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

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25//
26// $Id: G4eBremsstrahlungModel.cc,v 1.48 2010/10/26 10:35:22 vnivanch Exp $
27// GEANT4 tag $Name: emstand-V09-03-24 $
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)
56// 09-09-08  MigdalConstant increased in (2pi)^2 times (A.Schaelicke)
57// 13-10-10  Add angular distributon interface (VI)
58//
59// Class Description:
60//
61//
62// -------------------------------------------------------------------
63//
64//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
65//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
66
67#include "G4eBremsstrahlungModel.hh"
68#include "G4Electron.hh"
69#include "G4Positron.hh"
70#include "G4Gamma.hh"
71#include "Randomize.hh"
72#include "G4Material.hh"
73#include "G4Element.hh"
74#include "G4ElementVector.hh"
75#include "G4ProductionCutsTable.hh"
76#include "G4DataVector.hh"
77#include "G4ParticleChangeForLoss.hh"
78#include "G4ModifiedTsai.hh"
79
80//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
81
82using namespace std;
83
84G4eBremsstrahlungModel::G4eBremsstrahlungModel(const G4ParticleDefinition* p,
85                                               const G4String& nam)
86  : G4VEmModel(nam),
87    particle(0),
88    isElectron(true),
89    probsup(1.0),
90    MigdalConstant(classic_electr_radius*electron_Compton_length*electron_Compton_length*4.0*pi),
91    LPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)),
92    isInitialised(false)
93{
94  if(p) { SetParticle(p); }
95  theGamma = G4Gamma::Gamma();
96  minThreshold = 0.1*keV;
97  SetAngularDistribution(new G4ModifiedTsai());
98  highKinEnergy = HighEnergyLimit();
99  lowKinEnergy  = LowEnergyLimit();
100}
101
102//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
103
104G4eBremsstrahlungModel::~G4eBremsstrahlungModel()
105{
106  size_t n = partialSumSigma.size();
107  if(n > 0) {
108    for(size_t i=0; i<n; i++) {
109      delete partialSumSigma[i];
110    }
111  }
112}
113
114//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
115
116void G4eBremsstrahlungModel::SetParticle(const G4ParticleDefinition* p)
117{
118  particle = p;
119  if(p == G4Electron::Electron()) isElectron = true;
120  else                            isElectron = false;
121}
122
123//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
124
125G4double G4eBremsstrahlungModel::MinEnergyCut(const G4ParticleDefinition*,
126                                              const G4MaterialCutsCouple*)
127{
128  return minThreshold;
129}
130
131//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
132
133void G4eBremsstrahlungModel::Initialise(const G4ParticleDefinition* p,
134                                        const G4DataVector& cuts)
135{
136  if(p) { SetParticle(p); }
137  highKinEnergy = HighEnergyLimit();
138  lowKinEnergy  = LowEnergyLimit();
139  const G4ProductionCutsTable* theCoupleTable=
140        G4ProductionCutsTable::GetProductionCutsTable();
141
142  if(theCoupleTable) {
143    G4int numOfCouples = theCoupleTable->GetTableSize();
144
145    G4int nn = partialSumSigma.size();
146    G4int nc = cuts.size();
147    if(nn > 0) {
148      for (G4int ii=0; ii<nn; ii++){
149        G4DataVector* a=partialSumSigma[ii];
150        if ( a )  delete a;
151      }
152      partialSumSigma.clear();
153    }
154    if(numOfCouples>0) {
155      for (G4int i=0; i<numOfCouples; i++) {
156        G4double cute   = DBL_MAX;
157        if(i < nc) cute = cuts[i];
158        const G4MaterialCutsCouple* couple = theCoupleTable->GetMaterialCutsCouple(i);
159        const G4Material* material = couple->GetMaterial();
160        G4DataVector* dv = ComputePartialSumSigma(material, 0.5*highKinEnergy,
161                             std::min(cute, 0.25*highKinEnergy));
162        partialSumSigma.push_back(dv);
163      }
164    }
165  }
166  if(isInitialised) return;
167  fParticleChange = GetParticleChangeForLoss();
168  isInitialised = true;
169}
170
171//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
172
173G4double G4eBremsstrahlungModel::ComputeDEDXPerVolume(
174                                             const G4Material* material,
175                                             const G4ParticleDefinition* p,
176                                                   G4double kineticEnergy,
177                                                   G4double cutEnergy)
178{
179  if(!particle) { SetParticle(p); }
180  if(kineticEnergy < lowKinEnergy) { return 0.0; }
181
182  const G4double thigh = 100.*GeV;
183
184  G4double cut = std::min(cutEnergy, kineticEnergy);
185
186  G4double rate, loss;
187  const G4double factorHigh = 36./(1450.*GeV);
188  const G4double coef1 = -0.5;
189  const G4double coef2 = 2./9.;
190
191  const G4ElementVector* theElementVector = material->GetElementVector();
192  const G4double* theAtomicNumDensityVector = material->GetAtomicNumDensityVector();
193
194  G4double totalEnergy = kineticEnergy + electron_mass_c2;
195  G4double dedx = 0.0;
196
197  //  loop for elements in the material
198  for (size_t i=0; i<material->GetNumberOfElements(); i++) {
199
200    G4double Z     = (*theElementVector)[i]->GetZ();
201    G4double natom = theAtomicNumDensityVector[i];
202
203    // loss for MinKinEnergy<KineticEnergy<=100 GeV
204    if (kineticEnergy <= thigh) {
205
206      //      x = log(totalEnergy/electron_mass_c2);
207      loss = ComputeBremLoss(Z, kineticEnergy, cut) ;
208      if (!isElectron) loss *= PositronCorrFactorLoss(Z, kineticEnergy, cut);
209
210    // extrapolation for KineticEnergy>100 GeV
211    } else {
212
213      //      G4double xhigh = log(thigh/electron_mass_c2);
214      G4double cuthigh = thigh*0.5;
215
216      if (cut < thigh) {
217
218        loss = ComputeBremLoss(Z, thigh, cut) ;
219        if (!isElectron) loss *= PositronCorrFactorLoss(Z, thigh, cut) ;
220        rate = cut/totalEnergy;
221        loss *= (1. + coef1*rate + coef2*rate*rate);
222        rate = cut/thigh;
223        loss /= (1.+coef1*rate+coef2*rate*rate);
224
225      } else {
226
227        loss = ComputeBremLoss(Z, thigh, cuthigh) ;
228        if (!isElectron) loss *= PositronCorrFactorLoss(Z, thigh, cuthigh) ;
229        rate = cut/totalEnergy;
230        loss *= (1. + coef1*rate + coef2*rate*rate);
231        loss *= cut*factorHigh;
232      }
233    }
234    loss *= natom;
235
236    G4double kp2 = MigdalConstant*totalEnergy*totalEnergy
237                 * (material->GetElectronDensity()) ;
238
239    // now compute the correction due to the supression(s)
240    G4double kmin = 1.*eV;
241    G4double kmax = cut;
242
243    if (kmax > kmin) {
244
245      G4double floss = 0.;
246      G4int nmax = 100;
247
248      G4double vmin=log(kmin);
249      G4double vmax=log(kmax) ;
250      G4int nn = (G4int)(nmax*(vmax-vmin)/(log(highKinEnergy)-vmin)) ;
251      G4double u,fac,c,v,dv ;
252      if(nn > 0) {
253
254        dv = (vmax-vmin)/nn ;
255        v  = vmin-dv ;
256
257        for(G4int n=0; n<=nn; n++) {
258
259          v += dv;
260          u = exp(v);
261          fac = u*SupressionFunction(material,kineticEnergy,u);
262          fac *= probsup*(u*u/(u*u+kp2))+1.-probsup;
263          if ((n==0)||(n==nn)) c=0.5;
264          else                 c=1. ;
265          fac   *= c ;
266          floss += fac ;
267        }
268        floss *=dv/(kmax-kmin);
269
270      } else {
271        floss = 1.;
272      }
273      if(floss > 1.) floss = 1.;
274      // correct the loss
275      loss *= floss;
276    }
277    dedx += loss;
278  }
279  if(dedx < 0.) { dedx = 0.; }
280  return dedx;
281}
282
283//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
284
285G4double G4eBremsstrahlungModel::ComputeBremLoss(G4double Z, G4double T,
286                                                 G4double Cut)
287
288// compute loss due to soft brems
289{
290  static const G4double beta=1.0, ksi=2.0;
291  static const G4double clossh = 0.254 , closslow = 1./3. , alosslow = 1. ;
292  static const G4double Tlim= 10.*MeV ;
293
294  static const G4double xlim = 1.2 ;
295  static const G4int NZ = 8 ;
296  static const G4int Nloss = 11 ;
297  static const G4double ZZ[NZ] =
298        {2.,4.,6.,14.,26.,50.,82.,92.};
299  static const G4double coefloss[NZ][Nloss] = {
300  // Z=2
301 { 0.98916,        0.47564,        -0.2505,       -0.45186,        0.14462,
302   0.21307,      -0.013738,      -0.045689,     -0.0042914,      0.0034429,
303   0.00064189},
304
305  // Z=4
306 { 1.0626,        0.37662,       -0.23646,       -0.45188,        0.14295,
307   0.22906,      -0.011041,      -0.051398,     -0.0055123,      0.0039919,
308   0.00078003},
309  // Z=6
310 { 1.0954,          0.315,       -0.24011,       -0.43849,        0.15017,
311   0.23001,      -0.012846,      -0.052555,     -0.0055114,      0.0041283,
312   0.00080318},
313
314  // Z=14
315 { 1.1649,        0.18976,       -0.24972,       -0.30124,         0.1555,
316   0.13565,      -0.024765,      -0.027047,    -0.00059821,      0.0019373,
317   0.00027647},
318
319  // Z=26
320 { 1.2261,        0.14272,       -0.25672,       -0.28407,        0.13874,
321   0.13586,      -0.020562,      -0.026722,    -0.00089557,      0.0018665,
322   0.00026981},
323
324  // Z=50
325 { 1.3147,       0.020049,       -0.35543,       -0.13927,        0.17666,
326   0.073746,      -0.036076,      -0.013407,      0.0025727,     0.00084005,
327  -1.4082e-05},
328
329  // Z=82
330 { 1.3986,       -0.10586,       -0.49187,     -0.0048846,        0.23621,
331   0.031652,      -0.052938,     -0.0076639,      0.0048181,     0.00056486,
332  -0.00011995},
333
334  // Z=92
335 { 1.4217,         -0.116,       -0.55497,      -0.044075,        0.27506,
336   0.081364,      -0.058143,      -0.023402,      0.0031322,      0.0020201,
337   0.00017519}
338
339    } ;
340  static G4double aaa = 0.414;
341  static G4double bbb = 0.345;
342  static G4double ccc = 0.460;
343
344  G4int iz = 0;
345  G4double delz = 1.e6;
346  for (G4int ii=0; ii<NZ; ii++)
347    {
348      G4double dz = std::abs(Z-ZZ[ii]);
349      if(dz < delz)  {
350        iz = ii;
351        delz = dz;
352      }
353    }
354
355  G4double xx = log10(T/MeV);
356  G4double fl = 1.;
357
358  if (xx <= xlim)
359    {
360      xx /= xlim;
361      G4double yy = 1.0;
362      fl = 0.0;
363      for (G4int j=0; j<Nloss; j++) {
364        fl += yy+coefloss[iz][j];
365        yy *= xx;
366      }
367      if (fl < 0.00001) fl = 0.00001;
368      else if (fl > 1.0) fl = 1.0;
369    }
370
371  G4double loss;
372  G4double E = T+electron_mass_c2 ;
373
374  loss = Z*(Z+ksi)*E*E/(T+E)*exp(beta*log(Cut/T))*(2.-clossh*exp(log(Z)/4.));
375  if (T <= Tlim) loss /= exp(closslow*log(Tlim/T));
376  if( T <= Cut)  loss *= exp(alosslow*log(T/Cut));
377  //  correction
378  loss *= (aaa+bbb*T/Tlim)/(1.+ccc*T/Tlim);
379  loss *= fl;
380  loss /= Avogadro;
381
382  return loss;
383}
384
385//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
386
387G4double G4eBremsstrahlungModel::PositronCorrFactorLoss(G4double Z,
388                                 G4double kineticEnergy, G4double cut)
389
390//calculates the correction factor for the energy loss due to bremsstrahlung for positrons
391//the same correction is in the (discrete) bremsstrahlung
392
393{
394  static const G4double K = 132.9416*eV ;
395  static const G4double a1=4.15e-1, a3=2.10e-3, a5=54.0e-5 ;
396
397  G4double x   = log(kineticEnergy/(K*Z*Z)), x2 = x*x, x3 = x2*x;
398  G4double eta = 0.5+atan(a1*x+a3*x3+a5*x3*x2)/pi;
399  G4double e0  = cut/kineticEnergy;
400
401  G4double factor = 0.0;
402  if (e0 < 1.0) {
403    factor=log(1.-e0)/eta;
404    factor=exp(factor);
405  }
406  factor = eta*(1.-factor)/e0;
407
408  return factor;
409}
410
411//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
412
413G4double G4eBremsstrahlungModel::CrossSectionPerVolume(
414                                              const G4Material* material,
415                                              const G4ParticleDefinition* p,
416                                                    G4double kineticEnergy,
417                                                    G4double cutEnergy,
418                                                    G4double maxEnergy)
419{
420  if(!particle) { SetParticle(p); }
421  G4double cross = 0.0;
422  G4double tmax = min(maxEnergy, kineticEnergy);
423  G4double cut  = max(cutEnergy, minThreshold);
424  if(cut >= tmax) { return cross; }
425
426  const G4ElementVector* theElementVector = material->GetElementVector();
427  const G4double* theAtomNumDensityVector = material->GetAtomicNumDensityVector();
428  G4double dum=0.;
429 
430  for (size_t i=0; i<material->GetNumberOfElements(); i++) {
431
432    cross += theAtomNumDensityVector[i] * ComputeCrossSectionPerAtom(p,
433                      kineticEnergy, (*theElementVector)[i]->GetZ(), dum, cut);
434    if (tmax < kineticEnergy) {
435      cross -= theAtomNumDensityVector[i] * ComputeCrossSectionPerAtom(p,
436                     kineticEnergy, (*theElementVector)[i]->GetZ(), dum, tmax);
437    }
438  }
439
440  // now compute the correction due to the supression(s)
441
442  G4double kmax = tmax;
443  G4double kmin = cut;
444
445  G4double totalEnergy = kineticEnergy+electron_mass_c2 ;
446  G4double kp2 = MigdalConstant*totalEnergy*totalEnergy
447                                             *(material->GetElectronDensity());
448
449  G4double fsig = 0.;
450  G4int nmax = 100;
451  G4double vmin=log(kmin);
452  G4double vmax=log(kmax) ;
453  G4int nn = (G4int)(nmax*(vmax-vmin)/(log(highKinEnergy)-vmin));
454  G4double u,fac,c,v,dv,y ;
455  if(nn > 0) {
456
457      dv = (vmax-vmin)/nn ;
458      v  = vmin-dv ;
459      for(G4int n=0; n<=nn; n++) {
460
461        v += dv; 
462        u = exp(v);             
463        fac = SupressionFunction(material, kineticEnergy, u);
464        y = u/kmax;
465        fac *= (4.-4.*y+3.*y*y)/3.;
466        fac *= probsup*(u*u/(u*u+kp2))+1.-probsup;
467
468        if ((n==0)||(n==nn)) c=0.5;
469        else                 c=1. ;
470
471        fac  *= c;
472        fsig += fac;
473      }
474      y = kmin/kmax ;
475      fsig *=dv/(-4.*log(y)/3.-4.*(1.-y)/3.+0.5*(1.-y*y));
476
477  } else {
478
479      fsig = 1.;
480  }
481  if (fsig > 1.) fsig = 1.;
482
483  // correct the cross section
484  cross *= fsig;
485
486  return cross;
487}
488
489//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
490
491G4double G4eBremsstrahlungModel::ComputeCrossSectionPerAtom(
492                                              const G4ParticleDefinition*,
493                                                    G4double kineticEnergy, 
494                                                    G4double Z,   G4double,
495                                                    G4double cut, G4double)
496 
497// Calculates the cross section per atom in GEANT4 internal units.
498//
499 
500{
501  G4double cross = 0.0 ;
502  if ( kineticEnergy < 1*keV || kineticEnergy < cut) { return cross; }
503
504  static const G4double ksi=2.0, alfa=1.00;
505  static const G4double csigh = 0.127, csiglow = 0.25, asiglow = 0.020*MeV ;
506  static const G4double Tlim = 10.*MeV ;
507
508  static const G4double xlim = 1.2 ;
509  static const G4int NZ = 8 ;
510  static const G4int Nsig = 11 ;
511  static const G4double ZZ[NZ] =
512        {2.,4.,6.,14.,26.,50.,82.,92.} ;
513  static const G4double coefsig[NZ][Nsig] = {
514  // Z=2
515  { 0.4638,        0.37748,        0.32249,      -0.060362,      -0.065004,
516   -0.033457,      -0.004583,       0.011954,      0.0030404,     -0.0010077,
517   -0.00028131},
518
519  // Z=4
520  { 0.50008,        0.33483,        0.34364,      -0.086262,      -0.055361,
521   -0.028168,     -0.0056172,       0.011129,      0.0027528,    -0.00092265,
522   -0.00024348},
523
524  // Z=6
525  { 0.51587,        0.31095,        0.34996,       -0.11623,      -0.056167,
526   -0.0087154,     0.00053943,      0.0054092,     0.00077685,    -0.00039635,
527   -6.7818e-05},
528
529  // Z=14
530  { 0.55058,        0.25629,        0.35854,      -0.080656,      -0.054308,
531   -0.049933,    -0.00064246,       0.016597,      0.0021789,      -0.001327,
532   -0.00025983},
533
534  // Z=26
535  { 0.5791,        0.26152,        0.38953,       -0.17104,      -0.099172,
536    0.024596,       0.023718,     -0.0039205,     -0.0036658,     0.00041749,
537    0.00023408},
538
539  // Z=50
540  { 0.62085,        0.27045,        0.39073,       -0.37916,       -0.18878,
541    0.23905,       0.095028,      -0.068744,      -0.023809,      0.0062408,
542    0.0020407},
543
544  // Z=82
545  { 0.66053,        0.24513,        0.35404,       -0.47275,       -0.22837,
546    0.35647,        0.13203,        -0.1049,      -0.034851,      0.0095046,
547    0.0030535},
548
549  // Z=92
550  { 0.67143,        0.23079,        0.32256,       -0.46248,       -0.20013,
551    0.3506,        0.11779,        -0.1024,      -0.032013,      0.0092279,
552    0.0028592}
553
554    } ;
555
556  G4int iz = 0 ;
557  G4double delz = 1.e6 ;
558  for (G4int ii=0; ii<NZ; ii++)
559  {
560    G4double absdelz = std::abs(Z-ZZ[ii]); 
561    if(absdelz < delz)
562    {
563      iz = ii ;
564      delz = absdelz;
565    }
566  }
567
568  G4double xx = log10(kineticEnergy/MeV) ;
569  G4double fs = 1. ;
570
571  if (xx <= xlim) {
572
573    fs = coefsig[iz][Nsig-1] ;
574    for (G4int j=Nsig-2; j>=0; j--) {
575
576      fs = fs*xx+coefsig[iz][j] ;
577    }
578    if(fs < 0.) fs = 0.;
579  }
580
581  cross = Z*(Z+ksi)*(1.-csigh*exp(log(Z)/4.))*pow(log(kineticEnergy/cut),alfa);
582
583  if (kineticEnergy <= Tlim)
584     cross *= exp(csiglow*log(Tlim/kineticEnergy))
585              *(1.+asiglow/(sqrt(Z)*kineticEnergy));
586
587  if (!isElectron)
588     cross *= PositronCorrFactorSigma(Z, kineticEnergy, cut);
589
590  cross *= fs/Avogadro ;
591
592  if (cross < 0.) cross = 0.;
593  return cross;
594}
595
596//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
597 
598G4double G4eBremsstrahlungModel::PositronCorrFactorSigma( G4double Z,
599                                 G4double kineticEnergy, G4double cut)
600
601//Calculates the correction factor for the total cross section of the positron
602//  bremsstrahl.
603// Eta is the ratio of positron to electron energy loss by bremstrahlung.
604// A parametrized formula from L. Urban is used to estimate eta. It is a fit to
605// the results of L. Kim & al: Phys Rev. A33,3002 (1986)
606
607{
608  static const G4double K = 132.9416*eV;
609  static const G4double a1 = 4.15e-1, a3 = 2.10e-3, a5 = 54.0e-5;
610
611  G4double x    = log(kineticEnergy/(K*Z*Z));
612  G4double x2 = x*x;
613  G4double x3 = x2*x;
614  G4double eta  = 0.5 + atan(a1*x + a3*x3 + a5*x3*x2)/pi ;
615  G4double alfa = (1. - eta)/eta;
616  return eta*pow((1. - cut/kineticEnergy), alfa);
617}
618
619//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
620
621G4DataVector* G4eBremsstrahlungModel::ComputePartialSumSigma(
622              const G4Material* material,
623                    G4double kineticEnergy,
624                    G4double cut)
625
626// Build the table of cross section per element.
627//The table is built for MATERIALS.
628// This table is used by DoIt to select randomly an element in the material.
629{
630  G4int nElements = material->GetNumberOfElements();
631  const G4ElementVector* theElementVector = material->GetElementVector();
632  const G4double* theAtomNumDensityVector = material->GetAtomicNumDensityVector();
633  G4double dum = 0.;
634 
635  G4DataVector* dv = new G4DataVector();
636
637  G4double cross = 0.0;
638
639  for (G4int i=0; i<nElements; i++ ) {
640
641    cross += theAtomNumDensityVector[i] * ComputeCrossSectionPerAtom( particle,
642                       kineticEnergy, (*theElementVector)[i]->GetZ(), dum, cut);
643    dv->push_back(cross);
644  }
645  return dv;
646}
647
648//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
649
650void G4eBremsstrahlungModel::SampleSecondaries(std::vector<G4DynamicParticle*>* vdp, 
651                                               const G4MaterialCutsCouple* couple,
652                                               const G4DynamicParticle* dp,
653                                               G4double tmin,
654                                               G4double maxEnergy)
655// The emitted gamma energy is sampled using a parametrized formula
656// from L. Urban.
657// This parametrization is derived from :
658//    cross-section values of Seltzer and Berger for electron energies
659//    1 keV - 10 GeV,
660//    screened Bethe Heilter differential cross section above 10 GeV,
661//    Migdal corrections in both case.
662//  Seltzer & Berger: Nim B 12:95 (1985)
663//  Nelson, Hirayama & Rogers: Technical report 265 SLAC (1985)
664//  Migdal: Phys Rev 103:1811 (1956); Messel & Crawford: Pergamon Press (1970)
665//
666// A modified version of the random number techniques of Butcher&Messel is used
667//    (Nuc Phys 20(1960),15).
668{
669  G4double kineticEnergy = dp->GetKineticEnergy();
670  G4double tmax = min(maxEnergy, kineticEnergy);
671  if(tmin >= tmax) { return; }
672
673//
674// GEANT4 internal units.
675//
676  static const G4double
677     ah10 = 4.67733E+00, ah11 =-6.19012E-01, ah12 = 2.02225E-02,
678     ah20 =-7.34101E+00, ah21 = 1.00462E+00, ah22 =-3.20985E-02,
679     ah30 = 2.93119E+00, ah31 =-4.03761E-01, ah32 = 1.25153E-02;
680
681  static const G4double
682     bh10 = 4.23071E+00, bh11 =-6.10995E-01, bh12 = 1.95531E-02,
683     bh20 =-7.12527E+00, bh21 = 9.69160E-01, bh22 =-2.74255E-02,
684     bh30 = 2.69925E+00, bh31 =-3.63283E-01, bh32 = 9.55316E-03;
685
686  static const G4double
687     al00 =-2.05398E+00, al01 = 2.38815E-02, al02 = 5.25483E-04,
688     al10 =-7.69748E-02, al11 =-6.91499E-02, al12 = 2.22453E-03,
689     al20 = 4.06463E-02, al21 =-1.01281E-02, al22 = 3.40919E-04;
690
691  static const G4double
692     bl00 = 1.04133E+00, bl01 =-9.43291E-03, bl02 =-4.54758E-04,
693     bl10 = 1.19253E-01, bl11 = 4.07467E-02, bl12 =-1.30718E-03,
694     bl20 =-1.59391E-02, bl21 = 7.27752E-03, bl22 =-1.94405E-04;
695
696  static const G4double tlow = 1.*MeV;
697
698  G4double gammaEnergy;
699  G4bool LPMOK = false;
700  const G4Material* material = couple->GetMaterial();
701
702  // select randomly one element constituing the material
703  const G4Element* anElement = SelectRandomAtom(couple);
704
705  // Extract Z factors for this Element
706  G4double lnZ = 3.*(anElement->GetIonisation()->GetlogZ3());
707  G4double FZ = lnZ* (4.- 0.55*lnZ);
708  G4double ZZ = anElement->GetIonisation()->GetZZ3();
709
710  // limits of the energy sampling
711  G4double totalEnergy = kineticEnergy + electron_mass_c2;
712  G4ThreeVector direction = dp->GetMomentumDirection();
713  G4double xmin     = tmin/kineticEnergy;
714  G4double xmax     = tmax/kineticEnergy;
715  G4double kappa    = 0.0;
716  if(xmax >= 1.) { xmax = 1.; }
717  else   { kappa    = log(xmax)/log(xmin); }
718  G4double epsilmin = tmin/totalEnergy;
719  G4double epsilmax = tmax/totalEnergy;
720
721  // Migdal factor
722  G4double MigdalFactor = (material->GetElectronDensity())*MigdalConstant
723                        / (epsilmax*epsilmax);
724
725  G4double x, epsil, greject, migdal, grejmax, q;
726  G4double U  = log(kineticEnergy/electron_mass_c2);
727  G4double U2 = U*U;
728
729  // precalculated parameters
730  G4double ah, bh;
731  G4double screenfac = 0.0;
732
733  if (kineticEnergy > tlow) {
734       
735    G4double ah1 = ah10 + ZZ* (ah11 + ZZ* ah12);
736    G4double ah2 = ah20 + ZZ* (ah21 + ZZ* ah22);
737    G4double ah3 = ah30 + ZZ* (ah31 + ZZ* ah32);
738
739    G4double bh1 = bh10 + ZZ* (bh11 + ZZ* bh12);
740    G4double bh2 = bh20 + ZZ* (bh21 + ZZ* bh22);
741    G4double bh3 = bh30 + ZZ* (bh31 + ZZ* bh32);
742
743    ah = 1.   + (ah1*U2 + ah2*U + ah3) / (U2*U);
744    bh = 0.75 + (bh1*U2 + bh2*U + bh3) / (U2*U);
745
746    // limit of the screening variable
747    screenfac =
748      136.*electron_mass_c2/((anElement->GetIonisation()->GetZ3())*totalEnergy);
749    G4double screenmin = screenfac*epsilmin/(1.-epsilmin);
750
751    // Compute the maximum of the rejection function
752    G4double F1 = max(ScreenFunction1(screenmin) - FZ ,0.);
753    G4double F2 = max(ScreenFunction2(screenmin) - FZ ,0.);
754    grejmax = (F1 - epsilmin* (F1*ah - bh*epsilmin*F2))/(42.392 - FZ);
755
756  } else { 
757
758    G4double al0 = al00 + ZZ* (al01 + ZZ* al02);
759    G4double al1 = al10 + ZZ* (al11 + ZZ* al12);
760    G4double al2 = al20 + ZZ* (al21 + ZZ* al22);
761 
762    G4double bl0 = bl00 + ZZ* (bl01 + ZZ* bl02);
763    G4double bl1 = bl10 + ZZ* (bl11 + ZZ* bl12);
764    G4double bl2 = bl20 + ZZ* (bl21 + ZZ* bl22);
765 
766    ah = al0 + al1*U + al2*U2;
767    bh = bl0 + bl1*U + bl2*U2;
768
769    // Compute the maximum of the rejection function
770    grejmax = max(1. + xmin* (ah + bh*xmin), 1.+ah+bh);
771    G4double xm = -ah/(2.*bh);
772    if ( xmin < xm && xm < xmax) grejmax = max(grejmax, 1.+ xm* (ah + bh*xm));
773  }
774
775  //
776  //  sample the energy rate of the emitted gamma for e- kin energy > 1 MeV
777  //
778 
779  do {
780    if (kineticEnergy > tlow) {
781      do {
782        q = G4UniformRand();
783        x = pow(xmin, q + kappa*(1.0 - q));
784        epsil = x*kineticEnergy/totalEnergy;
785        G4double screenvar = screenfac*epsil/(1.0-epsil);
786        G4double F1 = max(ScreenFunction1(screenvar) - FZ ,0.);
787        G4double F2 = max(ScreenFunction2(screenvar) - FZ ,0.);
788        migdal = (1. + MigdalFactor)/(1. + MigdalFactor/(x*x));
789        greject = migdal*(F1 - epsil* (ah*F1 - bh*epsil*F2))/(42.392 - FZ);
790        /*
791        if ( greject > grejmax ) {
792            G4cout << "### G4eBremsstrahlungModel Warning: Majoranta exceeded! "
793                   << greject << " > " << grejmax
794                   << " x= " << x
795                   << " e= " << kineticEnergy
796                   << G4endl;
797        }
798        */     
799      } while( greject < G4UniformRand()*grejmax );
800
801    } else { 
802
803      do {
804        q = G4UniformRand();
805        x = pow(xmin, q + kappa*(1.0 - q));
806        migdal = (1. + MigdalFactor)/(1. + MigdalFactor/(x*x)); 
807        greject = migdal*(1. + x* (ah + bh*x));
808        /*
809        if ( greject > grejmax ) {
810          G4cout << "### G4eBremsstrahlungModel Warning: Majoranta exceeded! "
811                 << greject << " > " << grejmax
812                 << " x= " << x
813                 << " e= " << kineticEnergy
814                 << G4endl;
815        }
816        */
817      } while( greject < G4UniformRand()*grejmax );
818    }
819    gammaEnergy = x*kineticEnergy; 
820
821    if (LPMFlag()) {
822     // take into account the supression due to the LPM effect
823      if (G4UniformRand() <= SupressionFunction(material,kineticEnergy,
824                                                           gammaEnergy))
825        LPMOK = true;
826      }
827    else LPMOK = true;
828
829  } while (!LPMOK);
830
831  //
832  // angles of the emitted gamma. ( Z - axis along the parent particle)
833  // use general interface
834  //
835  G4double theta = GetAngularDistribution()->PolarAngle(totalEnergy,
836                                                        totalEnergy-gammaEnergy,
837                                                        (G4int)anElement->GetZ());
838
839  G4double sint = sin(theta);
840
841  G4double phi = twopi * G4UniformRand() ;
842
843  G4ThreeVector gammaDirection(sint*cos(phi),sint*sin(phi), cos(theta));
844  gammaDirection.rotateUz(direction);
845
846  // create G4DynamicParticle object for the Gamma
847  G4DynamicParticle* g = new G4DynamicParticle(theGamma,gammaDirection,
848                                                        gammaEnergy);
849  vdp->push_back(g);
850 
851  G4double totMomentum = sqrt(kineticEnergy*(totalEnergy + electron_mass_c2));
852  G4ThreeVector dir = totMomentum*direction - gammaEnergy*gammaDirection;
853  direction = dir.unit();
854
855  // energy of primary
856  G4double finalE = kineticEnergy - gammaEnergy;
857
858  // stop tracking and create new secondary instead of primary
859  if(gammaEnergy > SecondaryThreshold()) {
860    fParticleChange->ProposeTrackStatus(fStopAndKill);
861    fParticleChange->SetProposedKineticEnergy(0.0);
862    G4DynamicParticle* el = 
863      new G4DynamicParticle(const_cast<G4ParticleDefinition*>(particle),
864                            direction, finalE);
865    vdp->push_back(el);
866
867    // continue tracking
868  } else {
869    fParticleChange->SetProposedMomentumDirection(direction);
870    fParticleChange->SetProposedKineticEnergy(finalE);
871  }
872}
873
874//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
875
876const G4Element* G4eBremsstrahlungModel::SelectRandomAtom(
877           const G4MaterialCutsCouple* couple) 
878{
879  // select randomly 1 element within the material
880
881  const G4Material* material = couple->GetMaterial();
882  G4int nElements = material->GetNumberOfElements();
883  const G4ElementVector* theElementVector = material->GetElementVector();
884
885  const G4Element* elm = 0;
886
887  if(1 < nElements) {
888
889    --nElements; 
890    G4DataVector* dv = partialSumSigma[couple->GetIndex()];
891    G4double rval = G4UniformRand()*((*dv)[nElements]);
892
893    elm = (*theElementVector)[nElements];
894    for (G4int i=0; i<nElements; ++i) {
895      if (rval <= (*dv)[i]) {
896        elm = (*theElementVector)[i];
897        break;
898      }
899    }
900  } else { elm = (*theElementVector)[0]; }
901 
902  SetCurrentElement(elm);
903  return elm;
904}
905
906//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
907
908G4double G4eBremsstrahlungModel::SupressionFunction(const G4Material* material,
909                                 G4double kineticEnergy, G4double gammaEnergy)
910{
911  // supression due to the LPM effect+polarisation of the medium/
912  // supression due to the polarisation alone
913
914
915  G4double totEnergy = kineticEnergy+electron_mass_c2 ;
916  G4double totEnergySquare = totEnergy*totEnergy ;
917
918  G4double LPMEnergy = LPMconstant*(material->GetRadlen()) ;
919
920  G4double gammaEnergySquare = gammaEnergy*gammaEnergy ;
921
922  G4double electronDensity = material->GetElectronDensity();
923
924  G4double sp = gammaEnergySquare/
925   (gammaEnergySquare+MigdalConstant*totEnergySquare*electronDensity);
926
927  G4double supr = 1.0;
928
929  if (LPMFlag()) {
930
931    G4double s2lpm = LPMEnergy*gammaEnergy/totEnergySquare;
932
933    if (s2lpm < 1.) {
934
935      G4double LPMgEnergyLimit = totEnergySquare/LPMEnergy ;
936      G4double LPMgEnergyLimit2 = LPMgEnergyLimit*LPMgEnergyLimit;
937      G4double splim = LPMgEnergyLimit2/
938        (LPMgEnergyLimit2+MigdalConstant*totEnergySquare*electronDensity);
939      G4double w = 1.+1./splim ;
940
941      if ((1.-sp) < 1.e-6) w = s2lpm*(3.-sp);
942      else                 w = s2lpm*(1.+1./sp);
943
944      supr = (sqrt(w*w+4.*s2lpm)-w)/(sqrt(w*w+4.)-w) ;
945      supr /= sp;   
946    } 
947   
948  } 
949  return supr;
950}
951
952//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
953
954
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