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G4PairProductionRelModel.cc
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26 // $Id$
27 //
28 // -------------------------------------------------------------------
29 //
30 // GEANT4 Class file
31 //
32 //
33 // File name: G4PairProductionRelModel
34 //
35 // Author: Andreas Schaelicke
36 //
37 // Creation date: 02.04.2009
38 //
39 // Modifications:
40 //
41 // Class Description:
42 //
43 // Main References:
44 // J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 581.
45 // S.Klein, Rev. Mod. Phys. 71 (1999) 1501.
46 // T.Stanev et.al., Phys. Rev. D25 (1982) 1291.
47 // M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media,
48 // Wiley, 1972.
49 //
50 // -------------------------------------------------------------------
51 //
52 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
53 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
54 
55 #include "G4PairProductionRelModel.hh"
56 #include "G4PhysicalConstants.hh"
57 #include "G4SystemOfUnits.hh"
58 #include "G4Gamma.hh"
59 #include "G4Electron.hh"
60 #include "G4Positron.hh"
61 
62 #include "G4ParticleChangeForGamma.hh"
63 #include "G4LossTableManager.hh"
64 
65 
66 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
67 
68 using namespace std;
69 
70 
71 const G4double G4PairProductionRelModel::facFel = log(184.15);
72 const G4double G4PairProductionRelModel::facFinel = log(1194.); // 1440.
73 
74 const G4double G4PairProductionRelModel::preS1 = 1./(184.15*184.15);
75 const G4double G4PairProductionRelModel::logTwo = log(2.);
76 
77 const G4double G4PairProductionRelModel::xgi[]={ 0.0199, 0.1017, 0.2372, 0.4083,
78  0.5917, 0.7628, 0.8983, 0.9801 };
79 const G4double G4PairProductionRelModel::wgi[]={ 0.0506, 0.1112, 0.1569, 0.1813,
80  0.1813, 0.1569, 0.1112, 0.0506 };
81 const G4double G4PairProductionRelModel::Fel_light[] = {0., 5.31 , 4.79 , 4.74 , 4.71};
82 const G4double G4PairProductionRelModel::Finel_light[] = {0., 6.144 , 5.621 , 5.805 , 5.924};
83 
84 
85 
86 G4PairProductionRelModel::G4PairProductionRelModel(const G4ParticleDefinition*,
87  const G4String& nam)
88  : G4VEmModel(nam),
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  currentZ = z13 = z23 = lnZ = Fel = Finel = fCoulomb = phiLPM = gLPM = xiLPM = 0;
102 
103 }
104 
105 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
106 
107 G4PairProductionRelModel::~G4PairProductionRelModel()
108 {}
109 
110 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
111 
112 void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p,
113  const G4DataVector& cuts)
114 {
115  if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
116  InitialiseElementSelectors(p, cuts);
117 }
118 
119 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
120 
121 G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double totalEnergy, G4double Z)
122 {
123  G4double cross = 0.0;
124 
125  // number of intervals and integration step
126  G4double vcut = electron_mass_c2/totalEnergy ;
127 
128  // limits by the screening variable
129  G4double dmax = DeltaMax();
130  G4double dmin = min(DeltaMin(totalEnergy),dmax);
131  G4double vcut1 = 0.5 - 0.5*sqrt(1. - dmin/dmax) ;
132  vcut = max(vcut, vcut1);
133 
134 
135  G4double vmax = 0.5;
136  G4int n = 1; // needs optimisation
137 
138  G4double delta = (vmax - vcut)*totalEnergy/G4double(n);
139 
140  G4double e0 = vcut*totalEnergy;
141  G4double xs;
142 
143  // simple integration
144  for(G4int l=0; l<n; l++,e0 += delta) {
145  for(G4int i=0; i<8; i++) {
146 
147  G4double eg = (e0 + xgi[i]*delta);
148  if (fLPMflag && totalEnergy>100.*GeV)
149  xs = ComputeRelDXSectionPerAtom(eg,totalEnergy,Z);
150  else
151  xs = ComputeDXSectionPerAtom(eg,totalEnergy,Z);
152  cross += wgi[i]*xs;
153 
154  }
155  }
156 
157  cross *= delta*2.;
158 
159  return cross;
160 }
161 
162 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
163 
164 G4double
165 G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double eplusEnergy,
166  G4double totalEnergy,
167  G4double /*Z*/)
168 {
169  // most simple case - complete screening:
170 
171  // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
172  // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
173  // y = E+/k
174  G4double yp=eplusEnergy/totalEnergy;
175  G4double ym=1.-yp;
176 
177  G4double cross = 0.;
178  if (use_completescreening)
179  cross = (yp*yp + ym*ym + 2./3.*ym*yp)*(Fel - fCoulomb) + 1./9.*yp*ym;
180  else {
181  G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
182  cross = (yp*yp + ym*ym)*(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
183  + 2./3.*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
184  }
185  return cross/totalEnergy;
186 
187 }
188 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
189 
190 G4double
191 G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double eplusEnergy,
192  G4double totalEnergy,
193  G4double /*Z*/)
194 {
195  // most simple case - complete screening:
196 
197  // dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
198  // * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
199  // y = E+/k
200  G4double yp=eplusEnergy/totalEnergy;
201  G4double ym=1.-yp;
202 
203  CalcLPMFunctions(totalEnergy,eplusEnergy); // gamma
204 
205  G4double cross = 0.;
206  if (use_completescreening)
207  cross = xiLPM*(2./3.*phiLPM*(yp*yp + ym*ym) + gLPM)*(Fel - fCoulomb);
208  else {
209  G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
210  cross = (1./3.*gLPM + 2./3.*phiLPM)*(yp*yp + ym*ym)
211  *(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
212  + 2./3.*gLPM*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
213  cross *= xiLPM;
214  }
215  return cross/totalEnergy;
216 
217 }
218 
219 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
220 
221 void
222 G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplusEnergy)
223 {
224  // *** calculate lpm variable s & sprime ***
225  // Klein eqs. (78) & (79)
226  G4double sprime = sqrt(0.125*k*lpmEnergy/(eplusEnergy*(k-eplusEnergy)));
227 
228  G4double s1 = preS1*z23;
229  G4double logS1 = 2./3.*lnZ-2.*facFel;
230  G4double logTS1 = logTwo+logS1;
231 
232  xiLPM = 2.;
233 
234  if (sprime>1)
235  xiLPM = 1.;
236  else if (sprime>sqrt(2.)*s1) {
237  G4double h = log(sprime)/logTS1;
238  xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1;
239  }
240 
241  G4double s0 = sprime/sqrt(xiLPM);
242  // G4cout<<"k="<<k<<" y="<<eplusEnergy/k<<G4endl;
243  // G4cout<<"s0="<<s0<<G4endl;
244 
245  // *** calculate supression functions phi and G ***
246  // Klein eqs. (77)
247  G4double s2=s0*s0;
248  G4double s3=s0*s2;
249  G4double s4=s2*s2;
250 
251  if (s0<0.1) {
252  // high suppression limit
253  phiLPM = 6.*s0 - 18.84955592153876*s2 + 39.47841760435743*s3
254  - 57.69873135166053*s4;
255  gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4;
256  }
257  else if (s0<1.9516) {
258  // intermediate suppression
259  // using eq.77 approxim. valid s0<2.
260  phiLPM = 1.-exp(-6.*s0*(1.+(3.-pi)*s0)
261  +s3/(0.623+0.795*s0+0.658*s2));
262  if (s0<0.415827397755) {
263  // using eq.77 approxim. valid 0.07<s<2
264  G4double psiLPM = 1-exp(-4*s0-8*s2/(1+3.936*s0+4.97*s2-0.05*s3+7.50*s4));
265  gLPM = 3*psiLPM-2*phiLPM;
266  }
267  else {
268  // using alternative parametrisiation
269  G4double pre = -0.16072300849123999 + s0*3.7550300067531581 + s2*-1.7981383069010097
270  + s3*0.67282686077812381 + s4*-0.1207722909879257;
271  gLPM = tanh(pre);
272  }
273  }
274  else {
275  // low suppression limit valid s>2.
276  phiLPM = 1. - 0.0119048/s4;
277  gLPM = 1. - 0.0230655/s4;
278  }
279 
280  // *** make sure suppression is smaller than 1 ***
281  // *** caused by Migdal approximation in xi ***
282  if (xiLPM*phiLPM>1. || s0>0.57) xiLPM=1./phiLPM;
283 }
284 
285 
286 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
287 
288 G4double
289 G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
290  G4double gammaEnergy, G4double Z,
291  G4double, G4double, G4double)
292 {
293  // static const G4double gammaEnergyLimit = 1.5*MeV;
294  G4double crossSection = 0.0 ;
295  if ( Z < 0.9 ) return crossSection;
296  if ( gammaEnergy <= 2.0*electron_mass_c2 ) return crossSection;
297 
298  SetCurrentElement(Z);
299  // choose calculator according to parameters and switches
300  // in the moment only one calculator:
301  crossSection=ComputeXSectionPerAtom(gammaEnergy,Z);
302 
303  G4double xi = Finel/(Fel - fCoulomb); // inelastic contribution
304  crossSection*=4.*Z*(Z+xi)*fine_structure_const*classic_electr_radius*classic_electr_radius;
305 
306  return crossSection;
307 }
308 
309 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
310 
311 void
312 G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
313  const G4MaterialCutsCouple* couple,
314  const G4DynamicParticle* aDynamicGamma,
315  G4double,
316  G4double)
317 // The secondaries e+e- energies are sampled using the Bethe - Heitler
318 // cross sections with Coulomb correction.
319 // A modified version of the random number techniques of Butcher & Messel
320 // is used (Nuc Phys 20(1960),15).
321 //
322 // GEANT4 internal units.
323 //
324 // Note 1 : Effects due to the breakdown of the Born approximation at
325 // low energy are ignored.
326 // Note 2 : The differential cross section implicitly takes account of
327 // pair creation in both nuclear and atomic electron fields.
328 // However triplet prodution is not generated.
329 {
330  const G4Material* aMaterial = couple->GetMaterial();
331 
332  G4double GammaEnergy = aDynamicGamma->GetKineticEnergy();
333  G4ParticleMomentum GammaDirection = aDynamicGamma->GetMomentumDirection();
334 
335  G4double epsil ;
336  G4double epsil0 = electron_mass_c2/GammaEnergy ;
337  if(epsil0 > 1.0) { return; }
338 
339  // do it fast if GammaEnergy < 2. MeV
340  static const G4double Egsmall=2.*MeV;
341 
342  // select randomly one element constituing the material
343  const G4Element* anElement = SelectRandomAtom(aMaterial, theGamma, GammaEnergy);
344 
345  if (GammaEnergy < Egsmall) {
346 
347  epsil = epsil0 + (0.5-epsil0)*G4UniformRand();
348 
349  } else {
350  // now comes the case with GammaEnergy >= 2. MeV
351 
352  // Extract Coulomb factor for this Element
353  G4double FZ = 8.*(anElement->GetIonisation()->GetlogZ3());
354  if (GammaEnergy > 50.*MeV) FZ += 8.*(anElement->GetfCoulomb());
355 
356  // limits of the screening variable
357  G4double screenfac = 136.*epsil0/(anElement->GetIonisation()->GetZ3());
358  G4double screenmax = exp ((42.24 - FZ)/8.368) - 0.952 ;
359  G4double screenmin = min(4.*screenfac,screenmax);
360 
361  // limits of the energy sampling
362  G4double epsil1 = 0.5 - 0.5*sqrt(1. - screenmin/screenmax) ;
363  G4double epsilmin = max(epsil0,epsil1) , epsilrange = 0.5 - epsilmin;
364 
365  //
366  // sample the energy rate of the created electron (or positron)
367  //
368  //G4double epsil, screenvar, greject ;
369  G4double screenvar, greject ;
370 
371  G4double F10 = ScreenFunction1(screenmin) - FZ;
372  G4double F20 = ScreenFunction2(screenmin) - FZ;
373  G4double NormF1 = max(F10*epsilrange*epsilrange,0.);
374  G4double NormF2 = max(1.5*F20,0.);
375 
376  do {
377  if ( NormF1/(NormF1+NormF2) > G4UniformRand() ) {
378  epsil = 0.5 - epsilrange*pow(G4UniformRand(), 0.333333);
379  screenvar = screenfac/(epsil*(1-epsil));
380  if (fLPMflag && GammaEnergy>100.*GeV) {
381  CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
382  greject = xiLPM*((gLPM+2.*phiLPM)*Phi1(screenvar) - gLPM*Phi2(screenvar) - phiLPM*FZ)/F10;
383  }
384  else {
385  greject = (ScreenFunction1(screenvar) - FZ)/F10;
386  }
387 
388  } else {
389  epsil = epsilmin + epsilrange*G4UniformRand();
390  screenvar = screenfac/(epsil*(1-epsil));
391  if (fLPMflag && GammaEnergy>100.*GeV) {
392  CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
393  greject = xiLPM*((0.5*gLPM+phiLPM)*Phi1(screenvar) + 0.5*gLPM*Phi2(screenvar) - 0.5*(gLPM+phiLPM)*FZ)/F20;
394  }
395  else {
396  greject = (ScreenFunction2(screenvar) - FZ)/F20;
397  }
398  }
399 
400  } while( greject < G4UniformRand() );
401 
402  } // end of epsil sampling
403 
404  //
405  // fixe charges randomly
406  //
407 
408  G4double ElectTotEnergy, PositTotEnergy;
409  if (G4UniformRand() > 0.5) {
410 
411  ElectTotEnergy = (1.-epsil)*GammaEnergy;
412  PositTotEnergy = epsil*GammaEnergy;
413 
414  } else {
415 
416  PositTotEnergy = (1.-epsil)*GammaEnergy;
417  ElectTotEnergy = epsil*GammaEnergy;
418  }
419 
420  //
421  // scattered electron (positron) angles. ( Z - axis along the parent photon)
422  //
423  // universal distribution suggested by L. Urban
424  // (Geant3 manual (1993) Phys211),
425  // derived from Tsai distribution (Rev Mod Phys 49,421(1977))
426 
427  G4double u;
428  const G4double a1 = 0.625 , a2 = 3.*a1 , d = 27. ;
429 
430  if (9./(9.+d) >G4UniformRand()) u= - log(G4UniformRand()*G4UniformRand())/a1;
431  else u= - log(G4UniformRand()*G4UniformRand())/a2;
432 
433  G4double TetEl = u*electron_mass_c2/ElectTotEnergy;
434  G4double TetPo = u*electron_mass_c2/PositTotEnergy;
435  G4double Phi = twopi * G4UniformRand();
436  G4double dxEl= sin(TetEl)*cos(Phi),dyEl= sin(TetEl)*sin(Phi),dzEl=cos(TetEl);
437  G4double dxPo=-sin(TetPo)*cos(Phi),dyPo=-sin(TetPo)*sin(Phi),dzPo=cos(TetPo);
438 
439  //
440  // kinematic of the created pair
441  //
442  // the electron and positron are assumed to have a symetric
443  // angular distribution with respect to the Z axis along the parent photon.
444 
445  G4double ElectKineEnergy = max(0.,ElectTotEnergy - electron_mass_c2);
446 
447  G4ThreeVector ElectDirection (dxEl, dyEl, dzEl);
448  ElectDirection.rotateUz(GammaDirection);
449 
450  // create G4DynamicParticle object for the particle1
451  G4DynamicParticle* aParticle1= new G4DynamicParticle(
452  theElectron,ElectDirection,ElectKineEnergy);
453 
454  // the e+ is always created (even with Ekine=0) for further annihilation.
455 
456  G4double PositKineEnergy = max(0.,PositTotEnergy - electron_mass_c2);
457 
458  G4ThreeVector PositDirection (dxPo, dyPo, dzPo);
459  PositDirection.rotateUz(GammaDirection);
460 
461  // create G4DynamicParticle object for the particle2
462  G4DynamicParticle* aParticle2= new G4DynamicParticle(
463  thePositron,PositDirection,PositKineEnergy);
464 
465  // Fill output vector
466  fvect->push_back(aParticle1);
467  fvect->push_back(aParticle2);
468 
469  // kill incident photon
470  fParticleChange->SetProposedKineticEnergy(0.);
471  fParticleChange->ProposeTrackStatus(fStopAndKill);
472 }
473 
474 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
475 
476 
477 void G4PairProductionRelModel::SetupForMaterial(const G4ParticleDefinition*,
478  const G4Material* mat, G4double)
479 {
480  lpmEnergy = mat->GetRadlen()*fLPMconstant;
481  // G4cout<<" lpmEnergy="<<lpmEnergy<<G4endl;
482 }
483 
484 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
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