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25 //
26 //
27 //
28 // Physics model class G4DiffuseElasticV2
29 //
30 //
31 // G4 Model: optical diffuse elastic scattering with 4-momentum balance
32 //
33 // 24-May-07 V. Grichine
34 //
35 // 21.10.15 V. Grichine
36 // Bug fixed in BuildAngleTable, improving accuracy for
37 // angle bins at high energies > 50 GeV for pions.
38 //
39 // 24.11.17 W. Pokorski, code cleanup and performance improvements
40 //
41
42 #include "G4DiffuseElasticV2.hh"
43 #include "G4ParticleTable.hh"
44 #include "G4ParticleDefinition.hh"
45 #include "G4IonTable.hh"
46 #include "G4NucleiProperties.hh"
47
48 #include "Randomize.hh"
49 #include "G4Integrator.hh"
50 #include "globals.hh"
51 #include "G4PhysicalConstants.hh"
52 #include "G4SystemOfUnits.hh"
53
54 #include "G4Proton.hh"
55 #include "G4Neutron.hh"
56 #include "G4Deuteron.hh"
57 #include "G4Alpha.hh"
58 #include "G4PionPlus.hh"
59 #include "G4PionMinus.hh"
60
61 #include "G4Element.hh"
62 #include "G4ElementTable.hh"
63 #include "G4NistManager.hh"
64 #include "G4PhysicsTable.hh"
65 #include "G4PhysicsLogVector.hh"
66 #include "G4PhysicsFreeVector.hh"
67
68 #include "G4Exp.hh"
69
70 #include "G4HadronicParameters.hh"
71
72 /////////////////////////////////////////////////////////////////////////
73 //
74
75
76 G4DiffuseElasticV2::G4DiffuseElasticV2()
77 : G4HadronElastic("DiffuseElasticV2"), fParticle(0)
78 {
79 SetMinEnergy( 0.01*MeV );
80 SetMaxEnergy( G4HadronicParameters::Instance()->GetMaxEnergy() );
81
82 verboseLevel = 0;
83 lowEnergyRecoilLimit = 100.*keV;
84 lowEnergyLimitQ = 0.0*GeV;
85 lowEnergyLimitHE = 0.0*GeV;
86 lowestEnergyLimit = 0.0*keV;
87 plabLowLimit = 20.0*MeV;
88
89 theProton = G4Proton::Proton();
90 theNeutron = G4Neutron::Neutron();
91
92 fEnergyBin = 300; // Increased from the original 200 to have no wider log-energy-bins up to 10 PeV
93 fAngleBin = 200;
94
95 fEnergyVector = new G4PhysicsLogVector( theMinEnergy, theMaxEnergy, fEnergyBin );
96
97 fEnergyAngleVector = 0;
98 fEnergySumVector = 0;
99
100 fParticle = 0;
101 fWaveVector = 0.;
102 fAtomicWeight = 0.;
103 fAtomicNumber = 0.;
104 fNuclearRadius = 0.;
105 fBeta = 0.;
106 fZommerfeld = 0.;
107 fAm = 0.;
108 fAddCoulomb = false;
109 }
110
111 //////////////////////////////////////////////////////////////////////////////
112 //
113 // Destructor
114
115 G4DiffuseElasticV2::~G4DiffuseElasticV2()
116 {
117 if ( fEnergyVector )
118 {
119 delete fEnergyVector;
120 fEnergyVector = 0;
121 }
122 }
123
124 //////////////////////////////////////////////////////////////////////////////
125 //
126 // Initialisation for given particle using element table of application
127
128 void G4DiffuseElasticV2::Initialise()
129 {
130
131 const G4ElementTable* theElementTable = G4Element::GetElementTable();
132
133 std::size_t jEl, numOfEl = G4Element::GetNumberOfElements();
134
135 for( jEl = 0; jEl < numOfEl; ++jEl) // application element loop
136 {
137 fAtomicNumber = (*theElementTable)[jEl]->GetZ(); // atomic number
138 fAtomicWeight = G4NistManager::Instance()->GetAtomicMassAmu( static_cast< G4int >( fAtomicNumber ) );
139 fNuclearRadius = CalculateNuclearRad(fAtomicWeight);
140
141 if( verboseLevel > 0 )
142 {
143 G4cout<<"G4DiffuseElasticV2::Initialise() the element: "
144 <<(*theElementTable)[jEl]->GetName()<<G4endl;
145 }
146 fElementNumberVector.push_back(fAtomicNumber);
147 fElementNameVector.push_back((*theElementTable)[jEl]->GetName());
148
149 BuildAngleTable();
150
151 fEnergyAngleVectorBank.push_back(fEnergyAngleVector);
152 fEnergySumVectorBank.push_back(fEnergySumVector);
153
154 }
155 return;
156 }
157
158 ////////////////////////////////////////////////////////////////////////////
159 //
160 // return differential elastic probability d(probability)/d(t) with
161 // Coulomb correction. It is called from BuildAngleTable()
162
163 G4double
164 G4DiffuseElasticV2::GetDiffElasticSumProbA( G4double theta )
165 {
166
167 G4double sigma, bzero, bzero2, bonebyarg, bonebyarg2, damp, damp2;
168 G4double delta, diffuse, gamma;
169 G4double e1, e2, bone, bone2;
170
171 // G4double wavek = momentum/hbarc; // wave vector
172 // G4double r0 = 1.08*fermi;
173 // G4double rad = r0*G4Pow::GetInstance()->A13(A);
174
175 G4double kr = fWaveVector*fNuclearRadius; // wavek*rad;
176 G4double kr2 = kr*kr;
177 G4double krt = kr*theta;
178
179 bzero = BesselJzero(krt);
180 bzero2 = bzero*bzero;
181 bone = BesselJone(krt);
182 bone2 = bone*bone;
183 bonebyarg = BesselOneByArg(krt);
184 bonebyarg2 = bonebyarg*bonebyarg;
185
186 if ( fParticle == theProton )
187 {
188 diffuse = 0.63*fermi;
189 gamma = 0.3*fermi;
190 delta = 0.1*fermi*fermi;
191 e1 = 0.3*fermi;
192 e2 = 0.35*fermi;
193 }
194 else if ( fParticle == theNeutron )
195 {
196 diffuse = 0.63*fermi;
197 gamma = 0.3*fermi;
198 delta = 0.1*fermi*fermi;
199 e1 = 0.3*fermi;
200 e2 = 0.35*fermi;
201 }
202 else // as proton, if were not defined
203 {
204 diffuse = 0.63*fermi;
205 gamma = 0.3*fermi;
206 delta = 0.1*fermi*fermi;
207 e1 = 0.3*fermi;
208 e2 = 0.35*fermi;
209 }
210
211 G4double lambda = 15; // 15 ok
212 // G4double kgamma = fWaveVector*gamma; // wavek*delta;
213 G4double kgamma = lambda*(1.-G4Exp(-fWaveVector*gamma/lambda)); // wavek*delta;
214
215 if( fAddCoulomb ) // add Coulomb correction
216 {
217 G4double sinHalfTheta = std::sin(0.5*theta);
218 G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
219
220 kgamma += 0.5*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
221 }
222
223 G4double kgamma2 = kgamma*kgamma;
224
225 // G4double dk2t = delta*fWaveVector*fWaveVector*theta; // delta*wavek*wavek*theta;
226 // G4double dk2t2 = dk2t*dk2t;
227
228 // G4double pikdt = pi*fWaveVector*diffuse*theta;// pi*wavek*diffuse*theta;
229 G4double pikdt = lambda*(1. - G4Exp( -pi*fWaveVector*diffuse*theta/lambda ) ); // wavek*delta;
230
231 damp = DampFactor( pikdt );
232 damp2 = damp*damp;
233
234 G4double mode2k2 = ( e1*e1 + e2*e2 )*fWaveVector*fWaveVector;
235 G4double e2dk3t = -2.*e2*delta*fWaveVector*fWaveVector*fWaveVector*theta;
236
237 sigma = kgamma2;
238 // sigma += dk2t2;
239 sigma *= bzero2;
240 sigma += mode2k2*bone2;
241 sigma += e2dk3t*bzero*bone;
242
243 // sigma += kr2*(1 + 8.*fZommerfeld*fZommerfeld/kr2)*bonebyarg2; // correction at J1()/()
244 sigma += kr2*bonebyarg2; // correction at J1()/()
245
246 sigma *= damp2; // *rad*rad;
247
248 return sigma;
249 }
250
251
252 ////////////////////////////////////////////////////////////////////////////
253 //
254 // return differential elastic probability 2*pi*sin(theta)*d(probability)/d(omega)
255
256 G4double
257 G4DiffuseElasticV2::GetIntegrandFunction( G4double alpha )
258 {
259 G4double result;
260
261 result = GetDiffElasticSumProbA(alpha) * 2 * CLHEP::pi * std::sin(alpha);
262
263 return result;
264 }
265
266
267 /////////////////////////////////////////////////////////////////////////////
268 ///////////////////// Table preparation and reading ////////////////////////
269 ////////////////////////////////////////////////////////////////////////////
270 //
271 // Return inv momentum transfer -t > 0 from initialisation table
272
273 G4double G4DiffuseElasticV2::SampleInvariantT( const G4ParticleDefinition* aParticle, G4double p,
274 G4int Z, G4int A)
275 {
276 fParticle = aParticle;
277 G4double m1 = fParticle->GetPDGMass(), t;
278 G4double totElab = std::sqrt(m1*m1+p*p);
279 G4double mass2 = G4NucleiProperties::GetNuclearMass(A, Z);
280 G4LorentzVector lv1(p,0.0,0.0,totElab);
281 G4LorentzVector lv(0.0,0.0,0.0,mass2);
282 lv += lv1;
283
284 G4ThreeVector bst = lv.boostVector();
285 lv1.boost(-bst);
286
287 G4ThreeVector p1 = lv1.vect();
288 G4double momentumCMS = p1.mag();
289
290 if( aParticle == theNeutron)
291 {
292 G4double Tmax = NeutronTuniform( Z );
293 G4double pCMS2 = momentumCMS*momentumCMS;
294 G4double Tkin = std::sqrt(pCMS2+m1*m1)-m1;
295
296 if( Tkin <= Tmax )
297 {
298 t = 4.*pCMS2*G4UniformRand();
299 return t;
300 }
301 }
302
303 t = SampleTableT( aParticle, momentumCMS, G4double(Z), G4double(A) ); // sample theta in cms
304
305 return t;
306 }
307
308 ///////////////////////////////////////////////////////
309
310 G4double G4DiffuseElasticV2::NeutronTuniform(G4int Z)
311 {
312 G4double elZ = G4double(Z);
313 elZ -= 1.;
314 G4double Tkin = 12.*G4Exp(-elZ/10.) + 1.;
315
316 return Tkin;
317 }
318
319
320 ////////////////////////////////////////////////////////////////////////////
321 //
322 // Return inv momentum transfer -t > 0 from initialisation table
323
324 G4double G4DiffuseElasticV2::SampleTableT( const G4ParticleDefinition* aParticle, G4double p,
325 G4double Z, G4double A)
326 {
327 G4double alpha = SampleTableThetaCMS( aParticle, p, Z, A); // sample theta in cms
328 G4double t = 2*p*p*( 1 - std::cos(alpha) ); // -t !!!
329
330 return t;
331 }
332
333 ////////////////////////////////////////////////////////////////////////////
334 //
335 // Return scattering angle2 sampled in cms according to precalculated table.
336
337
338 G4double
339 G4DiffuseElasticV2::SampleTableThetaCMS(const G4ParticleDefinition* particle,
340 G4double momentum, G4double Z, G4double A)
341 {
342 std::size_t iElement;
343 G4int iMomentum;
344 unsigned long iAngle = 0;
345 G4double randAngle, position, theta1, theta2, E1, E2, W1, W2, W;
346 G4double m1 = particle->GetPDGMass();
347
348 for(iElement = 0; iElement < fElementNumberVector.size(); iElement++)
349 {
350 if( std::fabs(Z - fElementNumberVector[iElement]) < 0.5) break;
351 }
352
353 if ( iElement == fElementNumberVector.size() )
354 {
355 InitialiseOnFly(Z,A); // table preparation, if needed
356 }
357
358 fEnergyAngleVector = fEnergyAngleVectorBank[iElement];
359 fEnergySumVector = fEnergySumVectorBank[iElement];
360
361
362 G4double kinE = std::sqrt(momentum*momentum + m1*m1) - m1;
363
364 iMomentum = G4int(fEnergyVector->FindBin(kinE,1000) + 1);
365
366 position = (*(*fEnergySumVector)[iMomentum])[0]*G4UniformRand();
367
368 for(iAngle = 0; iAngle < fAngleBin; ++iAngle)
369 {
370 if (position > (*(*fEnergySumVector)[iMomentum])[iAngle]) break;
371 }
372
373
374 if (iMomentum == fEnergyBin -1 || iMomentum == 0 ) // the table edges
375 {
376 randAngle = GetScatteringAngle(iMomentum, iAngle, position);
377 }
378 else // kinE inside between energy table edges
379 {
380 theta2 = GetScatteringAngle(iMomentum, iAngle, position);
381
382 E2 = fEnergyVector->Energy(iMomentum);
383
384 iMomentum--;
385
386 theta1 = GetScatteringAngle(iMomentum, iAngle, position);
387
388 E1 = fEnergyVector->Energy(iMomentum);
389
390 W = 1.0/(E2 - E1);
391 W1 = (E2 - kinE)*W;
392 W2 = (kinE - E1)*W;
393
394 randAngle = W1*theta1 + W2*theta2;
395 }
396
397
398
399 if(randAngle < 0.) randAngle = 0.;
400
401 return randAngle;
402 }
403
404 //////////////////////////////////////////////////////////////////////////////
405 //
406 // Initialisation for given particle on fly using new element number
407
408 void G4DiffuseElasticV2::InitialiseOnFly(G4double Z, G4double A)
409 {
410 fAtomicNumber = Z; // atomic number
411 fAtomicWeight = G4NistManager::Instance()->GetAtomicMassAmu( static_cast< G4int >( Z ) );
412
413 fNuclearRadius = CalculateNuclearRad(fAtomicWeight);
414
415 if( verboseLevel > 0 )
416 {
417 G4cout<<"G4DiffuseElasticV2::InitialiseOnFly() the element with Z = "
418 <<Z<<"; and A = "<<A<<G4endl;
419 }
420 fElementNumberVector.push_back(fAtomicNumber);
421
422 BuildAngleTable();
423
424 fEnergyAngleVectorBank.push_back(fEnergyAngleVector);
425 fEnergySumVectorBank.push_back(fEnergySumVector);
426
427 return;
428 }
429
430 ///////////////////////////////////////////////////////////////////////////////
431 //
432 // Build for given particle and element table of momentum, angle probability.
433 // For the moment in lab system.
434
435 void G4DiffuseElasticV2::BuildAngleTable()
436 {
437 G4double partMom, kinE, a = 0., z = fParticle->GetPDGCharge(), m1 = fParticle->GetPDGMass();
438 G4double alpha1, alpha2, alphaMax, alphaCoulomb, delta = 0., sum = 0.;
439
440 G4Integrator<G4DiffuseElasticV2,G4double(G4DiffuseElasticV2::*)(G4double)> integral;
441
442 fEnergyAngleVector = new std::vector<std::vector<G4double>*>;
443 fEnergySumVector = new std::vector<std::vector<G4double>*>;
444
445 for( G4int i = 0; i < fEnergyBin; ++i)
446 {
447 kinE = fEnergyVector->Energy(i);
448 partMom = std::sqrt( kinE*(kinE + 2*m1) );
449
450 fWaveVector = partMom/hbarc;
451
452 G4double kR = fWaveVector*fNuclearRadius;
453 G4double kRmax = 18.6; // 10.6; 10.6, 18, 10.174; ~ 3 maxima of J1 or 15., 25.
454 G4double kRcoul = 1.9; // 1.2; 1.4, 2.5; // on the first slope of J1
455
456 alphaMax = kRmax/kR;
457
458 if ( alphaMax >= CLHEP::pi ) alphaMax = CLHEP::pi; // vmg21.10.15
459
460 alphaCoulomb = kRcoul/kR;
461
462 if( z )
463 {
464 a = partMom/m1; // beta*gamma for m1
465 fBeta = a/std::sqrt(1+a*a);
466 fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
467 fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
468 fAddCoulomb = true;
469 }
470
471 std::vector<G4double>* angleVector = new std::vector<G4double>(fAngleBin);
472 std::vector<G4double>* sumVector = new std::vector<G4double>(fAngleBin);
473
474
475 G4double delth = alphaMax/fAngleBin;
476
477 sum = 0.;
478
479 for(G4int j = (G4int)fAngleBin-1; j >= 0; --j)
480 {
481 alpha1 = delth*j;
482 alpha2 = alpha1 + delth;
483
484 if( fAddCoulomb && ( alpha2 < alphaCoulomb)) fAddCoulomb = false;
485
486 delta = integral.Legendre10(this, &G4DiffuseElasticV2::GetIntegrandFunction, alpha1, alpha2);
487
488 sum += delta;
489
490 (*angleVector)[j] = alpha1;
491 (*sumVector)[j] = sum;
492
493 }
494 fEnergyAngleVector->push_back(angleVector);
495 fEnergySumVector->push_back(sumVector);
496
497 }
498 return;
499 }
500
501 /////////////////////////////////////////////////////////////////////////////////
502 //
503 //
504
505 G4double
506 G4DiffuseElasticV2::GetScatteringAngle( G4int iMomentum, unsigned long iAngle, G4double position )
507 {
508 G4double x1, x2, y1, y2, randAngle = 0;
509
510 if( iAngle == 0 )
511 {
512 randAngle = (*(*fEnergyAngleVector)[iMomentum])[iAngle];
513 }
514 else
515 {
516 if ( iAngle >= (*fEnergyAngleVector)[iMomentum]->size() )
517 {
518 iAngle = (*fEnergyAngleVector)[iMomentum]->size() - 1;
519 }
520
521 y1 = (*(*fEnergySumVector)[iMomentum])[iAngle-1];
522 y2 = (*(*fEnergySumVector)[iMomentum])[iAngle];
523
524 x1 = (*(*fEnergyAngleVector)[iMomentum])[iAngle-1];
525 x2 = (*(*fEnergyAngleVector)[iMomentum])[iAngle];
526
527 if ( x1 == x2 ) randAngle = x2;
528 else
529 {
530 if ( y1 == y2 ) randAngle = x1 + ( x2 - x1 )*G4UniformRand();
531 else
532 {
533 randAngle = x1 + ( position - y1 )*( x2 - x1 )/( y2 - y1 );
534 }
535 }
536 }
537
538 return randAngle;
539 }
540
541
542
543
544 ////////////////////////////////////////////////////////////////////////////
545 //
546 // Return scattering angle in lab system (target at rest) knowing theta in CMS
547
548
549
550 G4double
551 G4DiffuseElasticV2::ThetaCMStoThetaLab( const G4DynamicParticle* aParticle,
552 G4double tmass, G4double thetaCMS)
553 {
554 const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
555 G4double m1 = theParticle->GetPDGMass();
556 G4LorentzVector lv1 = aParticle->Get4Momentum();
557 G4LorentzVector lv(0.0,0.0,0.0,tmass);
558
559 lv += lv1;
560
561 G4ThreeVector bst = lv.boostVector();
562
563 lv1.boost(-bst);
564
565 G4ThreeVector p1 = lv1.vect();
566 G4double ptot = p1.mag();
567
568 G4double phi = G4UniformRand()*twopi;
569 G4double cost = std::cos(thetaCMS);
570 G4double sint;
571
572 if( cost >= 1.0 )
573 {
574 cost = 1.0;
575 sint = 0.0;
576 }
577 else if( cost <= -1.0)
578 {
579 cost = -1.0;
580 sint = 0.0;
581 }
582 else
583 {
584 sint = std::sqrt((1.0-cost)*(1.0+cost));
585 }
586 if (verboseLevel>1)
587 {
588 G4cout << "cos(tcms)=" << cost << " std::sin(tcms)=" << sint << G4endl;
589 }
590 G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
591 v1 *= ptot;
592 G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(ptot*ptot + m1*m1));
593
594 nlv1.boost(bst);
595
596 G4ThreeVector np1 = nlv1.vect();
597
598 G4double thetaLab = np1.theta();
599
600 return thetaLab;
601 }
602 ////////////////////////////////////////////////////////////////////////////
603 //
604 // Return scattering angle in CMS system (target at rest) knowing theta in Lab
605
606
607
608 G4double
609 G4DiffuseElasticV2::ThetaLabToThetaCMS( const G4DynamicParticle* aParticle,
610 G4double tmass, G4double thetaLab)
611 {
612 const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
613 G4double m1 = theParticle->GetPDGMass();
614 G4double plab = aParticle->GetTotalMomentum();
615 G4LorentzVector lv1 = aParticle->Get4Momentum();
616 G4LorentzVector lv(0.0,0.0,0.0,tmass);
617
618 lv += lv1;
619
620 G4ThreeVector bst = lv.boostVector();
621
622 G4double phi = G4UniformRand()*twopi;
623 G4double cost = std::cos(thetaLab);
624 G4double sint;
625
626 if( cost >= 1.0 )
627 {
628 cost = 1.0;
629 sint = 0.0;
630 }
631 else if( cost <= -1.0)
632 {
633 cost = -1.0;
634 sint = 0.0;
635 }
636 else
637 {
638 sint = std::sqrt((1.0-cost)*(1.0+cost));
639 }
640 if (verboseLevel>1)
641 {
642 G4cout << "cos(tlab)=" << cost << " std::sin(tlab)=" << sint << G4endl;
643 }
644 G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
645 v1 *= plab;
646 G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(plab*plab + m1*m1));
647
648 nlv1.boost(-bst);
649
650 G4ThreeVector np1 = nlv1.vect();
651 G4double thetaCMS = np1.theta();
652
653 return thetaCMS;
654 }
655
656