source: trunk/source/processes/electromagnetic/standard/src/G4PairProductionRelModel.cc

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25//
26// $Id: G4PairProductionRelModel.cc,v 1.4 2010/10/26 09:06:04 vnivanch Exp $
27// GEANT4 tag $Name: emstand-V09-03-24 $
28//
29// -------------------------------------------------------------------
30//
31// GEANT4 Class file
32//
33//
34// File name: G4PairProductionRelModel
35//
36// Author: Andreas Schaelicke
37//
38// Creation date: 02.04.2009
39//
40// Modifications:
41//
42// Class Description:
43//
44// Main References:
45// J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 581.
46// S.Klein, Rev. Mod. Phys. 71 (1999) 1501.
47// T.Stanev et.al., Phys. Rev. D25 (1982) 1291.
48// M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media, Wiley, 1972.
49//
50// -------------------------------------------------------------------
51//
52//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
53//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
54
55#include "G4PairProductionRelModel.hh"
56#include "G4Gamma.hh"
57#include "G4Electron.hh"
58#include "G4Positron.hh"
59
60#include "G4ParticleChangeForGamma.hh"
61#include "G4LossTableManager.hh"
62
63
64//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
65
66using namespace std;
67
68
69const G4double G4PairProductionRelModel::facFel = log(184.15);
70const G4double G4PairProductionRelModel::facFinel = log(1194.); // 1440.
71
72const G4double G4PairProductionRelModel::preS1 = 1./(184.15*184.15);
73const G4double G4PairProductionRelModel::logTwo = log(2.);
74
75const G4double G4PairProductionRelModel::xgi[]={ 0.0199, 0.1017, 0.2372, 0.4083,
76 0.5917, 0.7628, 0.8983, 0.9801 };
77const G4double G4PairProductionRelModel::wgi[]={ 0.0506, 0.1112, 0.1569, 0.1813,
78 0.1813, 0.1569, 0.1112, 0.0506 };
79const G4double G4PairProductionRelModel::Fel_light[] = {0., 5.31 , 4.79 , 4.74 , 4.71} ;
80const G4double G4PairProductionRelModel::Finel_light[] = {0., 6.144 , 5.621 , 5.805 , 5.924} ;
81
82
83
84G4PairProductionRelModel::G4PairProductionRelModel(const G4ParticleDefinition*,
85 const G4String& nam)
86 : G4VEmModel(nam),
87 fLPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)*0.5),
88 fLPMflag(true),
89 lpmEnergy(0.),
90 use_completescreening(false)
91{
92 fParticleChange = 0;
93 theGamma = G4Gamma::Gamma();
94 thePositron = G4Positron::Positron();
95 theElectron = G4Electron::Electron();
96
97 nist = G4NistManager::Instance();
98
99 currentZ = z13 = z23 = lnZ = Fel = Finel = fCoulomb = phiLPM = gLPM = xiLPM = 0;
100
101}
102
103//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
104
105G4PairProductionRelModel::~G4PairProductionRelModel()
106{}
107
108//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
109
110void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p,
111 const G4DataVector& cuts)
112{
113 if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
114 InitialiseElementSelectors(p, cuts);
115}
116
117//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
118
119G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double totalEnergy, G4double Z)
120{
121 G4double cross = 0.0;
122
123 // number of intervals and integration step
124 G4double vcut = electron_mass_c2/totalEnergy ;
125
126 // limits by the screening variable
127 G4double dmax = DeltaMax();
128 G4double dmin = min(DeltaMin(totalEnergy),dmax);
129 G4double vcut1 = 0.5 - 0.5*sqrt(1. - dmin/dmax) ;
130 vcut = max(vcut, vcut1);
131
132
133 G4double vmax = 0.5;
134 G4int n = 1; // needs optimisation
135
136 G4double delta = (vmax - vcut)*totalEnergy/G4double(n);
137
138 G4double e0 = vcut*totalEnergy;
139 G4double xs;
140
141 // simple integration
142 for(G4int l=0; l<n; l++,e0 += delta) {
143 for(G4int i=0; i<8; i++) {
144
145 G4double eg = (e0 + xgi[i]*delta);
146 if (fLPMflag && totalEnergy>100.*GeV)
147 xs = ComputeRelDXSectionPerAtom(eg,totalEnergy,Z);
148 else
149 xs = ComputeDXSectionPerAtom(eg,totalEnergy,Z);
150 cross += wgi[i]*xs;
151
152 }
153 }
154
155 cross *= delta*2.;
156
157 return cross;
158}
159
160//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
161
162G4double
163G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double eplusEnergy,
164 G4double totalEnergy,
165 G4double /*Z*/)
166{
167 // most simple case - complete screening:
168
169 // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
170 // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
171 // y = E+/k
172 G4double yp=eplusEnergy/totalEnergy;
173 G4double ym=1.-yp;
174
175 G4double cross = 0.;
176 if (use_completescreening)
177 cross = (yp*yp + ym*ym + 2./3.*ym*yp)*(Fel - fCoulomb) + 1./9.*yp*ym;
178 else {
179 G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
180 cross = (yp*yp + ym*ym)*(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
181 + 2./3.*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
182 }
183 return cross/totalEnergy;
184
185}
186//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
187
188G4double
189G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double eplusEnergy,
190 G4double totalEnergy,
191 G4double /*Z*/)
192{
193 // most simple case - complete screening:
194
195 // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
196 // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
197 // y = E+/k
198 G4double yp=eplusEnergy/totalEnergy;
199 G4double ym=1.-yp;
200
201 CalcLPMFunctions(totalEnergy,eplusEnergy); // gamma
202
203 G4double cross = 0.;
204 if (use_completescreening)
205 cross = xiLPM*(2./3.*phiLPM*(yp*yp + ym*ym) + gLPM)*(Fel - fCoulomb);
206 else {
207 G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
208 cross = (1./3.*gLPM + 2./3.*phiLPM)*(yp*yp + ym*ym)
209 *(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
210 + 2./3.*gLPM*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
211 cross *= xiLPM;
212 }
213 return cross/totalEnergy;
214
215}
216
217//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
218
219void G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplus)
220{
221 // *** calculate lpm variable s & sprime ***
222 // Klein eqs. (78) & (79)
223 G4double sprime = sqrt(0.125*k*lpmEnergy/(eplus*(k-eplus)));
224
225 G4double s1 = preS1*z23;
226 G4double logS1 = 2./3.*lnZ-2.*facFel;
227 G4double logTS1 = logTwo+logS1;
228
229 xiLPM = 2.;
230
231 if (sprime>1)
232 xiLPM = 1.;
233 else if (sprime>sqrt(2.)*s1) {
234 G4double h = log(sprime)/logTS1;
235 xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1;
236 }
237
238 G4double s = sprime/sqrt(xiLPM);
239// G4cout<<"k="<<k<<" y="<<eplus/k<<G4endl;
240// G4cout<<"s="<<s<<G4endl;
241
242 // *** calculate supression functions phi and G ***
243 // Klein eqs. (77)
244 G4double s2=s*s;
245 G4double s3=s*s2;
246 G4double s4=s2*s2;
247
248 if (s<0.1) {
249 // high suppression limit
250 phiLPM = 6.*s - 18.84955592153876*s2 + 39.47841760435743*s3
251 - 57.69873135166053*s4;
252 gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4;
253 }
254 else if (s<1.9516) {
255 // intermediate suppression
256 // using eq.77 approxim. valid s<2.
257 phiLPM = 1.-exp(-6.*s*(1.+(3.-pi)*s)
258 +s3/(0.623+0.795*s+0.658*s2));
259 if (s<0.415827397755) {
260 // using eq.77 approxim. valid 0.07<s<2
261 G4double psiLPM = 1-exp(-4*s-8*s2/(1+3.936*s+4.97*s2-0.05*s3+7.50*s4));
262 gLPM = 3*psiLPM-2*phiLPM;
263 }
264 else {
265 // using alternative parametrisiation
266 G4double pre = -0.16072300849123999 + s*3.7550300067531581 + s2*-1.7981383069010097
267 + s3*0.67282686077812381 + s4*-0.1207722909879257;
268 gLPM = tanh(pre);
269 }
270 }
271 else {
272 // low suppression limit valid s>2.
273 phiLPM = 1. - 0.0119048/s4;
274 gLPM = 1. - 0.0230655/s4;
275 }
276
277 // *** make sure suppression is smaller than 1 ***
278 // *** caused by Migdal approximation in xi ***
279 if (xiLPM*phiLPM>1. || s>0.57) xiLPM=1./phiLPM;
280}
281
282
283//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
284
285G4double
286G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
287 G4double gammaEnergy, G4double Z,
288 G4double, G4double, G4double)
289{
290 // static const G4double gammaEnergyLimit = 1.5*MeV;
291 G4double crossSection = 0.0 ;
292 if ( Z < 0.9 ) return crossSection;
293 if ( gammaEnergy <= 2.0*electron_mass_c2 ) return crossSection;
294
295 SetCurrentElement(Z);
296 // choose calculator according to parameters and switches
297 // in the moment only one calculator:
298 crossSection=ComputeXSectionPerAtom(gammaEnergy,Z);
299
300 G4double xi = Finel/(Fel - fCoulomb); // inelastic contribution
301 crossSection*=4.*Z*(Z+xi)*fine_structure_const*classic_electr_radius*classic_electr_radius;
302
303 return crossSection;
304}
305
306//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
307
308void
309G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
310 const G4MaterialCutsCouple* couple,
311 const G4DynamicParticle* aDynamicGamma,
312 G4double,
313 G4double)
314// The secondaries e+e- energies are sampled using the Bethe - Heitler
315// cross sections with Coulomb correction.
316// A modified version of the random number techniques of Butcher & Messel
317// is used (Nuc Phys 20(1960),15).
318//
319// GEANT4 internal units.
320//
321// Note 1 : Effects due to the breakdown of the Born approximation at
322// low energy are ignored.
323// Note 2 : The differential cross section implicitly takes account of
324// pair creation in both nuclear and atomic electron fields.
325// However triplet prodution is not generated.
326{
327 const G4Material* aMaterial = couple->GetMaterial();
328
329 G4double GammaEnergy = aDynamicGamma->GetKineticEnergy();
330 G4ParticleMomentum GammaDirection = aDynamicGamma->GetMomentumDirection();
331
332 G4double epsil ;
333 G4double epsil0 = electron_mass_c2/GammaEnergy ;
334 if(epsil0 > 1.0) return;
335
336 // do it fast if GammaEnergy < 2. MeV
337 static const G4double Egsmall=2.*MeV;
338
339 // select randomly one element constituing the material
340 const G4Element* anElement = SelectRandomAtom(aMaterial, theGamma, GammaEnergy);
341
342 if (GammaEnergy < Egsmall) {
343
344 epsil = epsil0 + (0.5-epsil0)*G4UniformRand();
345
346 } else {
347 // now comes the case with GammaEnergy >= 2. MeV
348
349 // Extract Coulomb factor for this Element
350 G4double FZ = 8.*(anElement->GetIonisation()->GetlogZ3());
351 if (GammaEnergy > 50.*MeV) FZ += 8.*(anElement->GetfCoulomb());
352
353 // limits of the screening variable
354 G4double screenfac = 136.*epsil0/(anElement->GetIonisation()->GetZ3());
355 G4double screenmax = exp ((42.24 - FZ)/8.368) - 0.952 ;
356 G4double screenmin = min(4.*screenfac,screenmax);
357
358 // limits of the energy sampling
359 G4double epsil1 = 0.5 - 0.5*sqrt(1. - screenmin/screenmax) ;
360 G4double epsilmin = max(epsil0,epsil1) , epsilrange = 0.5 - epsilmin;
361
362 //
363 // sample the energy rate of the created electron (or positron)
364 //
365 //G4double epsil, screenvar, greject ;
366 G4double screenvar, greject ;
367
368 G4double F10 = ScreenFunction1(screenmin) - FZ;
369 G4double F20 = ScreenFunction2(screenmin) - FZ;
370 G4double NormF1 = max(F10*epsilrange*epsilrange,0.);
371 G4double NormF2 = max(1.5*F20,0.);
372
373 do {
374 if ( NormF1/(NormF1+NormF2) > G4UniformRand() ) {
375 epsil = 0.5 - epsilrange*pow(G4UniformRand(), 0.333333);
376 screenvar = screenfac/(epsil*(1-epsil));
377 if (fLPMflag && GammaEnergy>100.*GeV) {
378 CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
379 greject = xiLPM*((gLPM+2.*phiLPM)*Phi1(screenvar) - gLPM*Phi2(screenvar) - phiLPM*FZ)/F10;
380 }
381 else {
382 greject = (ScreenFunction1(screenvar) - FZ)/F10;
383 }
384
385 } else {
386 epsil = epsilmin + epsilrange*G4UniformRand();
387 screenvar = screenfac/(epsil*(1-epsil));
388 if (fLPMflag && GammaEnergy>100.*GeV) {
389 CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
390 greject = xiLPM*((0.5*gLPM+phiLPM)*Phi1(screenvar) + 0.5*gLPM*Phi2(screenvar) - 0.5*(gLPM+phiLPM)*FZ)/F20;
391 }
392 else {
393 greject = (ScreenFunction2(screenvar) - FZ)/F20;
394 }
395 }
396
397 } while( greject < G4UniformRand() );
398
399 } // end of epsil sampling
400
401 //
402 // fixe charges randomly
403 //
404
405 G4double ElectTotEnergy, PositTotEnergy;
406 if (G4UniformRand() > 0.5) {
407
408 ElectTotEnergy = (1.-epsil)*GammaEnergy;
409 PositTotEnergy = epsil*GammaEnergy;
410
411 } else {
412
413 PositTotEnergy = (1.-epsil)*GammaEnergy;
414 ElectTotEnergy = epsil*GammaEnergy;
415 }
416
417 //
418 // scattered electron (positron) angles. ( Z - axis along the parent photon)
419 //
420 // universal distribution suggested by L. Urban
421 // (Geant3 manual (1993) Phys211),
422 // derived from Tsai distribution (Rev Mod Phys 49,421(1977))
423
424 G4double u;
425 const G4double a1 = 0.625 , a2 = 3.*a1 , d = 27. ;
426
427 if (9./(9.+d) >G4UniformRand()) u= - log(G4UniformRand()*G4UniformRand())/a1;
428 else u= - log(G4UniformRand()*G4UniformRand())/a2;
429
430 G4double TetEl = u*electron_mass_c2/ElectTotEnergy;
431 G4double TetPo = u*electron_mass_c2/PositTotEnergy;
432 G4double Phi = twopi * G4UniformRand();
433 G4double dxEl= sin(TetEl)*cos(Phi),dyEl= sin(TetEl)*sin(Phi),dzEl=cos(TetEl);
434 G4double dxPo=-sin(TetPo)*cos(Phi),dyPo=-sin(TetPo)*sin(Phi),dzPo=cos(TetPo);
435
436 //
437 // kinematic of the created pair
438 //
439 // the electron and positron are assumed to have a symetric
440 // angular distribution with respect to the Z axis along the parent photon.
441
442 G4double ElectKineEnergy = max(0.,ElectTotEnergy - electron_mass_c2);
443
444 G4ThreeVector ElectDirection (dxEl, dyEl, dzEl);
445 ElectDirection.rotateUz(GammaDirection);
446
447 // create G4DynamicParticle object for the particle1
448 G4DynamicParticle* aParticle1= new G4DynamicParticle(
449 theElectron,ElectDirection,ElectKineEnergy);
450
451 // the e+ is always created (even with Ekine=0) for further annihilation.
452
453 G4double PositKineEnergy = max(0.,PositTotEnergy - electron_mass_c2);
454
455 G4ThreeVector PositDirection (dxPo, dyPo, dzPo);
456 PositDirection.rotateUz(GammaDirection);
457
458 // create G4DynamicParticle object for the particle2
459 G4DynamicParticle* aParticle2= new G4DynamicParticle(
460 thePositron,PositDirection,PositKineEnergy);
461
462 // Fill output vector
463 fvect->push_back(aParticle1);
464 fvect->push_back(aParticle2);
465
466 // kill incident photon
467 fParticleChange->SetProposedKineticEnergy(0.);
468 fParticleChange->ProposeTrackStatus(fStopAndKill);
469}
470
471//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
472
473
474void G4PairProductionRelModel::SetupForMaterial(const G4ParticleDefinition*,
475 const G4Material* mat, G4double)
476{
477 lpmEnergy = mat->GetRadlen()*fLPMconstant;
478 // G4cout<<" lpmEnergy="<<lpmEnergy<<G4endl;
479}
480
481//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
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