source: trunk/source/processes/electromagnetic/standard/src/G4PairProductionRelModel.cc @ 1316

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26// $Id: G4PairProductionRelModel.cc,v 1.3 2009/05/15 17:12:33 vnivanch Exp $
27// GEANT4 tag $Name: geant4-09-03 $
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    theCrossSectionTable(0),
88    nbins(10),
89    fLPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)*0.5),
90    fLPMflag(true),
91    lpmEnergy(0.),
92    use_completescreening(false)
93{
94  fParticleChange = 0;
95  theGamma    = G4Gamma::Gamma();
96  thePositron = G4Positron::Positron();
97  theElectron = G4Electron::Electron();
98
99  nist = G4NistManager::Instance(); 
100
101}
102
103//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
104
105G4PairProductionRelModel::~G4PairProductionRelModel()
106{
107  if(theCrossSectionTable) {
108    theCrossSectionTable->clearAndDestroy();
109    delete theCrossSectionTable;
110  }
111}
112
113//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
114
115void G4PairProductionRelModel::Initialise(const G4ParticleDefinition*,
116                                          const G4DataVector&)
117{
118  fParticleChange = GetParticleChangeForGamma();
119
120  if(theCrossSectionTable) {
121    theCrossSectionTable->clearAndDestroy();
122    delete theCrossSectionTable;
123  }
124
125  const G4ElementTable* theElementTable = G4Element::GetElementTable();
126  size_t nvect = G4Element::GetNumberOfElements();
127  theCrossSectionTable = new G4PhysicsTable(nvect);
128  G4PhysicsLogVector* ptrVector;
129  G4double emin = LowEnergyLimit();
130  G4double emax = HighEnergyLimit();
131  G4int n = nbins*G4int(log10(emax/emin));
132  G4bool spline = G4LossTableManager::Instance()->SplineFlag(); 
133  G4double e, value;
134
135  for(size_t j=0; j<nvect ; j++) { 
136
137    ptrVector  = new G4PhysicsLogVector(emin, emax, n);
138    ptrVector->SetSpline(spline);
139    G4double Z = (*theElementTable)[j]->GetZ();
140    G4VEmModel::SetCurrentElement((*theElementTable)[j]);
141    G4int   iz = G4int(Z);
142    indexZ[iz] = j;
143 
144    for(G4int i=0; i<nbins; i++) {
145      e = ptrVector->GetLowEdgeEnergy( i ) ;
146      value = ComputeCrossSectionPerAtom(theGamma, e, Z); 
147      ptrVector->PutValue( i, value );
148    }
149
150    theCrossSectionTable->insert(ptrVector);
151  }
152}
153
154//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
155/*
156G4double G4PairProductionRelModel::ComputeRelXSectionPerAtom(G4double k, G4double Z)
157{
158
159  G4double cross = 0.0;
160 
161
162
163
164}
165*/
166
167//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
168
169G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double totalEnergy, G4double Z)
170{
171  G4double cross = 0.0;
172
173  // number of intervals and integration step
174  G4double vcut = electron_mass_c2/totalEnergy ;
175
176  // limits by the screening variable
177  G4double dmax = DeltaMax();
178  G4double dmin = min(DeltaMin(totalEnergy),dmax);
179  G4double vcut1 = 0.5 - 0.5*sqrt(1. - dmin/dmax) ;
180  vcut = max(vcut, vcut1);
181
182
183  G4double vmax = 0.5;
184  G4int n = 1;  // needs optimisation
185
186  G4double delta = (vmax - vcut)*totalEnergy/G4double(n);
187
188  G4double e0 = vcut*totalEnergy;
189  G4double xs; 
190
191  // simple integration
192  for(G4int l=0; l<n; l++,e0 += delta) {
193    for(G4int i=0; i<8; i++) {
194
195      G4double eg = (e0 + xgi[i]*delta);
196      if (fLPMflag && totalEnergy>100.*GeV) 
197        xs = ComputeRelDXSectionPerAtom(eg,totalEnergy,Z);
198      else
199        xs = ComputeDXSectionPerAtom(eg,totalEnergy,Z);
200      cross += wgi[i]*xs;
201
202    }
203  }
204
205  cross *= delta*2.;
206
207  return cross;
208}
209
210//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
211
212G4double
213G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double eplusEnergy, 
214                                                  G4double totalEnergy, 
215                                                  G4double /*Z*/)
216{
217  // most simple case - complete screening:
218
219  //  dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
220  //     * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3)  + 1/9 * y*(1-y) ]
221  // y = E+/k
222  G4double yp=eplusEnergy/totalEnergy;
223  G4double ym=1.-yp;
224
225  G4double cross = 0.;
226  if (use_completescreening) 
227    cross = (yp*yp + ym*ym + 2./3.*ym*yp)*(Fel - fCoulomb) + 1./9.*yp*ym;
228  else {
229    G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
230    cross = (yp*yp + ym*ym)*(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
231      + 2./3.*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
232  }
233  return cross/totalEnergy;
234
235}
236//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
237
238G4double
239G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double eplusEnergy, 
240                                                     G4double totalEnergy, 
241                                                     G4double /*Z*/)
242{
243  // most simple case - complete screening:
244
245  //  dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
246  //     * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3)  + 1/9 * y*(1-y) ]
247  // y = E+/k
248  G4double yp=eplusEnergy/totalEnergy;
249  G4double ym=1.-yp;
250
251  CalcLPMFunctions(totalEnergy,eplusEnergy); // gamma
252
253  G4double cross = 0.;
254  if (use_completescreening) 
255    cross = xiLPM*(2./3.*phiLPM*(yp*yp + ym*ym) + gLPM)*(Fel - fCoulomb);
256  else {
257    G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
258    cross = (1./3.*gLPM + 2./3.*phiLPM)*(yp*yp + ym*ym)
259                             *(0.25*Phi1(delta) - lnZ/3. - fCoulomb) 
260           + 2./3.*gLPM*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
261    cross *= xiLPM;
262  }
263  return cross/totalEnergy;
264
265}
266
267//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
268
269void  G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplus)
270{
271  // *** calculate lpm variable s & sprime ***
272  // Klein eqs. (78) & (79)
273  G4double sprime = sqrt(0.125*k*lpmEnergy/(eplus*(k-eplus)));
274
275  G4double s1 = preS1*z23;
276  G4double logS1 = 2./3.*lnZ-2.*facFel;
277  G4double logTS1 = logTwo+logS1;
278
279  xiLPM = 2.;
280
281  if (sprime>1) 
282    xiLPM = 1.;
283  else if (sprime>sqrt(2.)*s1) {
284    G4double h  = log(sprime)/logTS1;
285    xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1;
286  }
287
288  G4double s = sprime/sqrt(xiLPM); 
289//   G4cout<<"k="<<k<<" y="<<eplus/k<<G4endl;
290//   G4cout<<"s="<<s<<G4endl;
291 
292  // *** calculate supression functions phi and G ***
293  // Klein eqs. (77)
294  G4double s2=s*s;
295  G4double s3=s*s2;
296  G4double s4=s2*s2;
297
298  if (s<0.1) {
299    // high suppression limit
300    phiLPM = 6.*s - 18.84955592153876*s2 + 39.47841760435743*s3
301      - 57.69873135166053*s4;
302    gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4;
303  }
304  else if (s<1.9516) {
305    // intermediate suppression
306    // using eq.77 approxim. valid s<2.     
307    phiLPM = 1.-exp(-6.*s*(1.+(3.-pi)*s)
308                +s3/(0.623+0.795*s+0.658*s2));
309    if (s<0.415827397755) {
310      // using eq.77 approxim. valid 0.07<s<2
311      G4double psiLPM = 1-exp(-4*s-8*s2/(1+3.936*s+4.97*s2-0.05*s3+7.50*s4));
312      gLPM = 3*psiLPM-2*phiLPM;
313    }
314    else {
315      // using alternative parametrisiation
316      G4double pre = -0.16072300849123999 + s*3.7550300067531581 + s2*-1.7981383069010097 
317        + s3*0.67282686077812381 + s4*-0.1207722909879257;
318      gLPM = tanh(pre);
319    }
320  }
321  else {
322    // low suppression limit valid s>2.
323    phiLPM = 1. - 0.0119048/s4;
324    gLPM = 1. - 0.0230655/s4;
325  }
326
327  // *** make sure suppression is smaller than 1 ***
328  // *** caused by Migdal approximation in xi    ***
329  if (xiLPM*phiLPM>1. || s>0.57)  xiLPM=1./phiLPM;
330}
331
332
333//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
334
335G4double
336G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
337                                                     G4double gammaEnergy, G4double Z,
338                                                     G4double, G4double, G4double)
339{
340  //  static const G4double gammaEnergyLimit = 1.5*MeV;
341  G4double crossSection = 0.0 ;
342  if ( Z < 1. ) return crossSection;
343  if ( gammaEnergy <= 2.0*electron_mass_c2 ) return crossSection;
344
345  SetCurrentElement(Z);
346  // choose calculator according to parameters and switches
347  // in the moment only one calculator:
348  crossSection=ComputeXSectionPerAtom(gammaEnergy,Z);
349
350  G4double xi = Finel/(Fel - fCoulomb); // inelastic contribution
351  crossSection*=4.*Z*(Z+xi)*fine_structure_const*classic_electr_radius*classic_electr_radius;
352
353  return crossSection;
354}
355
356//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
357
358void 
359G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
360                                            const G4MaterialCutsCouple* couple,
361                                            const G4DynamicParticle* aDynamicGamma,
362                                            G4double,
363                                            G4double)
364// The secondaries e+e- energies are sampled using the Bethe - Heitler
365// cross sections with Coulomb correction.
366// A modified version of the random number techniques of Butcher & Messel
367// is used (Nuc Phys 20(1960),15).
368//
369// GEANT4 internal units.
370//
371// Note 1 : Effects due to the breakdown of the Born approximation at
372//          low energy are ignored.
373// Note 2 : The differential cross section implicitly takes account of
374//          pair creation in both nuclear and atomic electron fields.
375//          However triplet prodution is not generated.
376{
377  const G4Material* aMaterial = couple->GetMaterial();
378
379  G4double GammaEnergy = aDynamicGamma->GetKineticEnergy();
380  G4ParticleMomentum GammaDirection = aDynamicGamma->GetMomentumDirection();
381
382  G4double epsil ;
383  G4double epsil0 = electron_mass_c2/GammaEnergy ;
384  if(epsil0 > 1.0) return;
385
386  // do it fast if GammaEnergy < 2. MeV
387  static const G4double Egsmall=2.*MeV;
388
389  // select randomly one element constituing the material
390  const G4Element* anElement = SelectRandomAtom(aMaterial, theGamma, GammaEnergy);
391
392  if (GammaEnergy < Egsmall) {
393
394    epsil = epsil0 + (0.5-epsil0)*G4UniformRand();
395
396  } else {
397    // now comes the case with GammaEnergy >= 2. MeV
398
399    // Extract Coulomb factor for this Element
400    G4double FZ = 8.*(anElement->GetIonisation()->GetlogZ3());
401    if (GammaEnergy > 50.*MeV) FZ += 8.*(anElement->GetfCoulomb());
402
403    // limits of the screening variable
404    G4double screenfac = 136.*epsil0/(anElement->GetIonisation()->GetZ3());
405    G4double screenmax = exp ((42.24 - FZ)/8.368) - 0.952 ;
406    G4double screenmin = min(4.*screenfac,screenmax);
407
408    // limits of the energy sampling
409    G4double epsil1 = 0.5 - 0.5*sqrt(1. - screenmin/screenmax) ;
410    G4double epsilmin = max(epsil0,epsil1) , epsilrange = 0.5 - epsilmin;
411
412    //
413    // sample the energy rate of the created electron (or positron)
414    //
415    //G4double epsil, screenvar, greject ;
416    G4double  screenvar, greject ;
417
418    G4double F10 = ScreenFunction1(screenmin) - FZ;
419    G4double F20 = ScreenFunction2(screenmin) - FZ;
420    G4double NormF1 = max(F10*epsilrange*epsilrange,0.); 
421    G4double NormF2 = max(1.5*F20,0.);
422
423    do {
424      if ( NormF1/(NormF1+NormF2) > G4UniformRand() ) {
425        epsil = 0.5 - epsilrange*pow(G4UniformRand(), 0.333333);
426        screenvar = screenfac/(epsil*(1-epsil));
427        if (fLPMflag && GammaEnergy>100.*GeV) {
428          CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
429          greject = xiLPM*((gLPM+2.*phiLPM)*Phi1(screenvar) - gLPM*Phi2(screenvar) - phiLPM*FZ)/F10;
430        }
431        else {
432          greject = (ScreenFunction1(screenvar) - FZ)/F10;
433        }
434             
435      } else { 
436        epsil = epsilmin + epsilrange*G4UniformRand();
437        screenvar = screenfac/(epsil*(1-epsil));
438        if (fLPMflag && GammaEnergy>100.*GeV) {
439          CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
440          greject = xiLPM*((0.5*gLPM+phiLPM)*Phi1(screenvar) + 0.5*gLPM*Phi2(screenvar) - 0.5*(gLPM+phiLPM)*FZ)/F20;
441        }
442        else {
443          greject = (ScreenFunction2(screenvar) - FZ)/F20;
444        }
445      }
446
447    } while( greject < G4UniformRand() );
448
449  }   //  end of epsil sampling
450   
451  //
452  // fixe charges randomly
453  //
454
455  G4double ElectTotEnergy, PositTotEnergy;
456  if (G4UniformRand() > 0.5) {
457
458    ElectTotEnergy = (1.-epsil)*GammaEnergy;
459    PositTotEnergy = epsil*GammaEnergy;
460     
461  } else {
462   
463    PositTotEnergy = (1.-epsil)*GammaEnergy;
464    ElectTotEnergy = epsil*GammaEnergy;
465  }
466
467  //
468  // scattered electron (positron) angles. ( Z - axis along the parent photon)
469  //
470  //  universal distribution suggested by L. Urban
471  // (Geant3 manual (1993) Phys211),
472  //  derived from Tsai distribution (Rev Mod Phys 49,421(1977))
473
474  G4double u;
475  const G4double a1 = 0.625 , a2 = 3.*a1 , d = 27. ;
476
477  if (9./(9.+d) >G4UniformRand()) u= - log(G4UniformRand()*G4UniformRand())/a1;
478  else                            u= - log(G4UniformRand()*G4UniformRand())/a2;
479
480  G4double TetEl = u*electron_mass_c2/ElectTotEnergy;
481  G4double TetPo = u*electron_mass_c2/PositTotEnergy;
482  G4double Phi  = twopi * G4UniformRand();
483  G4double dxEl= sin(TetEl)*cos(Phi),dyEl= sin(TetEl)*sin(Phi),dzEl=cos(TetEl);
484  G4double dxPo=-sin(TetPo)*cos(Phi),dyPo=-sin(TetPo)*sin(Phi),dzPo=cos(TetPo);
485   
486  //
487  // kinematic of the created pair
488  //
489  // the electron and positron are assumed to have a symetric
490  // angular distribution with respect to the Z axis along the parent photon.
491
492  G4double ElectKineEnergy = max(0.,ElectTotEnergy - electron_mass_c2);
493
494  G4ThreeVector ElectDirection (dxEl, dyEl, dzEl);
495  ElectDirection.rotateUz(GammaDirection);   
496
497  // create G4DynamicParticle object for the particle1 
498  G4DynamicParticle* aParticle1= new G4DynamicParticle(
499                     theElectron,ElectDirection,ElectKineEnergy);
500 
501  // the e+ is always created (even with Ekine=0) for further annihilation.
502
503  G4double PositKineEnergy = max(0.,PositTotEnergy - electron_mass_c2);
504
505  G4ThreeVector PositDirection (dxPo, dyPo, dzPo);
506  PositDirection.rotateUz(GammaDirection);   
507
508  // create G4DynamicParticle object for the particle2
509  G4DynamicParticle* aParticle2= new G4DynamicParticle(
510                      thePositron,PositDirection,PositKineEnergy);
511
512  // Fill output vector
513  fvect->push_back(aParticle1);
514  fvect->push_back(aParticle2);
515
516  // kill incident photon
517  fParticleChange->SetProposedKineticEnergy(0.);
518  fParticleChange->ProposeTrackStatus(fStopAndKill);   
519}
520
521//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
522
523
524void G4PairProductionRelModel::SetupForMaterial(const G4ParticleDefinition*,
525                                                const G4Material* mat, G4double)
526{
527  lpmEnergy = mat->GetRadlen()*fLPMconstant;
528  //  G4cout<<" lpmEnergy="<<lpmEnergy<<G4endl;
529}
530
531//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
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