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>> 26 // $Id: G4PairProductionRelModel.cc 83685 2014-09-09 12:39:00Z 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 // that consistent to Migdal's one; f <<
41 // computation; suppression is consis <<
42 // brem. model (F.Hariri) <<
43 // 28-05-18 New version with improved screenin <<
44 // LPM function approximation, effici <<
45 // Corrected call to selecting target <<
46 // (M. Novak) <<
47 // 40 //
48 // Class Description: 41 // Class Description:
49 // 42 //
50 // Main References: 43 // Main References:
51 // J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 44 // J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 581.
52 // S.Klein, Rev. Mod. Phys. 71 (1999) 1501. 45 // S.Klein, Rev. Mod. Phys. 71 (1999) 1501.
53 // T.Stanev et.al., Phys. Rev. D25 (1982) 129 46 // T.Stanev et.al., Phys. Rev. D25 (1982) 1291.
54 // M.L.Ter-Mikaelian, High-energy Electromagn << 47 // M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media,
55 // Wiley, 1972. 48 // Wiley, 1972.
56 // 49 //
57 // ------------------------------------------- 50 // -------------------------------------------------------------------
>> 51 //
>> 52 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 53 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
58 54
59 #include "G4PairProductionRelModel.hh" 55 #include "G4PairProductionRelModel.hh"
60 #include "G4PhysicalConstants.hh" 56 #include "G4PhysicalConstants.hh"
61 #include "G4SystemOfUnits.hh" 57 #include "G4SystemOfUnits.hh"
62 #include "G4Gamma.hh" 58 #include "G4Gamma.hh"
63 #include "G4Electron.hh" 59 #include "G4Electron.hh"
64 #include "G4Positron.hh" 60 #include "G4Positron.hh"
>> 61 #include "G4Log.hh"
>> 62
65 #include "G4ParticleChangeForGamma.hh" 63 #include "G4ParticleChangeForGamma.hh"
66 #include "G4LossTableManager.hh" 64 #include "G4LossTableManager.hh"
67 #include "G4ModifiedTsai.hh" <<
68 #include "G4Exp.hh" 65 #include "G4Exp.hh"
69 #include "G4Pow.hh" <<
70 #include "G4AutoLock.hh" <<
71 66
72 const G4int G4PairProductionRelModel::gMaxZet <<
73 67
74 // LPM constant: \alpha(mc^2)^2/(4\pi*\hbar c) << 68 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
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 69
108 // special data structure per element i.e. per << 70 using namespace std;
109 std::vector<G4PairProductionRelModel::ElementD <<
110 71
111 // LPM supression functions evaluated at initi << 72 const G4double G4PairProductionRelModel::facFel = G4Log(184.15);
112 G4PairProductionRelModel::LPMFuncs G4PairProdu << 73 const G4double G4PairProductionRelModel::facFinel = G4Log(1194.); // 1440.
>> 74
>> 75 const G4double G4PairProductionRelModel::preS1 = 1./(184.15*184.15);
>> 76 const G4double G4PairProductionRelModel::logTwo = G4Log(2.);
>> 77
>> 78 const G4double G4PairProductionRelModel::xgi[]={ 0.0199, 0.1017, 0.2372, 0.4083,
>> 79 0.5917, 0.7628, 0.8983, 0.9801 };
>> 80 const G4double G4PairProductionRelModel::wgi[]={ 0.0506, 0.1112, 0.1569, 0.1813,
>> 81 0.1813, 0.1569, 0.1112, 0.0506 };
>> 82 const G4double G4PairProductionRelModel::Fel_light[] = {0., 5.31 , 4.79 , 4.74 , 4.71};
>> 83 const G4double G4PairProductionRelModel::Finel_light[] = {0., 6.144 , 5.621 , 5.805 , 5.924};
>> 84
>> 85 static const G4double xsfactor =
>> 86 4*fine_structure_const*classic_electr_radius*classic_electr_radius;
>> 87 static const G4double Egsmall=2.*MeV;
113 88
114 namespace <<
115 { <<
116 G4Mutex thePairProdRelMutex = G4MUTEX_INITIA <<
117 } <<
118 89
119 // CTR <<
120 G4PairProductionRelModel::G4PairProductionRelM 90 G4PairProductionRelModel::G4PairProductionRelModel(const G4ParticleDefinition*,
121 << 91 const G4String& nam)
122 : G4VEmModel(nam), fIsUseLPMCorrection(true) << 92 : G4VEmModel(nam),
123 fLPMEnergy(0.), fG4Calc(G4Pow::GetInstance() << 93 fLPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)*0.5),
124 fTheElectron(G4Electron::Electron()), fThePo << 94 fLPMflag(true),
125 fParticleChange(nullptr) << 95 lpmEnergy(0.),
>> 96 use_completescreening(false)
126 { 97 {
127 // gamma energy below which the parametrized << 98 fParticleChange = 0;
128 fParametrizedXSectionThreshold = 30.0*CLHEP: << 99 theGamma = G4Gamma::Gamma();
129 // gamma energy below the Coulomb correction << 100 thePositron = G4Positron::Positron();
130 fCoulombCorrectionThreshold = 50.0*CLHEP: << 101 theElectron = G4Electron::Electron();
131 // set angular generator used in the final s << 102
132 SetAngularDistribution(new G4ModifiedTsai()) << 103 nist = G4NistManager::Instance();
>> 104
>> 105 currentZ = z13 = z23 = lnZ = Fel = Finel = fCoulomb = phiLPM = gLPM = xiLPM = 0;
>> 106
133 } 107 }
134 108
135 // DTR << 109 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 110
136 G4PairProductionRelModel::~G4PairProductionRel 111 G4PairProductionRelModel::~G4PairProductionRelModel()
137 { << 112 {}
138 if (isFirstInstance) { << 113
139 // clear ElementData container << 114 //....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 } <<
150 115
151 void G4PairProductionRelModel::Initialise(cons 116 void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p,
152 cons << 117 const G4DataVector& cuts)
153 { 118 {
154 if(nullptr == fParticleChange) { fParticleCh << 119 if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
155 << 120 if(IsMaster() && LowEnergyLimit() < HighEnergyLimit()) {
156 if (isFirstInstance || gElementData.empty()) << 121 InitialiseElementSelectors(p, cuts);
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); <<
173 } 122 }
174 } 123 }
175 124
>> 125 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 126
176 void G4PairProductionRelModel::InitialiseLocal 127 void G4PairProductionRelModel::InitialiseLocal(const G4ParticleDefinition*,
177 << 128 G4VEmModel* masterModel)
178 { 129 {
179 SetElementSelectors(masterModel->GetElementS << 130 if(LowEnergyLimit() < HighEnergyLimit()) {
>> 131 SetElementSelectors(masterModel->GetElementSelectors());
>> 132 }
180 } 133 }
181 134
182 G4double G4PairProductionRelModel::ComputeXSec << 135 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
183 << 136
>> 137 G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double totalEnergy, G4double Z)
184 { 138 {
185 G4double xSection = 0.0; << 139 G4double cross = 0.0;
186 // check if LPM suppression needs to be used << 140
187 const G4bool isLPM = (fIsUseLPMCorrection << 141 // number of intervals and integration step
188 // determine the kinematical limits (taken i << 142 G4double vcut = electron_mass_c2/totalEnergy ;
189 // the way in which the Coulomb correction i << 143
190 const G4int iz = std::min(gMaxZet, G4 << 144 // limits by the screening variable
191 const G4double eps0 = CLHEP::electron_mass << 145 G4double dmax = DeltaMax();
192 // Coulomb correction is always included in << 146 G4double dmin = min(DeltaMin(totalEnergy),dmax);
193 // that this DCS is only used to get the int << 147 G4double vcut1 = 0.5 - 0.5*sqrt(1. - dmin/dmax) ;
194 const G4double dmax = gElementData[iz]->fD << 148 vcut = max(vcut, vcut1);
195 const G4double dmin = 4.*eps0*gElementData << 149
196 const G4double eps1 = 0.5 - 0.5*std::sqrt( << 150
197 const G4double epsMin = std::max(eps0, eps1) << 151 G4double vmax = 0.5;
198 const G4double epsMax = 0.5; // DCS is symme << 152 G4int n = 1; // needs optimisation
199 // let Et be the total energy transferred to << 153
200 // the [Et-min, Et-max] interval will be div << 154 G4double delta = (vmax - vcut)*totalEnergy/G4double(n);
201 // with width of dInterv = (Et-max - Et-min) << 155
202 // be done in each sub-inteval using the xi << 156 G4double e0 = vcut*totalEnergy;
203 // that is in [0,1]. The 8-point GL q. is us << 157 G4double xs;
204 const G4int numSub = 2; << 158
205 const G4double dInterv= (epsMax - epsMin)*ga << 159 // simple integration
206 G4double minEti = epsMin*gammaEnergy; << 160 for(G4int l=0; l<n; l++,e0 += delta) {
207 for (G4int i = 0; i < numSub; ++i) { << 161 for(G4int i=0; i<8; i++) {
208 for (G4int ngl = 0; ngl < 8; ++ngl) { << 162
209 const G4double Et = (minEti + gXGL[ngl]* << 163 G4double eg = (e0 + xgi[i]*delta);
210 const G4double xs = isLPM ? ComputeRelDX << 164 if (fLPMflag && totalEnergy>100.*GeV)
211 : ComputeDXSec << 165 xs = ComputeRelDXSectionPerAtom(eg,totalEnergy,Z);
212 xSection += gWGL[ngl]*xs; << 166 else
>> 167 xs = ComputeDXSectionPerAtom(eg,totalEnergy,Z);
>> 168 cross += wgi[i]*xs;
>> 169
213 } 170 }
214 // update minimum Et of the sub-inteval <<
215 minEti += dInterv; <<
216 } 171 }
217 // apply corrections of variable transformat << 172
218 xSection = std::max(2.*xSection*dInterv, 0.) << 173 cross *= delta*2.;
219 return xSection; << 174
>> 175 return cross;
220 } 176 }
221 177
222 // DCS WITHOUT LPM SUPPRESSION << 178 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
223 // Computes DCS value for a given target eleme << 179
224 // total energy transferred to one of the e-/e << 180 G4double
225 // The constant factor 4 \alpha r_0^2 Z (Z +\e << 181 G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double eplusEnergy,
226 // the returned value will be differential in << 182 G4double totalEnergy,
227 // the eps=Et/Eg. The computed part of the DCS << 183 G4double /*Z*/)
228 // NORMAL CASE: DEFAULT STTING (i.e. fIsUseCom <<
229 // ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = (eps^2+ <<
230 // + 2*eps(1-eps)*[phi2(d)/4-ln(Z)/3-fc]/3 whe <<
231 // screening variable d=d(eps)=136Z^(-1/3)eps0 <<
232 // COMPLETE SCREENING (when d(eps) approx-equa <<
233 // ds/deps(Et,Eg,Z) = ds/deps(eps,Z) = (eps^2+ <<
234 // -eps(1-eps)/9 where Lel=phi1(0)/4-ln(Z)/3 i <<
235 // logarithm, fc is the Coulomb correction and <<
236 // phi1(0)/4-1/6-ln(Z)/3 = Lel-1/6 (due to phi <<
237 G4double G4PairProductionRelModel::ComputeDXSe <<
238 <<
239 <<
240 { 184 {
241 G4double xSection = 0.; << 185 // most simple case - complete screening:
242 const G4int iz = std::min(gMaxZet, G4lr << 186
243 const G4double eps = pEnergy/gammaEnergy; << 187 // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
244 const G4double epsm = 1.-eps; << 188 // * [ (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; << 189 // y = E+/k
246 if (fIsUseCompleteScreening) { << 190 G4double yp=eplusEnergy/totalEnergy;
247 // complete screening: << 191 G4double ym=1.-yp;
248 const G4double Lel = gElementData[iz]->f << 192
249 const G4double fc = gElementData[iz]->f << 193 G4double cross = 0.;
250 xSection = (eps*eps + epsm*epsm + 2.*dum/3 << 194 if (use_completescreening)
251 } else { << 195 cross = (yp*yp + ym*ym + 2./3.*ym*yp)*(Fel - fCoulomb) + 1./9.*yp*ym;
252 // normal case: << 196 else {
253 const G4double eps0 = CLHEP::electron_mas << 197 G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
254 const G4double fc = gElementData[iz]->f << 198 cross = (yp*yp + ym*ym)*(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
255 const G4double lnZ13 = gElementData[iz]->f << 199 + 2./3.*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
256 const G4double delta = gElementData[iz]->f <<
257 G4double phi1, phi2; <<
258 ComputePhi12(delta, phi1, phi2); <<
259 xSection = (eps*eps + epsm*epsm)*(0.25*ph <<
260 + 2.*dum*(0.25*phi2-lnZ13-fc)/3 <<
261 } 200 }
262 // non-const. part of the DCS differential i << 201 return cross/totalEnergy;
263 // ds/dEt=ds/deps deps/dEt with deps/dEt=1/E << 202
264 return std::max(xSection, 0.0)/gammaEnergy; <<
265 } 203 }
>> 204 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
266 205
267 // DCS WITH POSSIBLE LPM SUPPRESSION << 206 G4double
268 // Computes DCS value for a given target eleme << 207 G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double eplusEnergy,
269 // total energy transferred to one of the e-/e << 208 G4double totalEnergy,
270 // For a given Z, the LPM suppression will dep << 209 G4double /*Z*/)
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 { 210 {
290 G4double xSection = 0.; << 211 // most simple case - complete screening:
291 const G4int iz = std::min(gMaxZet, G4lr << 212
292 const G4double eps = pEnergy/gammaEnergy; << 213 // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
293 const G4double epsm = 1.-eps; << 214 // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
294 const G4double dum = eps*epsm; << 215 // y = E+/k
295 // evaluate LPM suppression functions << 216 G4double yp=eplusEnergy/totalEnergy;
296 G4double fXiS, fGS, fPhiS; << 217 G4double ym=1.-yp;
297 ComputeLPMfunctions(fXiS, fGS, fPhiS, eps, g << 218
298 if (fIsUseCompleteScreening) { << 219 CalcLPMFunctions(totalEnergy,eplusEnergy); // gamma
299 // complete screening: << 220
300 const G4double Lel = gElementData[iz]->f << 221 G4double cross = 0.;
301 const G4double fc = gElementData[iz]->f << 222 if (use_completescreening)
302 xSection = (Lel-fc)*((eps*eps+epsm*epsm)*2 << 223 cross = xiLPM*(2./3.*phiLPM*(yp*yp + ym*ym) + gLPM)*(Fel - fCoulomb);
303 } else { << 224 else {
304 // normal case: << 225 G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
305 const G4double eps0 = CLHEP::electron_mas << 226 cross = (1./3.*gLPM + 2./3.*phiLPM)*(yp*yp + ym*ym)
306 const G4double fc = gElementData[iz]->f << 227 *(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
307 const G4double lnZ13 = gElementData[iz]->f << 228 + 2./3.*gLPM*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
308 const G4double delta = gElementData[iz]->f << 229 cross *= xiLPM;
309 G4double phi1, phi2; <<
310 ComputePhi12(delta, phi1, phi2); <<
311 xSection = (eps*eps + epsm*epsm)*(2.*fPhi <<
312 + 2.*dum*fGS*(0.25*phi2-lnZ13-f <<
313 } 230 }
314 // non-const. part of the DCS differential i << 231 return cross/totalEnergy;
315 // ds/dEt=ds/deps deps/dEt with deps/dEt=1/E << 232
316 return std::max(fXiS*xSection, 0.0)/gammaEne <<
317 } 233 }
318 234
319 G4double << 235 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
320 G4PairProductionRelModel::ComputeCrossSectionP << 236
321 G4double gammaEnergy, G4double Z, G4doub << 237 void
>> 238 G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplusEnergy)
322 { 239 {
323 G4double crossSection = 0.0 ; << 240 // *** calculate lpm variable s & sprime ***
324 // check kinematical limit << 241 // Klein eqs. (78) & (79)
325 if ( gammaEnergy <= 2.0*electron_mass_c2 ) { << 242 G4double sprime = sqrt(0.125*k*lpmEnergy/(eplusEnergy*(k-eplusEnergy)));
326 // compute the atomic cross section either b << 243
327 // or by numerically integrationg the DCS (w << 244 G4double s1 = preS1*z23;
328 if ( gammaEnergy < fParametrizedXSectionThre << 245 G4double logS1 = 2./3.*lnZ-2.*facFel;
329 // using the parametrized cross sections ( << 246 G4double logTS1 = logTwo+logS1;
330 crossSection = ComputeParametrizedXSection << 247
331 } else { << 248 xiLPM = 2.;
332 // by numerical integration of the DCS: << 249
333 // Computes the cross section with or with << 250 if (sprime>1)
334 // settings (by default with if the gamma << 251 xiLPM = 1.;
335 // and using or not using complete sreenin << 252 else if (sprime>sqrt(2.)*s1) {
336 // Only the dependent part is computed in << 253 G4double h = G4Log(sprime)/logTS1;
337 // i.e. the result must be multiplied here << 254 xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1;
338 crossSection = ComputeXSectionPerAtom(gamm << 255 }
339 // apply the constant factors: << 256
340 // - eta(Z) is a correction to account int << 257 G4double s0 = sprime/sqrt(xiLPM);
341 // - gXSecFactor = 4 \alpha r_0^2 << 258 // G4cout<<"k="<<k<<" y="<<eplusEnergy/k<<G4endl;
342 const G4int iz = std::min(gMaxZet, G4l << 259 // G4cout<<"s0="<<s0<<G4endl;
343 const G4double eta = gElementData[iz]->fEt << 260
344 crossSection *= gXSecFactor*Z*(Z+eta) << 261 // *** calculate supression functions phi and G ***
>> 262 // Klein eqs. (77)
>> 263 G4double s2=s0*s0;
>> 264 G4double s3=s0*s2;
>> 265 G4double s4=s2*s2;
>> 266
>> 267 if (s0<0.1) {
>> 268 // high suppression limit
>> 269 phiLPM = 6.*s0 - 18.84955592153876*s2 + 39.47841760435743*s3
>> 270 - 57.69873135166053*s4;
>> 271 gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4;
>> 272 }
>> 273 else if (s0<1.9516) {
>> 274 // intermediate suppression
>> 275 // using eq.77 approxim. valid s0<2.
>> 276 phiLPM = 1.-G4Exp(-6.*s0*(1.+(3.-pi)*s0)
>> 277 +s3/(0.623+0.795*s0+0.658*s2));
>> 278 if (s0<0.415827397755) {
>> 279 // using eq.77 approxim. valid 0.07<s<2
>> 280 G4double psiLPM = 1-G4Exp(-4*s0-8*s2/(1+3.936*s0+4.97*s2-0.05*s3+7.50*s4));
>> 281 gLPM = 3*psiLPM-2*phiLPM;
>> 282 }
>> 283 else {
>> 284 // using alternative parametrisiation
>> 285 G4double pre = -0.16072300849123999 + s0*3.7550300067531581 + s2*-1.7981383069010097
>> 286 + s3*0.67282686077812381 + s4*-0.1207722909879257;
>> 287 gLPM = tanh(pre);
>> 288 }
345 } 289 }
346 // final protection << 290 else {
347 return std::max(crossSection, 0.); << 291 // low suppression limit valid s>2.
>> 292 phiLPM = 1. - 0.0119048/s4;
>> 293 gLPM = 1. - 0.0230655/s4;
>> 294 }
>> 295
>> 296 // *** make sure suppression is smaller than 1 ***
>> 297 // *** caused by Migdal approximation in xi ***
>> 298 if (xiLPM*phiLPM>1. || s0>0.57) xiLPM=1./phiLPM;
348 } 299 }
349 300
350 void G4PairProductionRelModel::SetupForMateria << 301
351 << 302 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 303
>> 304 G4double
>> 305 G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
>> 306 G4double gammaEnergy, G4double Z,
>> 307 G4double, G4double, G4double)
352 { 308 {
353 fLPMEnergy = mat->GetRadlen()*gLPMconstant; << 309 G4double crossSection = 0.0 ;
>> 310 // if ( Z < 0.9 ) return crossSection;
>> 311 if ( gammaEnergy <= 2.0*electron_mass_c2 ) return crossSection;
>> 312
>> 313 SetCurrentElement(Z);
>> 314 // choose calculator according to parameters and switches
>> 315 // in the moment only one calculator:
>> 316 crossSection=ComputeXSectionPerAtom(gammaEnergy,Z);
>> 317
>> 318 G4double xi = Finel/(Fel - fCoulomb); // inelastic contribution
>> 319 crossSection *= xsfactor*Z*(Z+xi);
>> 320
>> 321 return crossSection;
354 } 322 }
355 323
356 void << 324 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
>> 325
>> 326 void
357 G4PairProductionRelModel::SampleSecondaries(st 327 G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
358 co << 328 const G4MaterialCutsCouple* couple,
359 co << 329 const G4DynamicParticle* aDynamicGamma,
360 G4 << 330 G4double,
361 G4 << 331 G4double)
362 // The secondaries e+e- energies are sampled u 332 // The secondaries e+e- energies are sampled using the Bethe - Heitler
363 // cross sections with Coulomb correction. 333 // cross sections with Coulomb correction.
364 // A modified version of the random number tec 334 // A modified version of the random number techniques of Butcher & Messel
365 // is used (Nuc Phys 20(1960),15). 335 // is used (Nuc Phys 20(1960),15).
366 // 336 //
367 // GEANT4 internal units. 337 // GEANT4 internal units.
368 // 338 //
369 // Note 1 : Effects due to the breakdown of th 339 // Note 1 : Effects due to the breakdown of the Born approximation at
370 // low energy are ignored. 340 // low energy are ignored.
371 // Note 2 : The differential cross section imp << 341 // Note 2 : The differential cross section implicitly takes account of
372 // pair creation in both nuclear and 342 // pair creation in both nuclear and atomic electron fields.
373 // However triplet prodution is not g 343 // However triplet prodution is not generated.
374 { 344 {
375 const G4Material* mat = couple->GetM << 345 const G4Material* aMaterial = couple->GetMaterial();
376 const G4double gammaEnergy = aDynamicGamm << 346
377 const G4double eps0 = CLHEP::elect << 347 G4double GammaEnergy = aDynamicGamma->GetKineticEnergy();
378 // << 348 G4ParticleMomentum GammaDirection = aDynamicGamma->GetMomentumDirection();
379 // check kinematical limit: gamma energy(Eg) << 349
380 // (but the model should be used at higher e << 350 G4double epsil ;
381 if (eps0 > 0.5) { return; } << 351 G4double epsil0 = electron_mass_c2/GammaEnergy ;
382 // << 352 if(epsil0 > 1.0) { return; }
383 // select target atom of the material << 353
384 const G4Element* anElement = SelectTargetAto << 354 // do it fast if GammaEnergy < 2. MeV
385 aDyna << 355 SetupForMaterial(theGamma, aMaterial, GammaEnergy);
386 CLHEP::HepRandomEngine* rndmEngine = G4Rando << 356
387 // << 357 // select randomly one element constituing the material
388 // 'eps' is the total energy transferred to << 358 const G4Element* anElement =
389 // gamma energy units Eg. Since the correspo << 359 SelectRandomAtom(aMaterial, theGamma, GammaEnergy);
390 // the kinematical limits for eps0=mc^2/Eg < << 360
391 // 1. 'eps' is sampled uniformly on the [eps << 361 if (GammaEnergy < Egsmall) {
392 // 2. otherwise, on the [eps_min, 0.5] inter << 362
393 G4double eps; << 363 epsil = epsil0 + (0.5-epsil0)*G4UniformRand();
394 // case 1. << 364
395 static const G4double Egsmall = 2.*CLHEP::Me <<
396 if (gammaEnergy < Egsmall) { <<
397 eps = eps0 + (0.5-eps0)*rndmEngine->flat() <<
398 } else { 365 } else {
399 // case 2. << 366 // now comes the case with GammaEnergy >= 2. MeV
400 // get the Coulomb factor for the target e << 367
401 // F(Z) = 8*ln(Z)/3 if Eg <= 50 << 368 // Extract Coulomb factor for this Element
402 // F(Z) = 8*ln(Z)/3 + 8*fc(Z) if Eg > 50 << 369 G4double FZ = 8.*(anElement->GetIonisation()->GetlogZ3());
>> 370 if (GammaEnergy > 50.*MeV) { FZ += 8.*(anElement->GetfCoulomb()); }
>> 371
>> 372 // limits of the screening variable
>> 373 G4double screenfac = 136.*epsil0/(anElement->GetIonisation()->GetZ3());
>> 374 G4double screenmax = G4Exp ((42.24 - FZ)/8.368) - 0.952 ;
>> 375 G4double screenmin = min(4.*screenfac,screenmax);
>> 376
>> 377 // limits of the energy sampling
>> 378 G4double epsil1 = 0.5 - 0.5*sqrt(1. - screenmin/screenmax) ;
>> 379 G4double epsilmin = max(epsil0,epsil1) , epsilrange = 0.5 - epsilmin;
>> 380
403 // 381 //
404 // The screening variable 'delta(eps)' = 1 << 382 // 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 // 383 //
429 // sample the energy rate (eps) of the cre << 384 //G4double epsil, screenvar, greject ;
430 G4double F10, F20; << 385 G4double screenvar, greject ;
431 ScreenFunction12(deltaMin, F10, F20); << 386
432 F10 -= FZ; << 387 G4double F10 = ScreenFunction1(screenmin) - FZ;
433 F20 -= FZ; << 388 G4double F20 = ScreenFunction2(screenmin) - FZ;
434 const G4double NormF1 = std::max(F10 * e << 389 G4double NormF1 = max(F10*epsilrange*epsilrange,0.);
435 const G4double NormF2 = std::max(1.5 * F << 390 G4double NormF2 = max(1.5*F20,0.);
436 const G4double NormCond = NormF1/(NormF1 + << 391
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 { 392 do {
444 rndmEngine->flatArray(3, rndmv); << 393 if ( NormF1/(NormF1+NormF2) > G4UniformRand() ) {
445 if (NormCond > rndmv[0]) { << 394 epsil = 0.5 - epsilrange*nist->GetZ13(G4UniformRand());
446 eps = 0.5 - epsRange * fG4Calc->A13(rn << 395 screenvar = screenfac/(epsil*(1-epsil));
447 const G4double delta = deltaFactor/(ep << 396 if (fLPMflag && GammaEnergy>100.*GeV) {
448 if (isLPM) { << 397 CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
449 G4double lpmXiS, lpmGS, lpmPhiS, phi << 398 greject = xiLPM*((gLPM+2.*phiLPM)*Phi1(screenvar) -
450 ComputePhi12(delta, phi1, phi2); << 399 gLPM*Phi2(screenvar) - phiLPM*FZ)/F10;
451 ComputeLPMfunctions(lpmXiS, lpmGS, l << 400 }
452 greject = lpmXiS*((2.*lpmPhiS+lpmGS) << 401 else {
453 } else { << 402 greject = (ScreenFunction1(screenvar) - FZ)/F10;
454 greject = (ScreenFunction1(delta)-FZ << 403 }
455 } << 404
456 } else { << 405 } else {
457 eps = epsMin + epsRange*rndmv[1]; << 406 epsil = epsilmin + epsilrange*G4UniformRand();
458 const G4double delta = deltaFactor/(ep << 407 screenvar = screenfac/(epsil*(1-epsil));
459 if (isLPM) { << 408 if (fLPMflag && GammaEnergy>100.*GeV) {
460 G4double lpmXiS, lpmGS, lpmPhiS, phi << 409 CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
461 ComputePhi12(delta, phi1, phi2); << 410 greject = xiLPM*((0.5*gLPM+phiLPM)*Phi1(screenvar) +
462 ComputeLPMfunctions(lpmXiS, lpmGS, l << 411 0.5*gLPM*Phi2(screenvar) - 0.5*(gLPM+phiLPM)*FZ)/F20;
463 greject = lpmXiS*( (lpmPhiS+0.5*lpmG << 412 }
464 -0.5*(lpmGS+lpmPh << 413 else {
465 } else { << 414 greject = (ScreenFunction2(screenvar) - FZ)/F20;
466 greject = (ScreenFunction2(delta)-FZ << 415 }
467 } <<
468 } 416 }
469 // Loop checking, 03-Aug-2015, Vladimir << 417
470 } while (greject < rndmv[2]); << 418 } while( greject < G4UniformRand() );
471 // end of eps sampling << 419
472 } << 420 } // end of epsil sampling
>> 421
>> 422 //
>> 423 // fixe charges randomly
473 // 424 //
474 // select charges randomly << 425
475 G4double eTotEnergy, pTotEnergy; << 426 G4double ElectTotEnergy, PositTotEnergy;
476 if (rndmEngine->flat() > 0.5) { << 427 if (G4UniformRand() > 0.5) {
477 eTotEnergy = (1.-eps)*gammaEnergy; << 428
478 pTotEnergy = eps*gammaEnergy; << 429 ElectTotEnergy = (1.-epsil)*GammaEnergy;
>> 430 PositTotEnergy = epsil*GammaEnergy;
>> 431
479 } else { 432 } else {
480 pTotEnergy = (1.-eps)*gammaEnergy; << 433
481 eTotEnergy = eps*gammaEnergy; << 434 PositTotEnergy = (1.-epsil)*GammaEnergy;
>> 435 ElectTotEnergy = epsil*GammaEnergy;
482 } 436 }
>> 437
>> 438 //
>> 439 // scattered electron (positron) angles. ( Z - axis along the parent photon)
483 // 440 //
484 // sample pair kinematics << 441 // universal distribution suggested by L. Urban
485 // << 442 // (Geant3 manual (1993) Phys211),
486 const G4double eKinEnergy = std::max(0.,eTot << 443 // derived from Tsai distribution (Rev Mod Phys 49,421(1977))
487 const G4double pKinEnergy = std::max(0.,pTot << 444
>> 445 G4double u;
>> 446 static const G4double a1 = 0.625;
>> 447 static const G4double a2 = 3.*a1;
>> 448 static const G4double d = 27. ;
>> 449
>> 450 if (9./(9.+d) >G4UniformRand()) u= - G4Log(G4UniformRand()*G4UniformRand())/a1;
>> 451 else u= - G4Log(G4UniformRand()*G4UniformRand())/a2;
>> 452
>> 453 G4double TetEl = u*electron_mass_c2/ElectTotEnergy;
>> 454 G4double TetPo = u*electron_mass_c2/PositTotEnergy;
>> 455 G4double Phi = twopi * G4UniformRand();
>> 456 G4double dxEl= sin(TetEl)*cos(Phi),dyEl= sin(TetEl)*sin(Phi),dzEl=cos(TetEl);
>> 457 G4double dxPo=-sin(TetPo)*cos(Phi),dyPo=-sin(TetPo)*sin(Phi),dzPo=cos(TetPo);
>> 458
488 // 459 //
489 G4ThreeVector eDirection, pDirection; << 460 // kinematic of the created pair
490 // 461 //
491 GetAngularDistribution()->SamplePairDirectio << 462 // the electron and positron are assumed to have a symetric
492 eKinEnergy, pKinEnergy, eDirectio << 463 // angular distribution with respect to the Z axis along the parent photon.
493 // create G4DynamicParticle object for the p << 464
494 auto aParticle1 = new G4DynamicParticle(fThe << 465 G4double ElectKineEnergy = max(0.,ElectTotEnergy - electron_mass_c2);
>> 466
>> 467 G4ThreeVector ElectDirection (dxEl, dyEl, dzEl);
>> 468 ElectDirection.rotateUz(GammaDirection);
>> 469
>> 470 // create G4DynamicParticle object for the particle1
>> 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 = max(0.,PositTotEnergy - electron_mass_c2);
>> 477
>> 478 G4ThreeVector PositDirection (dxPo, dyPo, dzPo);
>> 479 PositDirection.rotateUz(GammaDirection);
>> 480
>> 481 // create G4DynamicParticle object for the particle2
>> 482 G4DynamicParticle* aParticle2= new G4DynamicParticle(
>> 483 thePositron,PositDirection,PositKineEnergy);
495 484
496 // create G4DynamicParticle object for the p <<
497 auto aParticle2 = new G4DynamicParticle(fThe <<
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 } <<
505 <<
506 // should be called only by the master and at <<
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 } 492 }
542 493
543 // s goes up to 2 with ds = 0.01 be default << 494 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
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