source: trunk/source/processes/electromagnetic/standard/src/G4eBremsstrahlungModel.cc@ 1199

Last change on this file since 1199 was 1196, checked in by garnier, 16 years ago

update CVS release candidate geant4.9.3.01
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[819]1//
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25//
[1055]26// $Id: G4eBremsstrahlungModel.cc,v 1.44 2009/04/09 18:41:18 vnivanch Exp $
[1196]27// GEANT4 tag $Name: geant4-09-03-cand-01 $
[819]28//
29// -------------------------------------------------------------------
30//
31// GEANT4 Class file
32//
33//
34// File name: G4eBremsstrahlungModel
35//
36// Author: Vladimir Ivanchenko on base of Laszlo Urban code
37//
38// Creation date: 03.01.2002
39//
40// Modifications:
41//
42// 11-11-02 Fix division by 0 (V.Ivanchenko)
43// 04-12-02 Change G4DynamicParticle constructor in PostStep (V.Ivanchenko)
44// 23-12-02 Change interface in order to move to cut per region (V.Ivanchenko)
45// 24-01-03 Fix for compounds (V.Ivanchenko)
46// 27-01-03 Make models region aware (V.Ivanchenko)
47// 13-02-03 Add name (V.Ivanchenko)
48// 09-05-03 Fix problem of supression function + optimise sampling (V.Ivanchenko)
49// 20-05-04 Correction to ensure unit independence (L.Urban)
50// 08-04-05 Major optimisation of internal interfaces (V.Ivantchenko)
51// 03-08-05 Add extra protection at initialisation (V.Ivantchenko)
52// 07-02-06 public function ComputeCrossSectionPerAtom() (mma)
53// 21-03-06 Fix problem of initialisation in case when cuts are not defined (VI)
54// 27-03-06 Fix calculation of fl parameter at low energy (energy loss) (VI)
55// 15-02-07 correct LPMconstant by a factor 2, thanks to G. Depaola (mma)
[961]56// 09-09-08 MigdalConstant increased in (2pi)^2 times (A.Schaelicke)
[819]57//
58// Class Description:
59//
60//
61// -------------------------------------------------------------------
62//
63//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
64//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
65
66#include "G4eBremsstrahlungModel.hh"
67#include "G4Electron.hh"
68#include "G4Positron.hh"
69#include "G4Gamma.hh"
70#include "Randomize.hh"
71#include "G4Material.hh"
72#include "G4Element.hh"
73#include "G4ElementVector.hh"
74#include "G4ProductionCutsTable.hh"
75#include "G4DataVector.hh"
76#include "G4ParticleChangeForLoss.hh"
77
78//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
79
80using namespace std;
81
82G4eBremsstrahlungModel::G4eBremsstrahlungModel(const G4ParticleDefinition* p,
83 const G4String& nam)
84 : G4VEmModel(nam),
85 particle(0),
86 isElectron(true),
87 probsup(1.0),
[961]88 MigdalConstant(classic_electr_radius*electron_Compton_length*electron_Compton_length*4.0*pi),
[819]89 LPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)),
90 isInitialised(false)
91{
92 if(p) SetParticle(p);
93 theGamma = G4Gamma::Gamma();
94 minThreshold = 1.0*keV;
95}
96
97//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
98
99G4eBremsstrahlungModel::~G4eBremsstrahlungModel()
100{
101 size_t n = partialSumSigma.size();
102 if(n > 0) {
103 for(size_t i=0; i<n; i++) {
104 delete partialSumSigma[i];
105 }
106 }
107}
108
109//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
110
111void G4eBremsstrahlungModel::SetParticle(const G4ParticleDefinition* p)
112{
113 particle = p;
114 if(p == G4Electron::Electron()) isElectron = true;
115 else isElectron = false;
116}
117
118//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
119
120G4double G4eBremsstrahlungModel::MinEnergyCut(const G4ParticleDefinition*,
121 const G4MaterialCutsCouple*)
122{
123 return minThreshold;
124}
125
126//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
127
128void G4eBremsstrahlungModel::Initialise(const G4ParticleDefinition* p,
129 const G4DataVector& cuts)
130{
131 if(p) SetParticle(p);
132 highKinEnergy = HighEnergyLimit();
133 lowKinEnergy = LowEnergyLimit();
134 const G4ProductionCutsTable* theCoupleTable=
135 G4ProductionCutsTable::GetProductionCutsTable();
136
137 if(theCoupleTable) {
138 G4int numOfCouples = theCoupleTable->GetTableSize();
139
140 G4int nn = partialSumSigma.size();
141 G4int nc = cuts.size();
142 if(nn > 0) {
143 for (G4int ii=0; ii<nn; ii++){
144 G4DataVector* a=partialSumSigma[ii];
145 if ( a ) delete a;
146 }
147 partialSumSigma.clear();
148 }
149 if(numOfCouples>0) {
150 for (G4int i=0; i<numOfCouples; i++) {
151 G4double cute = DBL_MAX;
152 if(i < nc) cute = cuts[i];
153 const G4MaterialCutsCouple* couple = theCoupleTable->GetMaterialCutsCouple(i);
154 const G4Material* material = couple->GetMaterial();
155 G4DataVector* dv = ComputePartialSumSigma(material, 0.5*highKinEnergy,
156 std::min(cute, 0.25*highKinEnergy));
157 partialSumSigma.push_back(dv);
158 }
159 }
160 }
161 if(isInitialised) return;
[1055]162 fParticleChange = GetParticleChangeForLoss();
[819]163 isInitialised = true;
164}
165
166//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
167
168G4double G4eBremsstrahlungModel::ComputeDEDXPerVolume(
169 const G4Material* material,
170 const G4ParticleDefinition* p,
171 G4double kineticEnergy,
172 G4double cutEnergy)
173{
174 if(!particle) SetParticle(p);
175 if(kineticEnergy < lowKinEnergy) return 0.0;
176
177 const G4double thigh = 100.*GeV;
178
179 G4double cut = std::min(cutEnergy, kineticEnergy);
180
181 G4double rate, loss;
182 const G4double factorHigh = 36./(1450.*GeV);
183 const G4double coef1 = -0.5;
184 const G4double coef2 = 2./9.;
185
186 const G4ElementVector* theElementVector = material->GetElementVector();
187 const G4double* theAtomicNumDensityVector = material->GetAtomicNumDensityVector();
188
189 G4double totalEnergy = kineticEnergy + electron_mass_c2;
190 G4double dedx = 0.0;
191
192 // loop for elements in the material
193 for (size_t i=0; i<material->GetNumberOfElements(); i++) {
194
195 G4double Z = (*theElementVector)[i]->GetZ();
196 G4double natom = theAtomicNumDensityVector[i];
197
198 // loss for MinKinEnergy<KineticEnergy<=100 GeV
199 if (kineticEnergy <= thigh) {
200
201 // x = log(totalEnergy/electron_mass_c2);
202 loss = ComputeBremLoss(Z, kineticEnergy, cut) ;
203 if (!isElectron) loss *= PositronCorrFactorLoss(Z, kineticEnergy, cut);
204
205 // extrapolation for KineticEnergy>100 GeV
206 } else {
207
208 // G4double xhigh = log(thigh/electron_mass_c2);
209 G4double cuthigh = thigh*0.5;
210
211 if (cut < thigh) {
212
213 loss = ComputeBremLoss(Z, thigh, cut) ;
214 if (!isElectron) loss *= PositronCorrFactorLoss(Z, thigh, cut) ;
215 rate = cut/totalEnergy;
216 loss *= (1. + coef1*rate + coef2*rate*rate);
217 rate = cut/thigh;
218 loss /= (1.+coef1*rate+coef2*rate*rate);
219
220 } else {
221
222 loss = ComputeBremLoss(Z, thigh, cuthigh) ;
223 if (!isElectron) loss *= PositronCorrFactorLoss(Z, thigh, cuthigh) ;
224 rate = cut/totalEnergy;
225 loss *= (1. + coef1*rate + coef2*rate*rate);
226 loss *= cut*factorHigh;
227 }
228 }
229 loss *= natom;
230
231 G4double kp2 = MigdalConstant*totalEnergy*totalEnergy
232 * (material->GetElectronDensity()) ;
233
234 // now compute the correction due to the supression(s)
235 G4double kmin = 1.*eV;
236 G4double kmax = cut;
237
238 if (kmax > kmin) {
239
240 G4double floss = 0.;
241 G4int nmax = 100;
242
243 G4double vmin=log(kmin);
244 G4double vmax=log(kmax) ;
245 G4int nn = (G4int)(nmax*(vmax-vmin)/(log(highKinEnergy)-vmin)) ;
246 G4double u,fac,c,v,dv ;
247 if(nn > 0) {
248
249 dv = (vmax-vmin)/nn ;
250 v = vmin-dv ;
251
252 for(G4int n=0; n<=nn; n++) {
253
254 v += dv;
255 u = exp(v);
256 fac = u*SupressionFunction(material,kineticEnergy,u);
257 fac *= probsup*(u*u/(u*u+kp2))+1.-probsup;
258 if ((n==0)||(n==nn)) c=0.5;
259 else c=1. ;
260 fac *= c ;
261 floss += fac ;
262 }
263 floss *=dv/(kmax-kmin);
264
265 } else {
266 floss = 1.;
267 }
268 if(floss > 1.) floss = 1.;
269 // correct the loss
270 loss *= floss;
271 }
272 dedx += loss;
273 }
274 if(dedx < 0.) dedx = 0.;
275 return dedx;
276}
277
278//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
279
280G4double G4eBremsstrahlungModel::ComputeBremLoss(G4double Z, G4double T,
281 G4double Cut)
282
283// compute loss due to soft brems
284{
285 static const G4double beta=1.0, ksi=2.0;
286 static const G4double clossh = 0.254 , closslow = 1./3. , alosslow = 1. ;
287 static const G4double Tlim= 10.*MeV ;
288
289 static const G4double xlim = 1.2 ;
290 static const G4int NZ = 8 ;
291 static const G4int Nloss = 11 ;
292 static const G4double ZZ[NZ] =
293 {2.,4.,6.,14.,26.,50.,82.,92.};
294 static const G4double coefloss[NZ][Nloss] = {
295 // Z=2
296 { 0.98916, 0.47564, -0.2505, -0.45186, 0.14462,
297 0.21307, -0.013738, -0.045689, -0.0042914, 0.0034429,
298 0.00064189},
299
300 // Z=4
301 { 1.0626, 0.37662, -0.23646, -0.45188, 0.14295,
302 0.22906, -0.011041, -0.051398, -0.0055123, 0.0039919,
303 0.00078003},
304 // Z=6
305 { 1.0954, 0.315, -0.24011, -0.43849, 0.15017,
306 0.23001, -0.012846, -0.052555, -0.0055114, 0.0041283,
307 0.00080318},
308
309 // Z=14
310 { 1.1649, 0.18976, -0.24972, -0.30124, 0.1555,
311 0.13565, -0.024765, -0.027047, -0.00059821, 0.0019373,
312 0.00027647},
313
314 // Z=26
315 { 1.2261, 0.14272, -0.25672, -0.28407, 0.13874,
316 0.13586, -0.020562, -0.026722, -0.00089557, 0.0018665,
317 0.00026981},
318
319 // Z=50
320 { 1.3147, 0.020049, -0.35543, -0.13927, 0.17666,
321 0.073746, -0.036076, -0.013407, 0.0025727, 0.00084005,
322 -1.4082e-05},
323
324 // Z=82
325 { 1.3986, -0.10586, -0.49187, -0.0048846, 0.23621,
326 0.031652, -0.052938, -0.0076639, 0.0048181, 0.00056486,
327 -0.00011995},
328
329 // Z=92
330 { 1.4217, -0.116, -0.55497, -0.044075, 0.27506,
331 0.081364, -0.058143, -0.023402, 0.0031322, 0.0020201,
332 0.00017519}
333
334 } ;
335 static G4double aaa = 0.414;
336 static G4double bbb = 0.345;
337 static G4double ccc = 0.460;
338
339 G4int iz = 0;
340 G4double delz = 1.e6;
341 for (G4int ii=0; ii<NZ; ii++)
342 {
343 G4double dz = std::abs(Z-ZZ[ii]);
344 if(dz < delz) {
345 iz = ii;
346 delz = dz;
347 }
348 }
349
350 G4double xx = log10(T/MeV);
351 G4double fl = 1.;
352
353 if (xx <= xlim)
354 {
355 xx /= xlim;
356 G4double yy = 1.0;
357 fl = 0.0;
358 for (G4int j=0; j<Nloss; j++) {
359 fl += yy+coefloss[iz][j];
360 yy *= xx;
361 }
362 if (fl < 0.00001) fl = 0.00001;
363 else if (fl > 1.0) fl = 1.0;
364 }
365
366 G4double loss;
367 G4double E = T+electron_mass_c2 ;
368
369 loss = Z*(Z+ksi)*E*E/(T+E)*exp(beta*log(Cut/T))*(2.-clossh*exp(log(Z)/4.));
370 if (T <= Tlim) loss /= exp(closslow*log(Tlim/T));
371 if( T <= Cut) loss *= exp(alosslow*log(T/Cut));
372 // correction
373 loss *= (aaa+bbb*T/Tlim)/(1.+ccc*T/Tlim);
374 loss *= fl;
375 loss /= Avogadro;
376
377 return loss;
378}
379
380//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
381
382G4double G4eBremsstrahlungModel::PositronCorrFactorLoss(G4double Z,
383 G4double kineticEnergy, G4double cut)
384
385//calculates the correction factor for the energy loss due to bremsstrahlung for positrons
386//the same correction is in the (discrete) bremsstrahlung
387
388{
389 static const G4double K = 132.9416*eV ;
390 static const G4double a1=4.15e-1, a3=2.10e-3, a5=54.0e-5 ;
391
392 G4double x = log(kineticEnergy/(K*Z*Z)), x2 = x*x, x3 = x2*x;
393 G4double eta = 0.5+atan(a1*x+a3*x3+a5*x3*x2)/pi;
394 G4double e0 = cut/kineticEnergy;
395
396 G4double factor = 0.0;
397 if (e0 < 1.0) {
398 factor=log(1.-e0)/eta;
399 factor=exp(factor);
400 }
401 factor = eta*(1.-factor)/e0;
402
403 return factor;
404}
405
406//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
407
408G4double G4eBremsstrahlungModel::CrossSectionPerVolume(
409 const G4Material* material,
410 const G4ParticleDefinition* p,
411 G4double kineticEnergy,
412 G4double cutEnergy,
413 G4double maxEnergy)
414{
415 if(!particle) SetParticle(p);
416 G4double cross = 0.0;
417 G4double tmax = min(maxEnergy, kineticEnergy);
418 G4double cut = max(cutEnergy, minThreshold);
419 if(cut >= tmax) return cross;
420
421 const G4ElementVector* theElementVector = material->GetElementVector();
422 const G4double* theAtomNumDensityVector = material->GetAtomicNumDensityVector();
423 G4double dum=0.;
424
425 for (size_t i=0; i<material->GetNumberOfElements(); i++) {
426
427 cross += theAtomNumDensityVector[i] * ComputeCrossSectionPerAtom(p,
428 kineticEnergy, (*theElementVector)[i]->GetZ(), dum, cut);
429 if (tmax < kineticEnergy) {
430 cross -= theAtomNumDensityVector[i] * ComputeCrossSectionPerAtom(p,
431 kineticEnergy, (*theElementVector)[i]->GetZ(), dum, tmax);
432 }
433 }
434
435 // now compute the correction due to the supression(s)
436
437 G4double kmax = tmax;
438 G4double kmin = cut;
439
440 G4double totalEnergy = kineticEnergy+electron_mass_c2 ;
441 G4double kp2 = MigdalConstant*totalEnergy*totalEnergy
442 *(material->GetElectronDensity());
443
444 G4double fsig = 0.;
445 G4int nmax = 100;
446 G4double vmin=log(kmin);
447 G4double vmax=log(kmax) ;
448 G4int nn = (G4int)(nmax*(vmax-vmin)/(log(highKinEnergy)-vmin));
449 G4double u,fac,c,v,dv,y ;
450 if(nn > 0) {
451
452 dv = (vmax-vmin)/nn ;
453 v = vmin-dv ;
454 for(G4int n=0; n<=nn; n++) {
455
456 v += dv;
457 u = exp(v);
458 fac = SupressionFunction(material, kineticEnergy, u);
459 y = u/kmax;
460 fac *= (4.-4.*y+3.*y*y)/3.;
461 fac *= probsup*(u*u/(u*u+kp2))+1.-probsup;
462
463 if ((n==0)||(n==nn)) c=0.5;
464 else c=1. ;
465
466 fac *= c;
467 fsig += fac;
468 }
469 y = kmin/kmax ;
470 fsig *=dv/(-4.*log(y)/3.-4.*(1.-y)/3.+0.5*(1.-y*y));
471
472 } else {
473
474 fsig = 1.;
475 }
476 if (fsig > 1.) fsig = 1.;
477
478 // correct the cross section
479 cross *= fsig;
480
481 return cross;
482}
483
484//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
485
486G4double G4eBremsstrahlungModel::ComputeCrossSectionPerAtom(
487 const G4ParticleDefinition*,
488 G4double kineticEnergy,
489 G4double Z, G4double,
490 G4double cut, G4double)
491
492// Calculates the cross section per atom in GEANT4 internal units.
493//
494
495{
496 G4double cross = 0.0 ;
497 if ( kineticEnergy < 1*keV || kineticEnergy < cut) return cross;
498
499 static const G4double ksi=2.0, alfa=1.00;
500 static const G4double csigh = 0.127, csiglow = 0.25, asiglow = 0.020*MeV ;
501 static const G4double Tlim = 10.*MeV ;
502
503 static const G4double xlim = 1.2 ;
504 static const G4int NZ = 8 ;
505 static const G4int Nsig = 11 ;
506 static const G4double ZZ[NZ] =
507 {2.,4.,6.,14.,26.,50.,82.,92.} ;
508 static const G4double coefsig[NZ][Nsig] = {
509 // Z=2
510 { 0.4638, 0.37748, 0.32249, -0.060362, -0.065004,
511 -0.033457, -0.004583, 0.011954, 0.0030404, -0.0010077,
512 -0.00028131},
513
514 // Z=4
515 { 0.50008, 0.33483, 0.34364, -0.086262, -0.055361,
516 -0.028168, -0.0056172, 0.011129, 0.0027528, -0.00092265,
517 -0.00024348},
518
519 // Z=6
520 { 0.51587, 0.31095, 0.34996, -0.11623, -0.056167,
521 -0.0087154, 0.00053943, 0.0054092, 0.00077685, -0.00039635,
522 -6.7818e-05},
523
524 // Z=14
525 { 0.55058, 0.25629, 0.35854, -0.080656, -0.054308,
526 -0.049933, -0.00064246, 0.016597, 0.0021789, -0.001327,
527 -0.00025983},
528
529 // Z=26
530 { 0.5791, 0.26152, 0.38953, -0.17104, -0.099172,
531 0.024596, 0.023718, -0.0039205, -0.0036658, 0.00041749,
532 0.00023408},
533
534 // Z=50
535 { 0.62085, 0.27045, 0.39073, -0.37916, -0.18878,
536 0.23905, 0.095028, -0.068744, -0.023809, 0.0062408,
537 0.0020407},
538
539 // Z=82
540 { 0.66053, 0.24513, 0.35404, -0.47275, -0.22837,
541 0.35647, 0.13203, -0.1049, -0.034851, 0.0095046,
542 0.0030535},
543
544 // Z=92
545 { 0.67143, 0.23079, 0.32256, -0.46248, -0.20013,
546 0.3506, 0.11779, -0.1024, -0.032013, 0.0092279,
547 0.0028592}
548
549 } ;
550
551 G4int iz = 0 ;
552 G4double delz = 1.e6 ;
553 for (G4int ii=0; ii<NZ; ii++)
554 {
555 G4double absdelz = std::abs(Z-ZZ[ii]);
556 if(absdelz < delz)
557 {
558 iz = ii ;
559 delz = absdelz;
560 }
561 }
562
563 G4double xx = log10(kineticEnergy/MeV) ;
564 G4double fs = 1. ;
565
566 if (xx <= xlim) {
567
568 fs = coefsig[iz][Nsig-1] ;
569 for (G4int j=Nsig-2; j>=0; j--) {
570
571 fs = fs*xx+coefsig[iz][j] ;
572 }
573 if(fs < 0.) fs = 0.;
574 }
575
576 cross = Z*(Z+ksi)*(1.-csigh*exp(log(Z)/4.))*pow(log(kineticEnergy/cut),alfa);
577
578 if (kineticEnergy <= Tlim)
579 cross *= exp(csiglow*log(Tlim/kineticEnergy))
580 *(1.+asiglow/(sqrt(Z)*kineticEnergy));
581
582 if (!isElectron)
583 cross *= PositronCorrFactorSigma(Z, kineticEnergy, cut);
584
585 cross *= fs/Avogadro ;
586
587 if (cross < 0.) cross = 0.;
588 return cross;
589}
590
591//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
592
593G4double G4eBremsstrahlungModel::PositronCorrFactorSigma( G4double Z,
594 G4double kineticEnergy, G4double cut)
595
596//Calculates the correction factor for the total cross section of the positron
597// bremsstrahl.
598// Eta is the ratio of positron to electron energy loss by bremstrahlung.
599// A parametrized formula from L. Urban is used to estimate eta. It is a fit to
600// the results of L. Kim & al: Phys Rev. A33,3002 (1986)
601
602{
603 static const G4double K = 132.9416*eV;
604 static const G4double a1 = 4.15e-1, a3 = 2.10e-3, a5 = 54.0e-5;
605
606 G4double x = log(kineticEnergy/(K*Z*Z));
607 G4double x2 = x*x;
608 G4double x3 = x2*x;
609 G4double eta = 0.5 + atan(a1*x + a3*x3 + a5*x3*x2)/pi ;
610 G4double alfa = (1. - eta)/eta;
611 return eta*pow((1. - cut/kineticEnergy), alfa);
612}
613
614//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
615
616G4DataVector* G4eBremsstrahlungModel::ComputePartialSumSigma(
617 const G4Material* material,
618 G4double kineticEnergy,
619 G4double cut)
620
621// Build the table of cross section per element.
622//The table is built for MATERIALS.
623// This table is used by DoIt to select randomly an element in the material.
624{
625 G4int nElements = material->GetNumberOfElements();
626 const G4ElementVector* theElementVector = material->GetElementVector();
627 const G4double* theAtomNumDensityVector = material->GetAtomicNumDensityVector();
628 G4double dum = 0.;
629
630 G4DataVector* dv = new G4DataVector();
631
632 G4double cross = 0.0;
633
634 for (G4int i=0; i<nElements; i++ ) {
635
636 cross += theAtomNumDensityVector[i] * ComputeCrossSectionPerAtom( particle,
637 kineticEnergy, (*theElementVector)[i]->GetZ(), dum, cut);
638 dv->push_back(cross);
639 }
640 return dv;
641}
642
643//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
644
645void G4eBremsstrahlungModel::SampleSecondaries(std::vector<G4DynamicParticle*>* vdp,
646 const G4MaterialCutsCouple* couple,
647 const G4DynamicParticle* dp,
648 G4double tmin,
649 G4double maxEnergy)
650// The emitted gamma energy is sampled using a parametrized formula
651// from L. Urban.
652// This parametrization is derived from :
653// cross-section values of Seltzer and Berger for electron energies
654// 1 keV - 10 GeV,
655// screened Bethe Heilter differential cross section above 10 GeV,
656// Migdal corrections in both case.
657// Seltzer & Berger: Nim B 12:95 (1985)
658// Nelson, Hirayama & Rogers: Technical report 265 SLAC (1985)
659// Migdal: Phys Rev 103:1811 (1956); Messel & Crawford: Pergamon Press (1970)
660//
661// A modified version of the random number techniques of Butcher&Messel is used
662// (Nuc Phys 20(1960),15).
663{
664 G4double kineticEnergy = dp->GetKineticEnergy();
665 G4double tmax = min(maxEnergy, kineticEnergy);
666 if(tmin >= tmax) return;
667
668//
669// GEANT4 internal units.
670//
671 static const G4double
672 ah10 = 4.67733E+00, ah11 =-6.19012E-01, ah12 = 2.02225E-02,
673 ah20 =-7.34101E+00, ah21 = 1.00462E+00, ah22 =-3.20985E-02,
674 ah30 = 2.93119E+00, ah31 =-4.03761E-01, ah32 = 1.25153E-02;
675
676 static const G4double
677 bh10 = 4.23071E+00, bh11 =-6.10995E-01, bh12 = 1.95531E-02,
678 bh20 =-7.12527E+00, bh21 = 9.69160E-01, bh22 =-2.74255E-02,
679 bh30 = 2.69925E+00, bh31 =-3.63283E-01, bh32 = 9.55316E-03;
680
681 static const G4double
682 al00 =-2.05398E+00, al01 = 2.38815E-02, al02 = 5.25483E-04,
683 al10 =-7.69748E-02, al11 =-6.91499E-02, al12 = 2.22453E-03,
684 al20 = 4.06463E-02, al21 =-1.01281E-02, al22 = 3.40919E-04;
685
686 static const G4double
687 bl00 = 1.04133E+00, bl01 =-9.43291E-03, bl02 =-4.54758E-04,
688 bl10 = 1.19253E-01, bl11 = 4.07467E-02, bl12 =-1.30718E-03,
689 bl20 =-1.59391E-02, bl21 = 7.27752E-03, bl22 =-1.94405E-04;
690
691 static const G4double tlow = 1.*MeV;
692
693 G4double gammaEnergy;
694 G4bool LPMOK = false;
695 const G4Material* material = couple->GetMaterial();
696
697 // select randomly one element constituing the material
698 const G4Element* anElement = SelectRandomAtom(couple);
699
700 // Extract Z factors for this Element
701 G4double lnZ = 3.*(anElement->GetIonisation()->GetlogZ3());
702 G4double FZ = lnZ* (4.- 0.55*lnZ);
703 G4double ZZ = anElement->GetIonisation()->GetZZ3();
704
705 // limits of the energy sampling
706 G4double totalEnergy = kineticEnergy + electron_mass_c2;
707 G4ThreeVector direction = dp->GetMomentumDirection();
708 G4double xmin = tmin/kineticEnergy;
709 G4double xmax = tmax/kineticEnergy;
710 G4double kappa = 0.0;
711 if(xmax >= 1.) xmax = 1.;
712 else kappa = log(xmax)/log(xmin);
713 G4double epsilmin = tmin/totalEnergy;
714 G4double epsilmax = tmax/totalEnergy;
715
716 // Migdal factor
717 G4double MigdalFactor = (material->GetElectronDensity())*MigdalConstant
718 / (epsilmax*epsilmax);
719
720 G4double x, epsil, greject, migdal, grejmax, q;
721 G4double U = log(kineticEnergy/electron_mass_c2);
722 G4double U2 = U*U;
723
724 // precalculated parameters
725 G4double ah, bh;
726 G4double screenfac = 0.0;
727
728 if (kineticEnergy > tlow) {
729
730 G4double ah1 = ah10 + ZZ* (ah11 + ZZ* ah12);
731 G4double ah2 = ah20 + ZZ* (ah21 + ZZ* ah22);
732 G4double ah3 = ah30 + ZZ* (ah31 + ZZ* ah32);
733
734 G4double bh1 = bh10 + ZZ* (bh11 + ZZ* bh12);
735 G4double bh2 = bh20 + ZZ* (bh21 + ZZ* bh22);
736 G4double bh3 = bh30 + ZZ* (bh31 + ZZ* bh32);
737
738 ah = 1. + (ah1*U2 + ah2*U + ah3) / (U2*U);
739 bh = 0.75 + (bh1*U2 + bh2*U + bh3) / (U2*U);
740
741 // limit of the screening variable
742 screenfac =
743 136.*electron_mass_c2/((anElement->GetIonisation()->GetZ3())*totalEnergy);
744 G4double screenmin = screenfac*epsilmin/(1.-epsilmin);
745
746 // Compute the maximum of the rejection function
747 G4double F1 = max(ScreenFunction1(screenmin) - FZ ,0.);
748 G4double F2 = max(ScreenFunction2(screenmin) - FZ ,0.);
749 grejmax = (F1 - epsilmin* (F1*ah - bh*epsilmin*F2))/(42.392 - FZ);
750
751 } else {
752
753 G4double al0 = al00 + ZZ* (al01 + ZZ* al02);
754 G4double al1 = al10 + ZZ* (al11 + ZZ* al12);
755 G4double al2 = al20 + ZZ* (al21 + ZZ* al22);
756
757 G4double bl0 = bl00 + ZZ* (bl01 + ZZ* bl02);
758 G4double bl1 = bl10 + ZZ* (bl11 + ZZ* bl12);
759 G4double bl2 = bl20 + ZZ* (bl21 + ZZ* bl22);
760
761 ah = al0 + al1*U + al2*U2;
762 bh = bl0 + bl1*U + bl2*U2;
763
764 // Compute the maximum of the rejection function
765 grejmax = max(1. + xmin* (ah + bh*xmin), 1.+ah+bh);
766 G4double xm = -ah/(2.*bh);
767 if ( xmin < xm && xm < xmax) grejmax = max(grejmax, 1.+ xm* (ah + bh*xm));
768 }
769
770 //
771 // sample the energy rate of the emitted gamma for e- kin energy > 1 MeV
772 //
773
774 do {
775 if (kineticEnergy > tlow) {
776 do {
777 q = G4UniformRand();
778 x = pow(xmin, q + kappa*(1.0 - q));
779 epsil = x*kineticEnergy/totalEnergy;
780 G4double screenvar = screenfac*epsil/(1.0-epsil);
781 G4double F1 = max(ScreenFunction1(screenvar) - FZ ,0.);
782 G4double F2 = max(ScreenFunction2(screenvar) - FZ ,0.);
783 migdal = (1. + MigdalFactor)/(1. + MigdalFactor/(x*x));
784 greject = migdal*(F1 - epsil* (ah*F1 - bh*epsil*F2))/(42.392 - FZ);
785 /*
786 if ( greject > grejmax ) {
787 G4cout << "### G4eBremsstrahlungModel Warning: Majoranta exceeded! "
788 << greject << " > " << grejmax
789 << " x= " << x
790 << " e= " << kineticEnergy
791 << G4endl;
792 }
793 */
794 } while( greject < G4UniformRand()*grejmax );
795
796 } else {
797
798 do {
799 q = G4UniformRand();
800 x = pow(xmin, q + kappa*(1.0 - q));
801 migdal = (1. + MigdalFactor)/(1. + MigdalFactor/(x*x));
802 greject = migdal*(1. + x* (ah + bh*x));
803 /*
804 if ( greject > grejmax ) {
805 G4cout << "### G4eBremsstrahlungModel Warning: Majoranta exceeded! "
806 << greject << " > " << grejmax
807 << " x= " << x
808 << " e= " << kineticEnergy
809 << G4endl;
810 }
811 */
812 } while( greject < G4UniformRand()*grejmax );
813 }
814 /*
815 if(x > 0.999) {
816 G4cout << "### G4eBremsstrahlungModel Warning: e= " << kineticEnergy
817 << " tlow= " << tlow
818 << " x= " << x
819 << " greject= " << greject
820 << " grejmax= " << grejmax
821 << " migdal= " << migdal
822 << G4endl;
823 // if(x >= 1.0) G4Exception("X=1");
824 }
825 */
826 gammaEnergy = x*kineticEnergy;
827
[961]828 if (LPMFlag()) {
[819]829 // take into account the supression due to the LPM effect
830 if (G4UniformRand() <= SupressionFunction(material,kineticEnergy,
831 gammaEnergy))
832 LPMOK = true;
833 }
834 else LPMOK = true;
835
836 } while (!LPMOK);
837
838 //
839 // angles of the emitted gamma. ( Z - axis along the parent particle)
840 //
841 // universal distribution suggested by L. Urban
842 // (Geant3 manual (1993) Phys211),
843 // derived from Tsai distribution (Rev Mod Phys 49,421(1977))
844
845 G4double u;
846 const G4double a1 = 0.625 , a2 = 3.*a1 , d = 27. ;
847
848 if (9./(9.+d) > G4UniformRand()) u = - log(G4UniformRand()*G4UniformRand())/a1;
849 else u = - log(G4UniformRand()*G4UniformRand())/a2;
850
851 G4double theta = u*electron_mass_c2/totalEnergy;
852
853 G4double sint = sin(theta);
854
855 G4double phi = twopi * G4UniformRand() ;
856
857 G4ThreeVector gammaDirection(sint*cos(phi),sint*sin(phi), cos(theta));
858 gammaDirection.rotateUz(direction);
859
860 // create G4DynamicParticle object for the Gamma
861 G4DynamicParticle* g = new G4DynamicParticle(theGamma,gammaDirection,
862 gammaEnergy);
863 vdp->push_back(g);
864
865 G4double totMomentum = sqrt(kineticEnergy*(totalEnergy + electron_mass_c2));
866 G4ThreeVector dir = totMomentum*direction - gammaEnergy*gammaDirection;
867 direction = dir.unit();
868
869 // energy of primary
870 G4double finalE = kineticEnergy - gammaEnergy;
871
872 // stop tracking and create new secondary instead of primary
[961]873 if(gammaEnergy > SecondaryThreshold()) {
[819]874 fParticleChange->ProposeTrackStatus(fStopAndKill);
875 fParticleChange->SetProposedKineticEnergy(0.0);
876 G4DynamicParticle* el =
877 new G4DynamicParticle(const_cast<G4ParticleDefinition*>(particle),
878 direction, finalE);
879 vdp->push_back(el);
880
881 // continue tracking
882 } else {
883 fParticleChange->SetProposedMomentumDirection(direction);
884 fParticleChange->SetProposedKineticEnergy(finalE);
885 }
886}
887
888//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
889
890const G4Element* G4eBremsstrahlungModel::SelectRandomAtom(
891 const G4MaterialCutsCouple* couple)
892{
893 // select randomly 1 element within the material
894
895 const G4Material* material = couple->GetMaterial();
896 G4int nElements = material->GetNumberOfElements();
897 const G4ElementVector* theElementVector = material->GetElementVector();
898
899 const G4Element* elm = 0;
900
901 if(1 < nElements) {
902
903 G4DataVector* dv = partialSumSigma[couple->GetIndex()];
904 G4double rval = G4UniformRand()*((*dv)[nElements-1]);
905
906 for (G4int i=0; i<nElements; i++) {
907 if (rval <= (*dv)[i]) elm = (*theElementVector)[i];
908 }
909 if(!elm) {
910 G4cout << "G4eBremsstrahlungModel::SelectRandomAtom: Warning -"
911 << " no elements found in "
912 << material->GetName()
913 << G4endl;
914 elm = (*theElementVector)[0];
915 }
916 } else elm = (*theElementVector)[0];
917
918 SetCurrentElement(elm);
919 return elm;
920}
921
922//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
923
924G4double G4eBremsstrahlungModel::SupressionFunction(const G4Material* material,
925 G4double kineticEnergy, G4double gammaEnergy)
926{
927 // supression due to the LPM effect+polarisation of the medium/
928 // supression due to the polarisation alone
929
930
931 G4double totEnergy = kineticEnergy+electron_mass_c2 ;
932 G4double totEnergySquare = totEnergy*totEnergy ;
933
934 G4double LPMEnergy = LPMconstant*(material->GetRadlen()) ;
935
936 G4double gammaEnergySquare = gammaEnergy*gammaEnergy ;
937
938 G4double electronDensity = material->GetElectronDensity();
939
940 G4double sp = gammaEnergySquare/
941 (gammaEnergySquare+MigdalConstant*totEnergySquare*electronDensity);
942
943 G4double supr = 1.0;
944
[961]945 if (LPMFlag()) {
[819]946
947 G4double s2lpm = LPMEnergy*gammaEnergy/totEnergySquare;
948
949 if (s2lpm < 1.) {
950
951 G4double LPMgEnergyLimit = totEnergySquare/LPMEnergy ;
952 G4double LPMgEnergyLimit2 = LPMgEnergyLimit*LPMgEnergyLimit;
953 G4double splim = LPMgEnergyLimit2/
954 (LPMgEnergyLimit2+MigdalConstant*totEnergySquare*electronDensity);
955 G4double w = 1.+1./splim ;
956
957 if ((1.-sp) < 1.e-6) w = s2lpm*(3.-sp);
958 else w = s2lpm*(1.+1./sp);
959
960 supr = (sqrt(w*w+4.*s2lpm)-w)/(sqrt(w*w+4.)-w) ;
961 supr /= sp;
962 }
963
964 }
965 return supr;
966}
967
968//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
969
970
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