 450
>> 451 G4double thetaPos = u*electron_mass_c2/PositTotEnergy;
>> 452 G4double sintp = std::sin(thetaPos);
>> 453 G4double costp = std::cos(thetaPos);
>> 454
>> 455 G4double phi = twopi * rndmEngine->flat();
>> 456 G4double sinp = std::sin(phi);
>> 457 G4double cosp = std::cos(phi);
>> 458
490 // 459 //
491 GetAngularDistribution()->SamplePairDirectio << 460 // kinematic of the created pair
492 eKinEnergy, pKinEnergy, eDirectio << 461 //
>> 462 // the electron and positron are assumed to have a symetric
>> 463 // angular distribution with respect to the Z axis along the parent photon.
>> 464
>> 465 G4double ElectKineEnergy = max(0.,ElectTotEnergy - electron_mass_c2);
>> 466
>> 467 G4ThreeVector ElectDirection (sinte*cosp, sinte*sinp, coste);
>> 468 ElectDirection.rotateUz(GammaDirection);
>> 469
493 // create G4DynamicParticle object for the p 470 // create G4DynamicParticle object for the particle1
494 auto aParticle1 = new G4DynamicParticle(fThe << 471 G4DynamicParticle* aParticle1= new G4DynamicParticle(
>> 472 theElectron,ElectDirection,ElectKineEnergy);
>> 473
>> 474 // the e+ is always created (even with Ekine=0) for further annihilation.
>> 475
>> 476 G4double PositKineEnergy = std::max(0.,PositTotEnergy - electron_mass_c2);
>> 477
>> 478 G4ThreeVector PositDirection (-sintp*cosp, -sintp*sinp, costp);
>> 479 PositDirection.rotateUz(GammaDirection);
495 480
496 // create G4DynamicParticle object for the p 481 // create G4DynamicParticle object for the particle2
497 auto aParticle2 = new G4DynamicParticle(fThe << 482 G4DynamicParticle* aParticle2= new G4DynamicParticle(
>> 483 thePositron,PositDirection,PositKineEnergy);
>> 484
498 // Fill output vector 485 // Fill output vector
499 fvect->push_back(aParticle1); 486 fvect->push_back(aParticle1);
500 fvect->push_back(aParticle2); 487 fvect->push_back(aParticle2);
>> 488
501 // kill incident photon 489 // kill incident photon
502 fParticleChange->SetProposedKineticEnergy(0. 490 fParticleChange->SetProposedKineticEnergy(0.);
503 fParticleChange->ProposeTrackStatus(fStopAnd 491 fParticleChange->ProposeTrackStatus(fStopAndKill);
504 } 492 }
505 493
506 // should be called only by the master and at << 494 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
507 void G4PairProductionRelModel::InitialiseEleme <<
508 { <<
509 // create for all elements that are in the d <<
510 auto elemTable = G4Element::GetElementTable( <<
511 for (auto const & elem : *elemTable) { <<
512 const G4int iz = std::min(gMaxZet, elem->G <<
513 if (nullptr == gElementData[iz]) { // crea <<
514 const G4double logZ13 = elem->GetIonisat <<
515 const G4double Z13 = elem->GetIonisat <<
516 const G4double fc = elem->GetfCoulom <<
517 const G4double FZLow = 8.*logZ13; <<
518 const G4double FZHigh = 8.*(logZ13 + fc) <<
519 G4double Fel; <<
520 G4double Finel; <<
521 if (iz<5) { // use data from Dirac-Fock <<
522 Fel = gFelLowZet[iz]; <<
523 Finel = gFinelLowZet[iz]; <<
524 } else { // use the results of the T <<
525 Fel = G4Log(184.) - logZ13; <<
526 Finel = G4Log(1194.) - 2.*logZ13; <<
527 } <<
528 auto elD = new ElementData() <<
529 elD->fLogZ13 = logZ13; <<
530 elD->fCoulomb = fc; <<
531 elD->fLradEl = Fel; <<
532 elD->fDeltaFactor = 136./Z13; <<
533 elD->fDeltaMaxLow = G4Exp((42.038 - F <<
534 elD->fDeltaMaxHigh = G4Exp((42.038 - F <<
535 elD->fEtaValue = Finel/(Fel-fc); <<
536 elD->fLPMVarS1Cond = std::sqrt(2.)*Z13 <<
537 elD->fLPMILVarS1Cond = 1./G4Log(elD->fLP <<
538 gElementData[iz] = elD; <<
539 } <<
540 } <<
541 } <<
542 <<
543 // s goes up to 2 with ds = 0.01 be default <<
544 void G4PairProductionRelModel::InitLPMFunction <<
545 if (!gLPMFuncs.fIsInitialized) { <<
546 const G4int num = gLPMFuncs.fSLimit*gLPMFu <<
547 gLPMFuncs.fLPMFuncG.resize(num); <<
548 gLPMFuncs.fLPMFuncPhi.resize(num); <<
549 for (G4int i=0; i<num; ++i) { <<
550 const G4double sval = i/gLPMFuncs.fISDel <<
551 ComputeLPMGsPhis(gLPMFuncs.fLPMFuncG[i], <<
552 } <<
553 gLPMFuncs.fIsInitialized = true; <<
554 } <<
555 } <<
556 495
557 // used only at initialisation time <<
558 void G4PairProductionRelModel::ComputeLPMGsPhi <<
559 if (varShat < 0.01) { <<
560 funcPhiS = 6.0*varShat*(1.0-CLHEP::pi*varS <<
561 funcGS = 12.0*varShat-2.0*funcPhiS; <<
562 } else { <<
563 const G4double varShat2 = varShat*varShat; <<
564 const G4double varShat3 = varShat*varShat2 <<
565 const G4double varShat4 = varShat2*varShat <<
566 if (varShat < 0.415827397755) { // Stanev <<
567 funcPhiS = 1.0-G4Exp( -6.0*varShat*(1.0+ <<
568 + varShat3/(0.623+0 <<
569 // 1-\exp \left\{-4s-\frac{8s^2}{1+3.936 <<
570 const G4double funcPsiS = 1.0-G4Exp( -4. <<
571 + 3.936*varShat+4.97*varS <<
572 // G(s) = 3 \psi(s) - 2 \phi(s) <<
573 funcGS = 3.0*funcPsiS - 2.0*funcPhiS; <<
574 } else if (varShat < 1.55) { <<
575 funcPhiS = 1.0-G4Exp( -6.0*varShat*(1.0+ <<
576 + varShat3/(0.623+0 <<
577 const G4double dum0 = -0.16072300849123 <<
578 -1.79813830690100 <<
579 +0.67282686077812 <<
580 -0.12077229098792 <<
581 funcGS = std::tanh(dum0); <<
582 } else { <<
583 funcPhiS = 1.0-0.01190476/varShat4; <<
584 if (varShat < 1.9156) { <<
585 const G4double dum0 = -0.1607230084912 <<
586 -1.7981383069010 <<
587 +0.6728268607781 <<
588 -0.1207722909879 <<
589 funcGS = std::tanh(dum0); <<
590 } else { <<
591 funcGS = 1.0-0.0230655/varShat4; <<
592 } <<
593 } <<
594 } <<
595 } <<
596 496
597 // used at run-time to get some pre-computed L << 497 void G4PairProductionRelModel::SetupForMaterial(const G4ParticleDefinition*,
598 void G4PairProductionRelModel::GetLPMFunctions << 498 const G4Material* mat, G4double)
599 <<
600 <<
601 if (sval < gLPMFuncs.fSLimit) { <<
602 G4double val = sval*gLPMFuncs.fISDelta <<
603 const G4int ilow = (G4int)val; <<
604 val -= ilow; <<
605 lpmGs = (gLPMFuncs.fLPMFuncG[ilow+1]-gL <<
606 + gLPMFuncs.fLPMFuncG[ilow]; <<
607 lpmPhis = (gLPMFuncs.fLPMFuncPhi[ilow+1]- <<
608 + gLPMFuncs.fLPMFuncPhi[ilow]; <<
609 } else { <<
610 G4double ss = sval*sval; <<
611 ss *= ss; <<
612 lpmPhis = 1.0-0.01190476/ss; <<
613 lpmGs = 1.0-0.0230655/ss; <<
614 } <<
615 } <<
616 <<
617 void G4PairProductionRelModel::ComputeLPMfunct <<
618 G4double &funcGS, G4double &f <<
619 const G4double egamma, const <<
620 { <<
621 // 1. y = E_+/E_{\gamma} with E_+ being the <<
622 // to one of the e-/e <<
623 // s' = \sqrt{ \frac{1}{8} \frac{1}{y(1-y)} <<
624 const G4double varSprime = std::sqrt(0.125*f <<
625 const G4double condition = gElementData[izet <<
626 funcXiS = 2.0; <<
627 if (varSprime > 1.0) { <<
628 funcXiS = 1.0; <<
629 } else if (varSprime > condition) { <<
630 const G4double dum = gElementData[izet]->f <<
631 const G4double funcHSprime = G4Log(varSpri <<
632 funcXiS = 1.0 + funcHSprime <<
633 - 0.08*(1.0-funcHSprime)*funcHSpr <<
634 } <<
635 // 2. s=\frac{s'}{\sqrt{\xi(s')}} <<
636 const G4double varShat = varSprime / std::sq <<
637 GetLPMFunctions(funcGS, funcPhiS, varShat); <<
638 // MAKE SURE SUPPRESSION IS SMALLER THAN 1: <<
639 if (funcXiS * funcPhiS > 1. || varShat > 0.5 <<
640 funcXiS = 1. / funcPhiS; <<
641 } <<
642 } <<
643 <<
644 // Calculates the microscopic cross section in <<
645 // G4BetheHeitlerModel and should be used belo <<
646 // from the cross section data above 80-90 GeV <<
647 // Parametrized formula (L. Urban) is used to <<
648 // given numerically in the table of [Hubbell, <<
649 // Overbo: "Pair, Triplet, and Total Atomic Cr <<
650 // Coefficients) for 1 MeV‐100 GeV Photons i <<
651 // physical and chemical reference data 9.4 (1 <<
652 // <<
653 // The formula gives a good approximation of t <<
654 // below 1.5 MeV: sigma=sigma(1.5MeV)*(GammaEn <<
655 // *(GammaEn <<
656 G4double <<
657 G4PairProductionRelModel::ComputeParametrizedX <<
658 <<
659 { 499 {
660 G4double xSection = 0.0 ; << 500 lpmEnergy = mat->GetRadlen()*fLPMconstant;
661 // short versions << 501 // G4cout<<" lpmEnergy="<<lpmEnergy<<G4endl;
662 static const G4double kMC2 = CLHEP::electro <<
663 // zero cross section below the kinematical <<
664 if (Z < 0.9 || gammaE <= 2.0*kMC2) { return <<
665 // <<
666 static const G4double gammaEnergyLimit = 1.5 <<
667 // set coefficients a, b c <<
668 static const G4double a0 = 8.7842e+2*CLHEP: <<
669 static const G4double a1 = -1.9625e+3*CLHEP: <<
670 static const G4double a2 = 1.2949e+3*CLHEP: <<
671 static const G4double a3 = -2.0028e+2*CLHEP: <<
672 static const G4double a4 = 1.2575e+1*CLHEP: <<
673 static const G4double a5 = -2.8333e-1*CLHEP: <<
674 <<
675 static const G4double b0 = -1.0342e+1*CLHEP: <<
676 static const G4double b1 = 1.7692e+1*CLHEP: <<
677 static const G4double b2 = -8.2381 *CLHEP: <<
678 static const G4double b3 = 1.3063 *CLHEP: <<
679 static const G4double b4 = -9.0815e-2*CLHEP: <<
680 static const G4double b5 = 2.3586e-3*CLHEP: <<
681 <<
682 static const G4double c0 = -4.5263e+2*CLHEP: <<
683 static const G4double c1 = 1.1161e+3*CLHEP: <<
684 static const G4double c2 = -8.6749e+2*CLHEP: <<
685 static const G4double c3 = 2.1773e+2*CLHEP: <<
686 static const G4double c4 = -2.0467e+1*CLHEP: <<
687 static const G4double c5 = 6.5372e-1*CLHEP: <<
688 // check low energy limit of the approximati <<
689 G4double gammaEnergyOrg = gammaE; <<
690 if (gammaE < gammaEnergyLimit) { gammaE = ga <<
691 // compute gamma energy variables <<
692 const G4double x = G4Log(gammaE/kMC2); <<
693 const G4double x2 = x *x; <<
694 const G4double x3 = x2*x; <<
695 const G4double x4 = x3*x; <<
696 const G4double x5 = x4*x; <<
697 // <<
698 const G4double F1 = a0 + a1*x + a2*x2 + a3*x <<
699 const G4double F2 = b0 + b1*x + b2*x2 + b3*x <<
700 const G4double F3 = c0 + c1*x + c2*x2 + c3*x <<
701 // compute the approximated cross section <<
702 xSection = (Z + 1.)*(F1*Z + F2*Z*Z + F3); <<
703 // check if we are below the limit of the ap <<
704 if (gammaEnergyOrg < gammaEnergyLimit) { <<
705 const G4double dum = (gammaEnergyOrg-2.*kM <<
706 xSection *= dum*dum; <<
707 } <<
708 return xSection; <<
709 } 502 }
710 503
711 << 504 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
712 505