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25 //
26 //
27 //
28 // Author: V. Grichine (Vladimir,Grichine@cern.ch)
29 //
30 //
31 // G4 Model: diffuse optical elastic scattering with 4-momentum balance
32 //
33 // Class Description
34 // Final state production model for hadron nuclear elastic scattering;
35 // Class Description - End
36 //
37 //
38 // 24.05.07 V. Grichine, first implementation for hadron (no Coulomb) elastic scattering
39 // 04.09.07 V. Grichine, implementation for Coulomb elastic scattering
40 // 12.06.11 V. Grichine, new interface to G4hadronElastic
41
42 #ifndef G4DiffuseElastic_h
43 #define G4DiffuseElastic_h 1
44
45 #include <CLHEP/Units/PhysicalConstants.h>
46 #include "globals.hh"
47 #include "G4HadronElastic.hh"
48 #include "G4HadProjectile.hh"
49 #include "G4Nucleus.hh"
50
51 #include "G4Pow.hh"
52
53
54 class G4ParticleDefinition;
55 class G4PhysicsTable;
56 class G4PhysicsLogVector;
57
58 class G4DiffuseElastic : public G4HadronElastic // G4HadronicInteraction
59 {
60 public:
61
62 G4DiffuseElastic();
63
64 // G4DiffuseElastic(const G4ParticleDefinition* aParticle);
65
66
67
68
69
70 virtual ~G4DiffuseElastic();
71
72 virtual G4bool IsApplicable(const G4HadProjectile &/*aTrack*/,
73 G4Nucleus & /*targetNucleus*/);
74
75 void Initialise();
76
77 void InitialiseOnFly(G4double Z, G4double A);
78
79 void BuildAngleTable();
80
81
82 // G4HadFinalState* ApplyYourself(const G4HadProjectile & aTrack, G4Nucleus & targetNucleus);
83
84 virtual G4double SampleInvariantT(const G4ParticleDefinition* p,
85 G4double plab,
86 G4int Z, G4int A);
87
88 G4double NeutronTuniform(G4int Z);
89
90 void SetPlabLowLimit(G4double value);
91
92 void SetHEModelLowLimit(G4double value);
93
94 void SetQModelLowLimit(G4double value);
95
96 void SetLowestEnergyLimit(G4double value);
97
98 void SetRecoilKinEnergyLimit(G4double value);
99
100 G4double SampleT(const G4ParticleDefinition* aParticle,
101 G4double p, G4double A);
102
103 G4double SampleTableT(const G4ParticleDefinition* aParticle,
104 G4double p, G4double Z, G4double A);
105
106 G4double SampleThetaCMS(const G4ParticleDefinition* aParticle, G4double p, G4double A);
107
108 G4double SampleTableThetaCMS(const G4ParticleDefinition* aParticle, G4double p,
109 G4double Z, G4double A);
110
111 G4double GetScatteringAngle(G4int iMomentum, G4int iAngle, G4double position);
112
113 G4double SampleThetaLab(const G4HadProjectile* aParticle,
114 G4double tmass, G4double A);
115
116 G4double GetDiffuseElasticXsc( const G4ParticleDefinition* particle,
117 G4double theta,
118 G4double momentum,
119 G4double A );
120
121 G4double GetInvElasticXsc( const G4ParticleDefinition* particle,
122 G4double theta,
123 G4double momentum,
124 G4double A, G4double Z );
125
126 G4double GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle,
127 G4double theta,
128 G4double momentum,
129 G4double A, G4double Z );
130
131 G4double GetInvElasticSumXsc( const G4ParticleDefinition* particle,
132 G4double tMand,
133 G4double momentum,
134 G4double A, G4double Z );
135
136 G4double IntegralElasticProb( const G4ParticleDefinition* particle,
137 G4double theta,
138 G4double momentum,
139 G4double A );
140
141
142 G4double GetCoulombElasticXsc( const G4ParticleDefinition* particle,
143 G4double theta,
144 G4double momentum,
145 G4double Z );
146
147 G4double GetInvCoulombElasticXsc( const G4ParticleDefinition* particle,
148 G4double tMand,
149 G4double momentum,
150 G4double A, G4double Z );
151
152 G4double GetCoulombTotalXsc( const G4ParticleDefinition* particle,
153 G4double momentum, G4double Z );
154
155 G4double GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
156 G4double momentum, G4double Z,
157 G4double theta1, G4double theta2 );
158
159
160 G4double CalculateParticleBeta( const G4ParticleDefinition* particle,
161 G4double momentum );
162
163 G4double CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 );
164
165 G4double CalculateAm( G4double momentum, G4double n, G4double Z);
166
167 G4double CalculateNuclearRad( G4double A);
168
169 G4double ThetaCMStoThetaLab(const G4DynamicParticle* aParticle,
170 G4double tmass, G4double thetaCMS);
171
172 G4double ThetaLabToThetaCMS(const G4DynamicParticle* aParticle,
173 G4double tmass, G4double thetaLab);
174
175 void TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom,
176 G4double Z, G4double A);
177
178
179
180 G4double BesselJzero(G4double z);
181 G4double BesselJone(G4double z);
182 G4double DampFactor(G4double z);
183 G4double BesselOneByArg(G4double z);
184
185 G4double GetDiffElasticProb(G4double theta);
186 G4double GetDiffElasticSumProb(G4double theta);
187 G4double GetDiffElasticSumProbA(G4double alpha);
188 G4double GetIntegrandFunction(G4double theta);
189
190
191 G4double GetNuclearRadius(){return fNuclearRadius;};
192
193 private:
194
195
196 G4ParticleDefinition* theProton;
197 G4ParticleDefinition* theNeutron;
198 G4ParticleDefinition* theDeuteron;
199 G4ParticleDefinition* theAlpha;
200
201 const G4ParticleDefinition* thePionPlus;
202 const G4ParticleDefinition* thePionMinus;
203
204 G4double lowEnergyRecoilLimit;
205 G4double lowEnergyLimitHE;
206 G4double lowEnergyLimitQ;
207 G4double lowestEnergyLimit;
208 G4double plabLowLimit;
209
210 G4int fEnergyBin;
211 G4int fAngleBin;
212
213 G4PhysicsLogVector* fEnergyVector;
214 G4PhysicsTable* fAngleTable;
215 std::vector<G4PhysicsTable*> fAngleBank;
216
217 std::vector<G4double> fElementNumberVector;
218 std::vector<G4String> fElementNameVector;
219
220 const G4ParticleDefinition* fParticle;
221 G4double fWaveVector;
222 G4double fAtomicWeight;
223 G4double fAtomicNumber;
224 G4double fNuclearRadius;
225 G4double fBeta;
226 G4double fZommerfeld;
227 G4double fAm;
228 G4bool fAddCoulomb;
229
230 };
231
232 inline G4bool G4DiffuseElastic::IsApplicable(const G4HadProjectile & projectile,
233 G4Nucleus & nucleus)
234 {
235 if( ( projectile.GetDefinition() == G4Proton::Proton() ||
236 projectile.GetDefinition() == G4Neutron::Neutron() ||
237 projectile.GetDefinition() == G4PionPlus::PionPlus() ||
238 projectile.GetDefinition() == G4PionMinus::PionMinus() ||
239 projectile.GetDefinition() == G4KaonPlus::KaonPlus() ||
240 projectile.GetDefinition() == G4KaonMinus::KaonMinus() ) &&
241
242 nucleus.GetZ_asInt() >= 2 ) return true;
243 else return false;
244 }
245
246 inline void G4DiffuseElastic::SetRecoilKinEnergyLimit(G4double value)
247 {
248 lowEnergyRecoilLimit = value;
249 }
250
251 inline void G4DiffuseElastic::SetPlabLowLimit(G4double value)
252 {
253 plabLowLimit = value;
254 }
255
256 inline void G4DiffuseElastic::SetHEModelLowLimit(G4double value)
257 {
258 lowEnergyLimitHE = value;
259 }
260
261 inline void G4DiffuseElastic::SetQModelLowLimit(G4double value)
262 {
263 lowEnergyLimitQ = value;
264 }
265
266 inline void G4DiffuseElastic::SetLowestEnergyLimit(G4double value)
267 {
268 lowestEnergyLimit = value;
269 }
270
271
272 /////////////////////////////////////////////////////////////
273 //
274 // Bessel J0 function based on rational approximation from
275 // J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
276
277 inline G4double G4DiffuseElastic::BesselJzero(G4double value)
278 {
279 G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
280
281 modvalue = std::fabs(value);
282
283 if ( value < 8.0 && value > -8.0 )
284 {
285 value2 = value*value;
286
287 fact1 = 57568490574.0 + value2*(-13362590354.0
288 + value2*( 651619640.7
289 + value2*(-11214424.18
290 + value2*( 77392.33017
291 + value2*(-184.9052456 ) ) ) ) );
292
293 fact2 = 57568490411.0 + value2*( 1029532985.0
294 + value2*( 9494680.718
295 + value2*(59272.64853
296 + value2*(267.8532712
297 + value2*1.0 ) ) ) );
298
299 bessel = fact1/fact2;
300 }
301 else
302 {
303 arg = 8.0/modvalue;
304
305 value2 = arg*arg;
306
307 shift = modvalue-0.785398164;
308
309 fact1 = 1.0 + value2*(-0.1098628627e-2
310 + value2*(0.2734510407e-4
311 + value2*(-0.2073370639e-5
312 + value2*0.2093887211e-6 ) ) );
313
314 fact2 = -0.1562499995e-1 + value2*(0.1430488765e-3
315 + value2*(-0.6911147651e-5
316 + value2*(0.7621095161e-6
317 - value2*0.934945152e-7 ) ) );
318
319 bessel = std::sqrt(0.636619772/modvalue)*(std::cos(shift)*fact1 - arg*std::sin(shift)*fact2 );
320 }
321 return bessel;
322 }
323
324 /////////////////////////////////////////////////////////////
325 //
326 // Bessel J1 function based on rational approximation from
327 // J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
328
329 inline G4double G4DiffuseElastic::BesselJone(G4double value)
330 {
331 G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
332
333 modvalue = std::fabs(value);
334
335 if ( modvalue < 8.0 )
336 {
337 value2 = value*value;
338
339 fact1 = value*(72362614232.0 + value2*(-7895059235.0
340 + value2*( 242396853.1
341 + value2*(-2972611.439
342 + value2*( 15704.48260
343 + value2*(-30.16036606 ) ) ) ) ) );
344
345 fact2 = 144725228442.0 + value2*(2300535178.0
346 + value2*(18583304.74
347 + value2*(99447.43394
348 + value2*(376.9991397
349 + value2*1.0 ) ) ) );
350 bessel = fact1/fact2;
351 }
352 else
353 {
354 arg = 8.0/modvalue;
355
356 value2 = arg*arg;
357
358 shift = modvalue - 2.356194491;
359
360 fact1 = 1.0 + value2*( 0.183105e-2
361 + value2*(-0.3516396496e-4
362 + value2*(0.2457520174e-5
363 + value2*(-0.240337019e-6 ) ) ) );
364
365 fact2 = 0.04687499995 + value2*(-0.2002690873e-3
366 + value2*( 0.8449199096e-5
367 + value2*(-0.88228987e-6
368 + value2*0.105787412e-6 ) ) );
369
370 bessel = std::sqrt( 0.636619772/modvalue)*(std::cos(shift)*fact1 - arg*std::sin(shift)*fact2);
371
372 if (value < 0.0) bessel = -bessel;
373 }
374 return bessel;
375 }
376
377 ////////////////////////////////////////////////////////////////////
378 //
379 // damp factor in diffraction x/sh(x), x was already *pi
380
381 inline G4double G4DiffuseElastic::DampFactor(G4double x)
382 {
383 G4double df;
384 G4double f2 = 2., f3 = 6., f4 = 24.; // first factorials
385
386 // x *= pi;
387
388 if( std::fabs(x) < 0.01 )
389 {
390 df = 1./(1. + x/f2 + x*x/f3 + x*x*x/f4);
391 }
392 else
393 {
394 df = x/std::sinh(x);
395 }
396 return df;
397 }
398
399
400 ////////////////////////////////////////////////////////////////////
401 //
402 // return J1(x)/x with special case for small x
403
404 inline G4double G4DiffuseElastic::BesselOneByArg(G4double x)
405 {
406 G4double x2, result;
407
408 if( std::fabs(x) < 0.01 )
409 {
410 x *= 0.5;
411 x2 = x*x;
412 result = 2. - x2 + x2*x2/6.;
413 }
414 else
415 {
416 result = BesselJone(x)/x;
417 }
418 return result;
419 }
420
421 ////////////////////////////////////////////////////////////////////
422 //
423 // return particle beta
424
425 inline G4double G4DiffuseElastic::CalculateParticleBeta( const G4ParticleDefinition* particle,
426 G4double momentum )
427 {
428 G4double mass = particle->GetPDGMass();
429 G4double a = momentum/mass;
430 fBeta = a/std::sqrt(1+a*a);
431
432 return fBeta;
433 }
434
435 ////////////////////////////////////////////////////////////////////
436 //
437 // return Zommerfeld parameter for Coulomb scattering
438
439 inline G4double G4DiffuseElastic::CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 )
440 {
441 fZommerfeld = CLHEP::fine_structure_const*Z1*Z2/beta;
442
443 return fZommerfeld;
444 }
445
446 ////////////////////////////////////////////////////////////////////
447 //
448 // return Wentzel correction for Coulomb scattering
449
450 inline G4double G4DiffuseElastic::CalculateAm( G4double momentum, G4double n, G4double Z)
451 {
452 G4double k = momentum/CLHEP::hbarc;
453 G4double ch = 1.13 + 3.76*n*n;
454 G4double zn = 1.77*k*(1.0/G4Pow::GetInstance()->A13(Z))*CLHEP::Bohr_radius;
455 G4double zn2 = zn*zn;
456 fAm = ch/zn2;
457
458 return fAm;
459 }
460
461 ////////////////////////////////////////////////////////////////////
462 //
463 // calculate nuclear radius for different atomic weights using different approximations
464
465 inline G4double G4DiffuseElastic::CalculateNuclearRad( G4double A)
466 {
467 G4double R, r0, a11, a12, a13, a2, a3;
468
469 a11 = 1.26; // 1.08, 1.16
470 a12 = 1.; // 1.08, 1.16
471 a13 = 1.12; // 1.08, 1.16
472 a2 = 1.1;
473 a3 = 1.;
474
475 // Special rms radii for light nucleii
476
477 if (A < 50.)
478 {
479 if (std::abs(A-1.) < 0.5) return 0.89*CLHEP::fermi; // p
480 else if(std::abs(A-2.) < 0.5) return 2.13*CLHEP::fermi; // d
481 else if( // std::abs(Z-1.) < 0.5 &&
482 std::abs(A-3.) < 0.5) return 1.80*CLHEP::fermi; // t
483
484 // else if(std::abs(Z-2.) < 0.5 && std::abs(A-3.) < 0.5) return 1.96CLHEP::fermi; // He3
485 else if( // std::abs(Z-2.) < 0.5 &&
486 std::abs(A-4.) < 0.5) return 1.68*CLHEP::fermi; // He4
487
488 else if( // std::abs(Z-3.) < 0.5
489 std::abs(A-7.) < 0.5 ) return 2.40*CLHEP::fermi; // Li7
490 else if( // std::abs(Z-4.) < 0.5
491 std::abs(A-9.) < 0.5) return 2.51*CLHEP::fermi; // Be9
492
493 else if( 10. < A && A <= 16. ) r0 = a11*( 1 - (1.0/G4Pow::GetInstance()->A23(A)) )*CLHEP::fermi; // 1.08CLHEP::fermi;
494 else if( 15. < A && A <= 20. ) r0 = a12*( 1 - (1.0/G4Pow::GetInstance()->A23(A)) )*CLHEP::fermi;
495 else if( 20. < A && A <= 30. ) r0 = a13*( 1 - (1.0/G4Pow::GetInstance()->A23(A)) )*CLHEP::fermi;
496 else r0 = a2*CLHEP::fermi;
497
498 R = r0*G4Pow::GetInstance()->A13(A);
499 }
500 else
501 {
502 r0 = a3*CLHEP::fermi;
503
504 R = r0*G4Pow::GetInstance()->powA(A, 0.27);
505 }
506 fNuclearRadius = R;
507 return R;
508 /*
509 G4double r0;
510 if( A < 50. )
511 {
512 if( A > 10. ) r0 = 1.16*( 1 - (1.0/G4Pow::GetInstance()->A23(A)) )*CLHEP::fermi; // 1.08CLHEP::fermi;
513 else r0 = 1.1*CLHEP::fermi;
514 fNuclearRadius = r0*G4Pow::GetInstance()->A13(A);
515 }
516 else
517 {
518 r0 = 1.7*CLHEP::fermi; // 1.7*CLHEP::fermi;
519 fNuclearRadius = r0*G4Pow::GetInstance()->powA(A, 0.27); // 0.27);
520 }
521 return fNuclearRadius;
522 */
523 }
524
525 ////////////////////////////////////////////////////////////////////
526 //
527 // return Coulomb scattering differential xsc with Wentzel correction
528
529 inline G4double G4DiffuseElastic::GetCoulombElasticXsc( const G4ParticleDefinition* particle,
530 G4double theta,
531 G4double momentum,
532 G4double Z )
533 {
534 G4double sinHalfTheta = std::sin(0.5*theta);
535 G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
536 G4double beta = CalculateParticleBeta( particle, momentum);
537 G4double z = particle->GetPDGCharge();
538 G4double n = CalculateZommerfeld( beta, z, Z );
539 G4double am = CalculateAm( momentum, n, Z);
540 G4double k = momentum/CLHEP::hbarc;
541 G4double ch = 0.5*n/k;
542 G4double ch2 = ch*ch;
543 G4double xsc = ch2/(sinHalfTheta2+am)/(sinHalfTheta2+am);
544
545 return xsc;
546 }
547
548
549 ////////////////////////////////////////////////////////////////////
550 //
551 // return Coulomb scattering total xsc with Wentzel correction
552
553 inline G4double G4DiffuseElastic::GetCoulombTotalXsc( const G4ParticleDefinition* particle,
554 G4double momentum, G4double Z )
555 {
556 G4double beta = CalculateParticleBeta( particle, momentum);
557 G4cout<<"beta = "<<beta<<G4endl;
558 G4double z = particle->GetPDGCharge();
559 G4double n = CalculateZommerfeld( beta, z, Z );
560 G4cout<<"fZomerfeld = "<<n<<G4endl;
561 G4double am = CalculateAm( momentum, n, Z);
562 G4cout<<"cof Am = "<<am<<G4endl;
563 G4double k = momentum/CLHEP::hbarc;
564 G4cout<<"k = "<<k*CLHEP::fermi<<" 1/fermi"<<G4endl;
565 G4cout<<"k*Bohr_radius = "<<k*CLHEP::Bohr_radius<<G4endl;
566 G4double ch = n/k;
567 G4double ch2 = ch*ch;
568 G4double xsc = ch2*CLHEP::pi/(am +am*am);
569
570 return xsc;
571 }
572
573 ////////////////////////////////////////////////////////////////////
574 //
575 // return Coulomb scattering xsc with Wentzel correction integrated between
576 // theta1 and < theta2
577
578 inline G4double G4DiffuseElastic::GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
579 G4double momentum, G4double Z,
580 G4double theta1, G4double theta2 )
581 {
582 G4double c1 = std::cos(theta1);
583 G4cout<<"c1 = "<<c1<<G4endl;
584 G4double c2 = std::cos(theta2);
585 G4cout<<"c2 = "<<c2<<G4endl;
586 G4double beta = CalculateParticleBeta( particle, momentum);
587 // G4cout<<"beta = "<<beta<<G4endl;
588 G4double z = particle->GetPDGCharge();
589 G4double n = CalculateZommerfeld( beta, z, Z );
590 // G4cout<<"fZomerfeld = "<<n<<G4endl;
591 G4double am = CalculateAm( momentum, n, Z);
592 // G4cout<<"cof Am = "<<am<<G4endl;
593 G4double k = momentum/CLHEP::hbarc;
594 // G4cout<<"k = "<<k*CLHEP::fermi<<" 1/fermi"<<G4endl;
595 // G4cout<<"k*Bohr_radius = "<<k*CLHEP::Bohr_radius<<G4endl;
596 G4double ch = n/k;
597 G4double ch2 = ch*ch;
598 am *= 2.;
599 G4double xsc = ch2*CLHEP::twopi*(c1-c2);
600 xsc /= (1 - c1 + am)*(1 - c2 + am);
601
602 return xsc;
603 }
604
605 #endif
606