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25 //
26 //
27 // -------------------------------------------------------------------
28 //
29 // GEANT4 Class file
30 //
31 //
32 // File name: G4BetheHeitlerModel
33 //
34 // Author: Vladimir Ivanchenko on base of Michel Maire code
35 //
36 // Creation date: 15.03.2005
37 //
38 // Modifications by Vladimir Ivanchenko, Michel Maire, Mihaly Novak
39 //
40 // Class Description:
41 //
42 // -------------------------------------------------------------------
43 //
44
45 #include "G4BetheHeitlerModel.hh"
46 #include "G4PhysicalConstants.hh"
47 #include "G4SystemOfUnits.hh"
48 #include "G4Electron.hh"
49 #include "G4Positron.hh"
50 #include "G4Gamma.hh"
51 #include "Randomize.hh"
52 #include "G4ParticleChangeForGamma.hh"
53 #include "G4Pow.hh"
54 #include "G4Exp.hh"
55 #include "G4ModifiedTsai.hh"
56 #include "G4EmParameters.hh"
57 #include "G4EmElementXS.hh"
58 #include "G4AutoLock.hh"
59
60 const G4int G4BetheHeitlerModel::gMaxZet = 120;
61 std::vector<G4BetheHeitlerModel::ElementData*> G4BetheHeitlerModel::gElementData;
62
63 namespace
64 {
65 G4Mutex theBetheHMutex = G4MUTEX_INITIALIZER;
66 }
67
68 G4BetheHeitlerModel::G4BetheHeitlerModel(const G4ParticleDefinition*,
69 const G4String& nam)
70 : G4VEmModel(nam),
71 fG4Calc(G4Pow::GetInstance()), fTheGamma(G4Gamma::Gamma()),
72 fTheElectron(G4Electron::Electron()), fThePositron(G4Positron::Positron()),
73 fParticleChange(nullptr)
74 {
75 SetAngularDistribution(new G4ModifiedTsai());
76 }
77
78 G4BetheHeitlerModel::~G4BetheHeitlerModel()
79 {
80 if (isFirstInstance) {
81 for (auto const & ptr : gElementData) { delete ptr; }
82 gElementData.clear();
83 }
84 delete fXSection;
85 }
86
87 void G4BetheHeitlerModel::Initialise(const G4ParticleDefinition* p,
88 const G4DataVector& cuts)
89 {
90 if (!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
91
92 if (isFirstInstance || gElementData.empty()) {
93 G4AutoLock l(&theBetheHMutex);
94 if (gElementData.empty()) {
95 isFirstInstance = true;
96 gElementData.resize(gMaxZet+1, nullptr);
97
98 // EPICS2017 flag should be checked only once
99 useEPICS2017 = G4EmParameters::Instance()->UseEPICS2017XS();
100 if (useEPICS2017) {
101 fXSection = new G4EmElementXS(1, 100, "convEPICS2017", "/epics2017/pair/pp-cs-");
102 }
103 }
104 // static data should be initialised only in the one instance
105 InitialiseElementData();
106 l.unlock();
107 }
108 // element selectors should be initialised in the master thread
109 if(IsMaster()) {
110 InitialiseElementSelectors(p, cuts);
111 }
112 }
113
114 void G4BetheHeitlerModel::InitialiseLocal(const G4ParticleDefinition*,
115 G4VEmModel* masterModel)
116 {
117 SetElementSelectors(masterModel->GetElementSelectors());
118 }
119
120 // Calculates the microscopic cross section in GEANT4 internal units.
121 // A parametrized formula from L. Urban is used to estimate
122 // the total cross section.
123 // It gives a good description of the data from 1.5 MeV to 100 GeV.
124 // below 1.5 MeV: sigma=sigma(1.5MeV)*(GammaEnergy-2electronmass)
125 // *(GammaEnergy-2electronmass)
126 G4double
127 G4BetheHeitlerModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
128 G4double gammaEnergy, G4double Z,
129 G4double, G4double, G4double)
130 {
131 G4double xSection = 0.0 ;
132 // short versions
133 static const G4double kMC2 = CLHEP::electron_mass_c2;
134 // zero cross section below the kinematical limit: Eg<2mc^2
135 if (Z < 0.9 || gammaEnergy <= 2.0*kMC2) { return xSection; }
136
137 G4int iZ = G4lrint(Z);
138 if (useEPICS2017 && iZ < 101) {
139 return fXSection->GetXS(iZ, gammaEnergy);
140 }
141
142 //
143 static const G4double gammaEnergyLimit = 1.5*CLHEP::MeV;
144 // set coefficients a, b c
145 static const G4double a0 = 8.7842e+2*CLHEP::microbarn;
146 static const G4double a1 = -1.9625e+3*CLHEP::microbarn;
147 static const G4double a2 = 1.2949e+3*CLHEP::microbarn;
148 static const G4double a3 = -2.0028e+2*CLHEP::microbarn;
149 static const G4double a4 = 1.2575e+1*CLHEP::microbarn;
150 static const G4double a5 = -2.8333e-1*CLHEP::microbarn;
151
152 static const G4double b0 = -1.0342e+1*CLHEP::microbarn;
153 static const G4double b1 = 1.7692e+1*CLHEP::microbarn;
154 static const G4double b2 = -8.2381 *CLHEP::microbarn;
155 static const G4double b3 = 1.3063 *CLHEP::microbarn;
156 static const G4double b4 = -9.0815e-2*CLHEP::microbarn;
157 static const G4double b5 = 2.3586e-3*CLHEP::microbarn;
158
159 static const G4double c0 = -4.5263e+2*CLHEP::microbarn;
160 static const G4double c1 = 1.1161e+3*CLHEP::microbarn;
161 static const G4double c2 = -8.6749e+2*CLHEP::microbarn;
162 static const G4double c3 = 2.1773e+2*CLHEP::microbarn;
163 static const G4double c4 = -2.0467e+1*CLHEP::microbarn;
164 static const G4double c5 = 6.5372e-1*CLHEP::microbarn;
165 // check low energy limit of the approximation (1.5 MeV)
166 G4double gammaEnergyOrg = gammaEnergy;
167 if (gammaEnergy < gammaEnergyLimit) { gammaEnergy = gammaEnergyLimit; }
168 // compute gamma energy variables
169 const G4double x = G4Log(gammaEnergy/kMC2);
170 const G4double x2 = x *x;
171 const G4double x3 = x2*x;
172 const G4double x4 = x3*x;
173 const G4double x5 = x4*x;
174 //
175 const G4double F1 = a0 + a1*x + a2*x2 + a3*x3 + a4*x4 + a5*x5;
176 const G4double F2 = b0 + b1*x + b2*x2 + b3*x3 + b4*x4 + b5*x5;
177 const G4double F3 = c0 + c1*x + c2*x2 + c3*x3 + c4*x4 + c5*x5;
178 // compute the approximated cross section
179 xSection = (Z + 1.)*(F1*Z + F2*Z*Z + F3);
180 // check if we are below the limit of the approximation and apply correction
181 if (gammaEnergyOrg < gammaEnergyLimit) {
182 const G4double dum = (gammaEnergyOrg-2.*kMC2)/(gammaEnergyLimit-2.*kMC2);
183 xSection *= dum*dum;
184 }
185 // make sure that the cross section is never negative
186 xSection = std::max(xSection, 0.);
187 return xSection;
188 }
189
190 // The secondaries e+e- energies are sampled using the Bethe - Heitler
191 // cross sections with Coulomb correction.
192 // A modified version of the random number techniques of Butcher & Messel
193 // is used (Nuc Phys 20(1960),15).
194 //
195 // GEANT4 internal units.
196 //
197 // Note 1 : Effects due to the breakdown of the Born approximation at
198 // low energy are ignored.
199 // Note 2 : The differential cross section implicitly takes account of
200 // pair creation in both nuclear and atomic electron fields.
201 // However triplet prodution is not generated.
202 void G4BetheHeitlerModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
203 const G4MaterialCutsCouple* couple,
204 const G4DynamicParticle* aDynamicGamma,
205 G4double, G4double)
206 {
207 // set some constant values
208 const G4double gammaEnergy = aDynamicGamma->GetKineticEnergy();
209 const G4double eps0 = CLHEP::electron_mass_c2/gammaEnergy;
210 //
211 // check kinematical limit: gamma energy(Eg) must be at least 2 e- rest mass
212 if (eps0 > 0.5) { return; }
213 //
214 // select target element of the material (probs. are based on partial x-secs)
215 const G4Element* anElement = SelectTargetAtom(couple, fTheGamma, gammaEnergy,
216 aDynamicGamma->GetLogKineticEnergy());
217
218 //
219 // get the random engine
220 CLHEP::HepRandomEngine* rndmEngine = G4Random::getTheEngine();
221 //
222 // 'eps' is the total energy transferred to one of the e-/e+ pair in initial
223 // gamma energy units Eg. Since the corresponding DCS is symmetric on eps=0.5,
224 // the kinematical limits for eps0=mc^2/Eg <= eps <= 0.5
225 // 1. 'eps' is sampled uniformly on the [eps0, 0.5] inteval if Eg<Egsmall
226 // 2. otherwise, on the [eps_min, 0.5] interval according to the DCS (case 2.)
227 G4double eps;
228 // case 1.
229 static const G4double Egsmall = 2.*CLHEP::MeV;
230 if (gammaEnergy < Egsmall) {
231 eps = eps0 + (0.5-eps0)*rndmEngine->flat();
232 } else {
233 // case 2.
234 // get the Coulomb factor for the target element (Z) and gamma energy (Eg)
235 // F(Z) = 8*ln(Z)/3 if Eg <= 50 [MeV] => no Coulomb correction
236 // F(Z) = 8*ln(Z)/3 + 8*fc(Z) if Eg > 50 [MeV] => fc(Z) is the Coulomb cor.
237 //
238 // The screening variable 'delta(eps)' = 136*Z^{-1/3}*eps0/[eps(1-eps)]
239 // Due to the Coulomb correction, the DCS can go below zero even at
240 // kinematicaly allowed eps > eps0 values. In order to exclude this eps
241 // range with negative DCS, the minimum eps value will be set to eps_min =
242 // max[eps0, epsp] with epsp is the solution of SF(delta(epsp)) - F(Z)/2 = 0
243 // with SF being the screening function (SF1=SF2 at high value of delta).
244 // The solution is epsp = 0.5 - 0.5*sqrt[ 1 - 4*136*Z^{-1/3}eps0/deltap]
245 // with deltap = Exp[(42.038-F(Z))/8.29]-0.958. So the limits are:
246 // - when eps=eps_max = 0.5 => delta_min = 136*Z^{-1/3}*eps0/4
247 // - epsp = 0.5 - 0.5*sqrt[ 1 - delta_min/deltap]
248 // - and eps_min = max[eps0, epsp]
249 static const G4double midEnergy = 50.*CLHEP::MeV;
250 const G4int iZet = std::min(gMaxZet, anElement->GetZasInt());
251 const G4double deltaFactor = 136.*eps0/anElement->GetIonisation()->GetZ3();
252 G4double deltaMax = gElementData[iZet]->fDeltaMaxLow;
253 G4double FZ = 8.*anElement->GetIonisation()->GetlogZ3();
254 if (gammaEnergy > midEnergy) {
255 FZ += 8.*(anElement->GetfCoulomb());
256 deltaMax = gElementData[iZet]->fDeltaMaxHigh;
257 }
258 const G4double deltaMin = 4.*deltaFactor;
259 //
260 // compute the limits of eps
261 const G4double epsp = 0.5 - 0.5*std::sqrt(1. - deltaMin/deltaMax) ;
262 const G4double epsMin = std::max(eps0,epsp);
263 const G4double epsRange = 0.5 - epsMin;
264 //
265 // sample the energy rate (eps) of the created electron (or positron)
266 G4double F10, F20;
267 ScreenFunction12(deltaMin, F10, F20);
268 F10 -= FZ;
269 F20 -= FZ;
270 const G4double NormF1 = std::max(F10 * epsRange * epsRange, 0.);
271 const G4double NormF2 = std::max(1.5 * F20 , 0.);
272 const G4double NormCond = NormF1/(NormF1 + NormF2);
273 // we will need 3 uniform random number for each trial of sampling
274 G4double rndmv[3];
275 G4double greject = 0.;
276 do {
277 rndmEngine->flatArray(3, rndmv);
278 if (NormCond > rndmv[0]) {
279 eps = 0.5 - epsRange * fG4Calc->A13(rndmv[1]);
280 const G4double delta = deltaFactor/(eps*(1.-eps));
281 greject = (ScreenFunction1(delta)-FZ)/F10;
282 } else {
283 eps = epsMin + epsRange*rndmv[1];
284 const G4double delta = deltaFactor/(eps*(1.-eps));
285 greject = (ScreenFunction2(delta)-FZ)/F20;
286 }
287 // Loop checking, 03-Aug-2015, Vladimir Ivanchenko
288 } while (greject < rndmv[2]);
289 } // end of eps sampling
290 //
291 // select charges randomly
292 G4double eTotEnergy, pTotEnergy;
293 if (rndmEngine->flat() > 0.5) {
294 eTotEnergy = (1.-eps)*gammaEnergy;
295 pTotEnergy = eps*gammaEnergy;
296 } else {
297 pTotEnergy = (1.-eps)*gammaEnergy;
298 eTotEnergy = eps*gammaEnergy;
299 }
300 //
301 // sample pair kinematics
302 const G4double eKinEnergy = std::max(0.,eTotEnergy - CLHEP::electron_mass_c2);
303 const G4double pKinEnergy = std::max(0.,pTotEnergy - CLHEP::electron_mass_c2);
304 //
305 G4ThreeVector eDirection, pDirection;
306 //
307 GetAngularDistribution()->SamplePairDirections(aDynamicGamma,
308 eKinEnergy, pKinEnergy,
309 eDirection, pDirection);
310 // create G4DynamicParticle object for the particle1
311 auto aParticle1= new G4DynamicParticle(fTheElectron,eDirection,eKinEnergy);
312 // create G4DynamicParticle object for the particle2
313 auto aParticle2= new G4DynamicParticle(fThePositron,pDirection,pKinEnergy);
314 // Fill output vector
315 fvect->push_back(aParticle1);
316 fvect->push_back(aParticle2);
317 // kill incident photon
318 fParticleChange->SetProposedKineticEnergy(0.);
319 fParticleChange->ProposeTrackStatus(fStopAndKill);
320 }
321
322 // should be called only by the master and at initialisation
323 void G4BetheHeitlerModel::InitialiseElementData()
324 {
325 // create for all elements that are in the detector
326 auto elemTable = G4Element::GetElementTable();
327 for (auto const & elem : *elemTable) {
328 const G4int Z = elem->GetZasInt();
329 const G4int iz = std::min(gMaxZet, Z);
330 if (nullptr == gElementData[iz]) { // create it if doesn't exist yet
331 G4double FZLow = 8.*elem->GetIonisation()->GetlogZ3();
332 G4double FZHigh = FZLow + 8.*elem->GetfCoulomb();
333 auto elD = new ElementData();
334 elD->fDeltaMaxLow = G4Exp((42.038 - FZLow )/8.29) - 0.958;
335 elD->fDeltaMaxHigh = G4Exp((42.038 - FZHigh)/8.29) - 0.958;
336 gElementData[iz] = elD;
337 }
338 if (useEPICS2017 && Z < 101) {
339 fXSection->Retrieve(Z);
340 }
341 }
342
343 }
344
345