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19// * technical work of the GEANT4 collaboration. *
20// * By using, copying, modifying or distributing the software (or *
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25//
26//
27// $Id: G4NuclNuclDiffuseElastic.hh,v 1.8 2009/04/10 13:22:25 grichine Exp $
28// GEANT4 tag $Name: geant4-09-03 $
29//
30//
31// G4 Model: optical elastic scattering with 4-momentum balance
32//
33// Class Description
34// Final state production model for nucleus-nucleus elastic scattering;
35// Coulomb amplitude is not considered as correction
36// (as in G4DiffuseElastic)
37// Class Description - End
38//
39//
40// 17.03.09 V. Grichine implementation for Coulomb elastic scattering
41
42
43#ifndef G4NuclNuclDiffuseElastic_h
44#define G4NuclNuclDiffuseElastic_h 1
45
46#include "globals.hh"
47#include <complex>
48#include "G4Integrator.hh"
49
50#include "G4HadronicInteraction.hh"
51#include "G4HadProjectile.hh"
52#include "G4Nucleus.hh"
53
54using namespace std;
55
56class G4ParticleDefinition;
57class G4PhysicsTable;
58class G4PhysicsLogVector;
59
60class G4NuclNuclDiffuseElastic : public G4HadronicInteraction
61{
62public:
63
64 G4NuclNuclDiffuseElastic();
65
66 G4NuclNuclDiffuseElastic(const G4ParticleDefinition* aParticle);
67
68
69
70
71
72 virtual ~G4NuclNuclDiffuseElastic();
73
74 void Initialise();
75
76 void InitialiseOnFly(G4double Z, G4double A);
77
78 void BuildAngleTable();
79
80
81 G4HadFinalState * ApplyYourself(const G4HadProjectile & aTrack,
82 G4Nucleus & targetNucleus);
83
84
85 void SetPlabLowLimit(G4double value);
86
87 void SetHEModelLowLimit(G4double value);
88
89 void SetQModelLowLimit(G4double value);
90
91 void SetLowestEnergyLimit(G4double value);
92
93 void SetRecoilKinEnergyLimit(G4double value);
94
95 G4double SampleT(const G4ParticleDefinition* aParticle,
96 G4double p, G4double A);
97
98 G4double SampleTableT(const G4ParticleDefinition* aParticle,
99 G4double p, G4double Z, G4double A);
100
101 G4double SampleThetaCMS(const G4ParticleDefinition* aParticle, G4double p, G4double A);
102
103 G4double SampleTableThetaCMS(const G4ParticleDefinition* aParticle, G4double p,
104 G4double Z, G4double A);
105
106 G4double GetScatteringAngle(G4int iMomentum, G4int iAngle, G4double position);
107
108 G4double SampleThetaLab(const G4HadProjectile* aParticle,
109 G4double tmass, G4double A);
110
111 G4double GetDiffuseElasticXsc( const G4ParticleDefinition* particle,
112 G4double theta,
113 G4double momentum,
114 G4double A );
115
116 G4double GetInvElasticXsc( const G4ParticleDefinition* particle,
117 G4double theta,
118 G4double momentum,
119 G4double A, G4double Z );
120
121 G4double GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle,
122 G4double theta,
123 G4double momentum,
124 G4double A, G4double Z );
125
126 G4double GetInvElasticSumXsc( const G4ParticleDefinition* particle,
127 G4double tMand,
128 G4double momentum,
129 G4double A, G4double Z );
130
131 G4double IntegralElasticProb( const G4ParticleDefinition* particle,
132 G4double theta,
133 G4double momentum,
134 G4double A );
135
136
137 G4double GetCoulombElasticXsc( const G4ParticleDefinition* particle,
138 G4double theta,
139 G4double momentum,
140 G4double Z );
141
142 G4double GetInvCoulombElasticXsc( const G4ParticleDefinition* particle,
143 G4double tMand,
144 G4double momentum,
145 G4double A, G4double Z );
146
147 G4double GetCoulombTotalXsc( const G4ParticleDefinition* particle,
148 G4double momentum, G4double Z );
149
150 G4double GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
151 G4double momentum, G4double Z,
152 G4double theta1, G4double theta2 );
153
154
155 G4double CalculateParticleBeta( const G4ParticleDefinition* particle,
156 G4double momentum );
157
158 G4double CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 );
159
160 G4double CalculateAm( G4double momentum, G4double n, G4double Z);
161
162 G4double CalculateNuclearRad( G4double A);
163
164 G4double ThetaCMStoThetaLab(const G4DynamicParticle* aParticle,
165 G4double tmass, G4double thetaCMS);
166
167 G4double ThetaLabToThetaCMS(const G4DynamicParticle* aParticle,
168 G4double tmass, G4double thetaLab);
169
170 void TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom,
171 G4double Z, G4double A);
172
173
174
175 G4double BesselJzero(G4double z);
176 G4double BesselJone(G4double z);
177 G4double DampFactor(G4double z);
178 G4double BesselOneByArg(G4double z);
179
180 G4double GetDiffElasticProb(G4double theta);
181 G4double GetDiffElasticSumProb(G4double theta);
182 G4double GetDiffElasticSumProbA(G4double alpha);
183 G4double GetIntegrandFunction(G4double theta);
184
185 G4double GetNuclearRadius(){return fNuclearRadius;};
186
187
188 // Technical math functions for strong Coulomb contribution
189
190 G4complex GammaLogarithm(G4complex xx);
191
192 G4double GetErf(G4double x);
193
194 G4complex GetErfcComp(G4complex z, G4int nMax);
195 G4complex GetErfcSer(G4complex z, G4int nMax);
196 G4complex GetErfcInt(G4complex z); // , G4int nMax);
197
198 G4complex GetErfComp(G4complex z, G4int nMax); // AandS algorithm != Ser, Int
199 G4complex GetErfSer(G4complex z, G4int nMax);
200
201 G4double GetExpCos(G4double x);
202 G4double GetExpSin(G4double x);
203 G4complex GetErfInt(G4complex z); // , G4int nMax);
204
205
206 G4complex TestErfcComp(G4complex z, G4int nMax);
207 G4complex TestErfcSer(G4complex z, G4int nMax);
208 G4complex TestErfcInt(G4complex z); // , G4int nMax);
209
210 G4complex CoulombAmplitude(G4double theta);
211 void CalculateCoulombPhaseZero();
212 void CalculateRutherfordAnglePar();
213
214 G4double ProfileNear(G4double theta);
215 G4double ProfileFar(G4double theta);
216
217 G4complex PhaseNear(G4double theta);
218 G4complex PhaseFar(G4double theta);
219
220 G4complex GammaLess(G4double theta);
221 G4complex GammaMore(G4double theta);
222
223 G4complex AmplitudeNear(G4double theta);
224 G4complex AmplitudeFar(G4double theta);
225 G4complex Amplitude(G4double theta);
226 G4double AmplitudeMod2(G4double theta);
227 void InitParameters(const G4ParticleDefinition* theParticle,
228 G4double partMom, G4double Z, G4double A);
229
230 G4double GetProfileLambda(){return fProfileLambda;};
231
232 void SetProfileLambda(G4double pl) {fProfileLambda = pl;};
233 void SetProfileDelta(G4double pd) {fProfileDelta = pd;};
234 void SetProfileAlpha(G4double pa){fProfileAlpha = pa;};
235
236private:
237
238
239 G4ParticleDefinition* theProton;
240 G4ParticleDefinition* theNeutron;
241 G4ParticleDefinition* theDeuteron;
242 G4ParticleDefinition* theAlpha;
243
244 const G4ParticleDefinition* thePionPlus;
245 const G4ParticleDefinition* thePionMinus;
246
247 G4double lowEnergyRecoilLimit;
248 G4double lowEnergyLimitHE;
249 G4double lowEnergyLimitQ;
250 G4double lowestEnergyLimit;
251 G4double plabLowLimit;
252
253 G4int fEnergyBin;
254 G4int fAngleBin;
255
256 G4PhysicsLogVector* fEnergyVector;
257 G4PhysicsTable* fAngleTable;
258 std::vector<G4PhysicsTable*> fAngleBank;
259
260 std::vector<G4double> fElementNumberVector;
261 std::vector<G4String> fElementNameVector;
262
263 const G4ParticleDefinition* fParticle;
264 G4double fWaveVector;
265 G4double fAtomicWeight;
266 G4double fAtomicNumber;
267
268 G4double fNuclearRadius1;
269 G4double fNuclearRadius2;
270 G4double fNuclearRadius;
271
272 G4double fBeta;
273 G4double fZommerfeld;
274 G4double fAm;
275 G4bool fAddCoulomb;
276
277 G4double fCoulombPhase0;
278 G4double fHalfRutThetaTg;
279 G4double fRutherfordTheta;
280
281 G4double fProfileLambda;
282 G4double fProfileDelta;
283 G4double fProfileAlpha;
284
285 G4double fReZ;
286
287};
288
289
290inline void G4NuclNuclDiffuseElastic::SetRecoilKinEnergyLimit(G4double value)
291{
292 lowEnergyRecoilLimit = value;
293}
294
295inline void G4NuclNuclDiffuseElastic::SetPlabLowLimit(G4double value)
296{
297 plabLowLimit = value;
298}
299
300inline void G4NuclNuclDiffuseElastic::SetHEModelLowLimit(G4double value)
301{
302 lowEnergyLimitHE = value;
303}
304
305inline void G4NuclNuclDiffuseElastic::SetQModelLowLimit(G4double value)
306{
307 lowEnergyLimitQ = value;
308}
309
310inline void G4NuclNuclDiffuseElastic::SetLowestEnergyLimit(G4double value)
311{
312 lowestEnergyLimit = value;
313}
314
315
316/////////////////////////////////////////////////////////////
317//
318// Bessel J0 function based on rational approximation from
319// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
320
321inline G4double G4NuclNuclDiffuseElastic::BesselJzero(G4double value)
322{
323 G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
324
325 modvalue = fabs(value);
326
327 if ( value < 8.0 && value > -8.0 )
328 {
329 value2 = value*value;
330
331 fact1 = 57568490574.0 + value2*(-13362590354.0
332 + value2*( 651619640.7
333 + value2*(-11214424.18
334 + value2*( 77392.33017
335 + value2*(-184.9052456 ) ) ) ) );
336
337 fact2 = 57568490411.0 + value2*( 1029532985.0
338 + value2*( 9494680.718
339 + value2*(59272.64853
340 + value2*(267.8532712
341 + value2*1.0 ) ) ) );
342
343 bessel = fact1/fact2;
344 }
345 else
346 {
347 arg = 8.0/modvalue;
348
349 value2 = arg*arg;
350
351 shift = modvalue-0.785398164;
352
353 fact1 = 1.0 + value2*(-0.1098628627e-2
354 + value2*(0.2734510407e-4
355 + value2*(-0.2073370639e-5
356 + value2*0.2093887211e-6 ) ) );
357
358 fact2 = -0.1562499995e-1 + value2*(0.1430488765e-3
359 + value2*(-0.6911147651e-5
360 + value2*(0.7621095161e-6
361 - value2*0.934945152e-7 ) ) );
362
363 bessel = sqrt(0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2 );
364 }
365 return bessel;
366}
367
368/////////////////////////////////////////////////////////////
369//
370// Bessel J1 function based on rational approximation from
371// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
372
373inline G4double G4NuclNuclDiffuseElastic::BesselJone(G4double value)
374{
375 G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
376
377 modvalue = fabs(value);
378
379 if ( modvalue < 8.0 )
380 {
381 value2 = value*value;
382
383 fact1 = value*(72362614232.0 + value2*(-7895059235.0
384 + value2*( 242396853.1
385 + value2*(-2972611.439
386 + value2*( 15704.48260
387 + value2*(-30.16036606 ) ) ) ) ) );
388
389 fact2 = 144725228442.0 + value2*(2300535178.0
390 + value2*(18583304.74
391 + value2*(99447.43394
392 + value2*(376.9991397
393 + value2*1.0 ) ) ) );
394 bessel = fact1/fact2;
395 }
396 else
397 {
398 arg = 8.0/modvalue;
399
400 value2 = arg*arg;
401
402 shift = modvalue - 2.356194491;
403
404 fact1 = 1.0 + value2*( 0.183105e-2
405 + value2*(-0.3516396496e-4
406 + value2*(0.2457520174e-5
407 + value2*(-0.240337019e-6 ) ) ) );
408
409 fact2 = 0.04687499995 + value2*(-0.2002690873e-3
410 + value2*( 0.8449199096e-5
411 + value2*(-0.88228987e-6
412 + value2*0.105787412e-6 ) ) );
413
414 bessel = sqrt( 0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2);
415
416 if (value < 0.0) bessel = -bessel;
417 }
418 return bessel;
419}
420
421////////////////////////////////////////////////////////////////////
422//
423// damp factor in diffraction x/sh(x), x was already *pi
424
425inline G4double G4NuclNuclDiffuseElastic::DampFactor(G4double x)
426{
427 G4double df;
428 G4double f2 = 2., f3 = 6., f4 = 24.; // first factorials
429
430 // x *= pi;
431
432 if( std::fabs(x) < 0.01 )
433 {
434 df = 1./(1. + x/f2 + x*x/f3 + x*x*x/f4);
435 }
436 else
437 {
438 df = x/std::sinh(x);
439 }
440 return df;
441}
442
443
444////////////////////////////////////////////////////////////////////
445//
446// return J1(x)/x with special case for small x
447
448inline G4double G4NuclNuclDiffuseElastic::BesselOneByArg(G4double x)
449{
450 G4double x2, result;
451
452 if( std::fabs(x) < 0.01 )
453 {
454 x *= 0.5;
455 x2 = x*x;
456 result = 2. - x2 + x2*x2/6.;
457 }
458 else
459 {
460 result = BesselJone(x)/x;
461 }
462 return result;
463}
464
465////////////////////////////////////////////////////////////////////
466//
467// return particle beta
468
469inline G4double G4NuclNuclDiffuseElastic::CalculateParticleBeta( const G4ParticleDefinition* particle,
470 G4double momentum )
471{
472 G4double mass = particle->GetPDGMass();
473 G4double a = momentum/mass;
474 fBeta = a/std::sqrt(1+a*a);
475
476 return fBeta;
477}
478
479////////////////////////////////////////////////////////////////////
480//
481// return Zommerfeld parameter for Coulomb scattering
482
483inline G4double G4NuclNuclDiffuseElastic::CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 )
484{
485 fZommerfeld = fine_structure_const*Z1*Z2/beta;
486
487 return fZommerfeld;
488}
489
490////////////////////////////////////////////////////////////////////
491//
492// return Wentzel correction for Coulomb scattering
493
494inline G4double G4NuclNuclDiffuseElastic::CalculateAm( G4double momentum, G4double n, G4double Z)
495{
496 G4double k = momentum/hbarc;
497 G4double ch = 1.13 + 3.76*n*n;
498 G4double zn = 1.77*k*std::pow(Z,-1./3.)*Bohr_radius;
499 G4double zn2 = zn*zn;
500 fAm = ch/zn2;
501
502 return fAm;
503}
504
505////////////////////////////////////////////////////////////////////
506//
507// calculate nuclear radius for different atomic weights using different approximations
508
509inline G4double G4NuclNuclDiffuseElastic::CalculateNuclearRad( G4double A)
510{
511 G4double r0, radius;
512
513 if( A < 50. )
514 {
515 if( A > 10. ) r0 = 1.16*( 1 - std::pow(A, -2./3.) )*fermi; // 1.08*fermi;
516 else r0 = 1.1*fermi;
517
518 radius = r0*std::pow(A, 1./3.);
519 }
520 else
521 {
522 r0 = 1.7*fermi; // 1.7*fermi;
523
524 radius = r0*std::pow(A, 0.27); // 0.27);
525 }
526 return radius;
527}
528
529////////////////////////////////////////////////////////////////////
530//
531// return Coulomb scattering differential xsc with Wentzel correction
532
533inline G4double G4NuclNuclDiffuseElastic::GetCoulombElasticXsc( const G4ParticleDefinition* particle,
534 G4double theta,
535 G4double momentum,
536 G4double Z )
537{
538 G4double sinHalfTheta = std::sin(0.5*theta);
539 G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
540 G4double beta = CalculateParticleBeta( particle, momentum);
541 G4double z = particle->GetPDGCharge();
542 G4double n = CalculateZommerfeld( beta, z, Z );
543 G4double am = CalculateAm( momentum, n, Z);
544 G4double k = momentum/hbarc;
545 G4double ch = 0.5*n/k;
546 G4double ch2 = ch*ch;
547 G4double xsc = ch2/(sinHalfTheta2+am)/(sinHalfTheta2+am);
548
549 return xsc;
550}
551
552
553////////////////////////////////////////////////////////////////////
554//
555// return Coulomb scattering total xsc with Wentzel correction
556
557inline G4double G4NuclNuclDiffuseElastic::GetCoulombTotalXsc( const G4ParticleDefinition* particle,
558 G4double momentum, G4double Z )
559{
560 G4double beta = CalculateParticleBeta( particle, momentum);
561 G4cout<<"beta = "<<beta<<G4endl;
562 G4double z = particle->GetPDGCharge();
563 G4double n = CalculateZommerfeld( beta, z, Z );
564 G4cout<<"fZomerfeld = "<<n<<G4endl;
565 G4double am = CalculateAm( momentum, n, Z);
566 G4cout<<"cof Am = "<<am<<G4endl;
567 G4double k = momentum/hbarc;
568 G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl;
569 G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl;
570 G4double ch = n/k;
571 G4double ch2 = ch*ch;
572 G4double xsc = ch2*pi/(am +am*am);
573
574 return xsc;
575}
576
577////////////////////////////////////////////////////////////////////
578//
579// return Coulomb scattering xsc with Wentzel correction integrated between
580// theta1 and < theta2
581
582inline G4double G4NuclNuclDiffuseElastic::GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
583 G4double momentum, G4double Z,
584 G4double theta1, G4double theta2 )
585{
586 G4double c1 = std::cos(theta1);
587 G4cout<<"c1 = "<<c1<<G4endl;
588 G4double c2 = std::cos(theta2);
589 G4cout<<"c2 = "<<c2<<G4endl;
590 G4double beta = CalculateParticleBeta( particle, momentum);
591 // G4cout<<"beta = "<<beta<<G4endl;
592 G4double z = particle->GetPDGCharge();
593 G4double n = CalculateZommerfeld( beta, z, Z );
594 // G4cout<<"fZomerfeld = "<<n<<G4endl;
595 G4double am = CalculateAm( momentum, n, Z);
596 // G4cout<<"cof Am = "<<am<<G4endl;
597 G4double k = momentum/hbarc;
598 // G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl;
599 // G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl;
600 G4double ch = n/k;
601 G4double ch2 = ch*ch;
602 am *= 2.;
603 G4double xsc = ch2*twopi*(c1-c2);
604 xsc /= (1 - c1 + am)*(1 - c2 + am);
605
606 return xsc;
607}
608
609///////////////////////////////////////////////////////////////////
610//
611// For the calculation of arg Gamma(z) one needs complex extension
612// of ln(Gamma(z))
613
614inline G4complex G4NuclNuclDiffuseElastic::GammaLogarithm(G4complex zz)
615{
616 static G4double cof[6] = { 76.18009172947146, -86.50532032941677,
617 24.01409824083091, -1.231739572450155,
618 0.1208650973866179e-2, -0.5395239384953e-5 } ;
619 register G4int j;
620 G4complex z = zz - 1.0;
621 G4complex tmp = z + 5.5;
622 tmp -= (z + 0.5) * std::log(tmp);
623 G4complex ser = G4complex(1.000000000190015,0.);
624
625 for ( j = 0; j <= 5; j++ )
626 {
627 z += 1.0;
628 ser += cof[j]/z;
629 }
630 return -tmp + std::log(2.5066282746310005*ser);
631}
632
633/////////////////////////////////////////////////////////////////
634//
635//
636
637inline G4double G4NuclNuclDiffuseElastic::GetErf(G4double x)
638{
639 G4double t, z, tmp, result;
640
641 z = std::fabs(x);
642 t = 1.0/(1.0+0.5*z);
643
644 tmp = t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+
645 t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+
646 t*(-0.82215223+t*0.17087277)))))))));
647
648 if( x >= 0.) result = 1. - tmp;
649 else result = 1. + tmp;
650
651 return result;
652}
653
654/////////////////////////////////////////////////////////////////
655//
656//
657
658inline G4complex G4NuclNuclDiffuseElastic::GetErfcComp(G4complex z, G4int nMax)
659{
660 G4complex erfcz = 1. - GetErfComp( z, nMax);
661 return erfcz;
662}
663
664/////////////////////////////////////////////////////////////////
665//
666//
667
668inline G4complex G4NuclNuclDiffuseElastic::GetErfcSer(G4complex z, G4int nMax)
669{
670 G4complex erfcz = 1. - GetErfSer( z, nMax);
671 return erfcz;
672}
673
674/////////////////////////////////////////////////////////////////
675//
676//
677
678inline G4complex G4NuclNuclDiffuseElastic::GetErfcInt(G4complex z) // , G4int nMax)
679{
680 G4complex erfcz = 1. - GetErfInt( z); // , nMax);
681 return erfcz;
682}
683
684/////////////////////////////////////////////////////////////////
685//
686//
687
688inline G4complex G4NuclNuclDiffuseElastic::TestErfcComp(G4complex z, G4int nMax)
689{
690 G4complex miz = G4complex( z.imag(), -z.real() );
691 G4complex erfcz = 1. - GetErfComp( miz, nMax);
692 G4complex w = std::exp(-z*z)*erfcz;
693 return w;
694}
695
696/////////////////////////////////////////////////////////////////
697//
698//
699
700inline G4complex G4NuclNuclDiffuseElastic::TestErfcSer(G4complex z, G4int nMax)
701{
702 G4complex miz = G4complex( z.imag(), -z.real() );
703 G4complex erfcz = 1. - GetErfSer( miz, nMax);
704 G4complex w = std::exp(-z*z)*erfcz;
705 return w;
706}
707
708/////////////////////////////////////////////////////////////////
709//
710//
711
712inline G4complex G4NuclNuclDiffuseElastic::TestErfcInt(G4complex z) // , G4int nMax)
713{
714 G4complex miz = G4complex( z.imag(), -z.real() );
715 G4complex erfcz = 1. - GetErfInt( miz); // , nMax);
716 G4complex w = std::exp(-z*z)*erfcz;
717 return w;
718}
719
720/////////////////////////////////////////////////////////////////
721//
722//
723
724inline G4complex G4NuclNuclDiffuseElastic::GetErfComp(G4complex z, G4int nMax)
725{
726 G4int n;
727 G4double n2, cofn, shny, chny, fn, gn;
728
729 G4double x = z.real();
730 G4double y = z.imag();
731
732 G4double outRe = 0., outIm = 0.;
733
734 G4double twox = 2.*x;
735 G4double twoxy = twox*y;
736 G4double twox2 = twox*twox;
737
738 G4double cof1 = std::exp(-x*x)/pi;
739
740 G4double cos2xy = std::cos(twoxy);
741 G4double sin2xy = std::sin(twoxy);
742
743 G4double twoxcos2xy = twox*cos2xy;
744 G4double twoxsin2xy = twox*sin2xy;
745
746 for( n = 1; n <= nMax; n++)
747 {
748 n2 = n*n;
749
750 cofn = std::exp(-0.5*n2)/(n2+twox2); // /(n2+0.5*twox2);
751
752 chny = std::cosh(n*y);
753 shny = std::sinh(n*y);
754
755 fn = twox - twoxcos2xy*chny + n*sin2xy*shny;
756 gn = twoxsin2xy*chny + n*cos2xy*shny;
757
758 fn *= cofn;
759 gn *= cofn;
760
761 outRe += fn;
762 outIm += gn;
763 }
764 outRe *= 2*cof1;
765 outIm *= 2*cof1;
766
767 if(std::abs(x) < 0.0001)
768 {
769 outRe += GetErf(x);
770 outIm += cof1*y;
771 }
772 else
773 {
774 outRe += GetErf(x) + cof1*(1-cos2xy)/twox;
775 outIm += cof1*sin2xy/twox;
776 }
777 return G4complex(outRe, outIm);
778}
779
780/////////////////////////////////////////////////////////////////
781//
782//
783
784inline G4complex G4NuclNuclDiffuseElastic::GetErfSer(G4complex z, G4int nMax)
785{
786 G4int n;
787 G4double a =1., b = 1., tmp;
788 G4complex sum = z, d = z;
789
790 for( n = 1; n <= nMax; n++)
791 {
792 a *= 2.;
793 b *= 2.*n +1.;
794 d *= z*z;
795
796 tmp = a/b;
797
798 sum += tmp*d;
799 }
800 sum *= 2.*std::exp(-z*z)/std::sqrt(pi);
801
802 return sum;
803}
804
805/////////////////////////////////////////////////////////////////////
806
807inline G4double G4NuclNuclDiffuseElastic::GetExpCos(G4double x)
808{
809 G4double result;
810
811 result = std::exp(x*x-fReZ*fReZ);
812 result *= std::cos(2.*x*fReZ);
813 return result;
814}
815
816/////////////////////////////////////////////////////////////////////
817
818inline G4double G4NuclNuclDiffuseElastic::GetExpSin(G4double x)
819{
820 G4double result;
821
822 result = std::exp(x*x-fReZ*fReZ);
823 result *= std::sin(2.*x*fReZ);
824 return result;
825}
826
827
828
829/////////////////////////////////////////////////////////////////
830//
831//
832
833inline G4complex G4NuclNuclDiffuseElastic::GetErfInt(G4complex z) // , G4int nMax)
834{
835 G4double outRe, outIm;
836
837 G4double x = z.real();
838 G4double y = z.imag();
839 fReZ = x;
840
841 G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
842
843 outRe = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpSin, 0., y );
844 outIm = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpCos, 0., y );
845
846 outRe *= 2./sqrt(pi);
847 outIm *= 2./sqrt(pi);
848
849 outRe += GetErf(x);
850
851 return G4complex(outRe, outIm);
852}
853
854
855/////////////////////////////////////////////////////////////////
856//
857//
858
859inline G4complex G4NuclNuclDiffuseElastic::CoulombAmplitude(G4double theta)
860{
861 G4complex ca;
862
863 G4double sinHalfTheta = std::sin(0.5*theta);
864 G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
865 sinHalfTheta2 += fAm;
866 G4double order = 2.*fCoulombPhase0 - fZommerfeld*std::log(sinHalfTheta2);
867 G4complex z = G4complex(0., order);
868 ca = std::exp(z);
869 ca *= -fZommerfeld/(2.*fWaveVector*sinHalfTheta2);
870
871 return ca;
872}
873
874/////////////////////////////////////////////////////////////////
875//
876//
877
878
879inline void G4NuclNuclDiffuseElastic::CalculateCoulombPhaseZero()
880{
881 G4complex z = G4complex(1,fZommerfeld);
882 G4complex gammalog = GammaLogarithm(z);
883 fCoulombPhase0 = gammalog.imag();
884}
885
886
887/////////////////////////////////////////////////////////////////
888//
889//
890
891
892inline void G4NuclNuclDiffuseElastic::CalculateRutherfordAnglePar()
893{
894 fHalfRutThetaTg = fZommerfeld/(fWaveVector*fNuclearRadius);
895 fRutherfordTheta = 2.*std::atan(fHalfRutThetaTg);
896 G4cout<<"fRutherfordTheta = "<<fRutherfordTheta/degree<<" degree"<<G4endl;
897
898}
899
900/////////////////////////////////////////////////////////////////
901//
902//
903
904inline G4double G4NuclNuclDiffuseElastic::ProfileNear(G4double theta)
905{
906 G4double dTheta = fRutherfordTheta - theta;
907 G4double result = 0., argument = 0.;
908
909 if(std::abs(dTheta) < 0.001) result = fProfileAlpha*fProfileDelta;
910 else
911 {
912 argument = fProfileDelta*dTheta;
913 result = pi*argument*std::exp(fProfileAlpha*argument);
914 result /= std::sinh(pi*argument);
915 result -= 1.;
916 result /= dTheta;
917 }
918 return result;
919}
920
921/////////////////////////////////////////////////////////////////
922//
923//
924
925inline G4double G4NuclNuclDiffuseElastic::ProfileFar(G4double theta)
926{
927 G4double dTheta = fRutherfordTheta + theta;
928 G4double argument = fProfileDelta*dTheta;
929
930 G4double result = pi*argument*std::exp(fProfileAlpha*argument);
931 result /= std::sinh(pi*argument);
932 result /= dTheta;
933
934 return result;
935}
936
937/////////////////////////////////////////////////////////////////
938//
939//
940
941inline G4complex G4NuclNuclDiffuseElastic::PhaseNear(G4double theta)
942{
943 G4double twosigma = 2.*fCoulombPhase0;
944 twosigma -= fZommerfeld*std::log(fHalfRutThetaTg/(1.+fHalfRutThetaTg*fHalfRutThetaTg));
945 twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi;
946 twosigma -= fProfileLambda*theta - 0.25*pi;
947
948 G4complex z = G4complex(0., twosigma);
949
950 return std::exp(z);
951}
952
953/////////////////////////////////////////////////////////////////
954//
955//
956
957inline G4complex G4NuclNuclDiffuseElastic::PhaseFar(G4double theta)
958{
959 G4double twosigma = 2.*fCoulombPhase0;
960 twosigma -= fZommerfeld*std::log(fHalfRutThetaTg/(1.+fHalfRutThetaTg*fHalfRutThetaTg));
961 twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi;
962 twosigma += fProfileLambda*theta - 0.25*pi;
963
964 G4complex z = G4complex(0., twosigma);
965
966 return std::exp(z);
967}
968
969/////////////////////////////////////////////////////////////////
970//
971//
972
973
974inline G4complex G4NuclNuclDiffuseElastic::GammaLess(G4double theta)
975{
976 G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg*fHalfRutThetaTg);
977 G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg*fHalfRutThetaTg);
978
979 G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
980 G4double kappa = u/std::sqrt(pi);
981 G4double dTheta = theta - fRutherfordTheta;
982 u *= dTheta;
983 G4double u2 = u*u;
984 G4double u2m2p3 = u2*2./3.;
985
986 G4complex im = G4complex(0.,1.);
987 G4complex order = G4complex(u,u);
988 order /= std::sqrt(2.);
989 G4complex gamma = pi*kappa*GetErfcInt(-order)*std::exp(im*(u*u+0.25*pi));
990 G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
991 G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
992 G4complex out = gamma*(1. - a1*dTheta) - a0;
993 return out;
994}
995
996/////////////////////////////////////////////////////////////////
997//
998//
999
1000inline G4complex G4NuclNuclDiffuseElastic::GammaMore(G4double theta)
1001{
1002 G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg*fHalfRutThetaTg);
1003 G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg*fHalfRutThetaTg);
1004
1005 G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
1006 G4double kappa = u/std::sqrt(pi);
1007 G4double dTheta = theta - fRutherfordTheta;
1008 u *= dTheta;
1009 G4double u2 = u*u;
1010 G4double u2m2p3 = u2*2./3.;
1011
1012 G4complex im = G4complex(0.,1.);
1013 G4complex order = G4complex(u,u);
1014 order /= std::sqrt(2.);
1015 G4complex gamma = pi*kappa*GetErfcInt(order)*std::exp(im*(u*u+0.25*pi));
1016 G4complex a0 = 0.5*(1. + 3.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
1017 G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
1018 G4complex out = -gamma*(1. - a1*dTheta) - a0;
1019 return out;
1020}
1021
1022/////////////////////////////////////////////////////////////////
1023//
1024//
1025
1026inline G4complex G4NuclNuclDiffuseElastic::AmplitudeNear(G4double theta)
1027{
1028 G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi);
1029 G4complex out = G4complex(kappa/fWaveVector,0.);
1030 out *= PhaseNear(theta);
1031
1032 if(theta <= fRutherfordTheta)
1033 {
1034 out *= GammaLess(theta) + ProfileNear(theta);
1035 out += CoulombAmplitude(theta);
1036 }
1037 else
1038 {
1039 out *= GammaMore(theta) + ProfileNear(theta);
1040 }
1041 return out;
1042}
1043
1044/////////////////////////////////////////////////////////////////
1045//
1046//
1047
1048inline G4complex G4NuclNuclDiffuseElastic::AmplitudeFar(G4double theta)
1049{
1050 G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi);
1051 G4complex out = G4complex(kappa/fWaveVector,0.);
1052 out *= ProfileFar(theta)*PhaseFar(theta);
1053 return out;
1054}
1055
1056
1057/////////////////////////////////////////////////////////////////
1058//
1059//
1060
1061inline G4complex G4NuclNuclDiffuseElastic::Amplitude(G4double theta)
1062{
1063
1064 G4complex out = AmplitudeNear(theta) + AmplitudeFar(theta);
1065 return out;
1066}
1067
1068/////////////////////////////////////////////////////////////////
1069//
1070//
1071
1072inline G4double G4NuclNuclDiffuseElastic::AmplitudeMod2(G4double theta)
1073{
1074 G4complex out = Amplitude(theta);
1075 G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
1076 return mod2;
1077}
1078
1079
1080///////////////////////////////////////////////////////////////////////////////
1081//
1082// Test for given particle and element table of momentum, angle probability.
1083// For the moment in lab system.
1084
1085inline void G4NuclNuclDiffuseElastic::InitParameters(const G4ParticleDefinition* theParticle,
1086 G4double partMom, G4double Z, G4double A)
1087{
1088 fAtomicNumber = Z; // atomic number
1089 fAtomicWeight = A; // number of nucleons
1090
1091 fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight);
1092 G4double A1 = G4double( theParticle->GetBaryonNumber() );
1093 fNuclearRadius1 = CalculateNuclearRad(A1);
1094 // fNuclearRadius = std::sqrt(fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2);
1095 fNuclearRadius = fNuclearRadius1 + fNuclearRadius2;
1096
1097 G4double a = 0.;
1098 G4double z = theParticle->GetPDGCharge();
1099 G4double m1 = theParticle->GetPDGMass();
1100
1101 fWaveVector = partMom/hbarc;
1102
1103 G4double lambda = fWaveVector*fNuclearRadius;
1104
1105 if( z )
1106 {
1107 a = partMom/m1; // beta*gamma for m1
1108 fBeta = a/std::sqrt(1+a*a);
1109 fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
1110 fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
1111 }
1112 fProfileLambda = lambda*std::sqrt(1.-2*fZommerfeld/lambda);
1113 G4cout<<"fProfileLambda = "<<fProfileLambda<<G4endl;
1114 fProfileDelta = 0.1*fProfileLambda;
1115 fProfileAlpha = 0.05*fProfileLambda;
1116
1117 CalculateCoulombPhaseZero();
1118 CalculateRutherfordAnglePar();
1119
1120 return;
1121}
1122
1123
1124
1125
1126
1127#endif
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