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25//
26//
27// $Id: G4NuclNuclDiffuseElastic.hh,v 1.13 2010/09/28 16:28:58 gcosmo Exp $
28// GEANT4 tag $Name: geant4-09-03-ref-09 $
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 G4complex GammaLogB2n(G4complex xx);
192
193 G4double GetErf(G4double x);
194
195 G4complex GetErfcComp(G4complex z, G4int nMax);
196 G4complex GetErfcSer(G4complex z, G4int nMax);
197 G4complex GetErfcInt(G4complex z); // , G4int nMax);
198
199 G4complex GetErfComp(G4complex z, G4int nMax); // AandS algorithm != Ser, Int
200 G4complex GetErfSer(G4complex z, G4int nMax);
201
202 G4double GetExpCos(G4double x);
203 G4double GetExpSin(G4double x);
204 G4complex GetErfInt(G4complex z); // , G4int nMax);
205
206 G4double GetLegendrePol(G4int n, G4double x);
207
208 G4complex TestErfcComp(G4complex z, G4int nMax);
209 G4complex TestErfcSer(G4complex z, G4int nMax);
210 G4complex TestErfcInt(G4complex z); // , G4int nMax);
211
212 G4complex CoulombAmplitude(G4double theta);
213 void CalculateCoulombPhaseZero();
214 G4double CalculateCoulombPhase(G4int n);
215 void CalculateRutherfordAnglePar();
216
217 G4double ProfileNear(G4double theta);
218 G4double ProfileFar(G4double theta);
219
220 G4complex PhaseNear(G4double theta);
221 G4complex PhaseFar(G4double theta);
222
223 G4complex GammaLess(G4double theta);
224 G4complex GammaMore(G4double theta);
225
226 G4complex AmplitudeNear(G4double theta);
227 G4complex AmplitudeFar(G4double theta);
228 G4complex Amplitude(G4double theta);
229 G4double AmplitudeMod2(G4double theta);
230
231 G4complex AmplitudeGla(G4double theta);
232 G4double AmplitudeGlaMod2(G4double theta);
233
234 G4complex AmplitudeGG(G4double theta);
235 G4double AmplitudeGGMod2(G4double theta);
236
237 void InitParameters(const G4ParticleDefinition* theParticle,
238 G4double partMom, G4double Z, G4double A);
239
240 void InitParametersGla(const G4DynamicParticle* aParticle,
241 G4double partMom, G4double Z, G4double A);
242
243 G4double GetHadronNucleonXscNS( G4ParticleDefinition* pParticle,
244 G4double pTkin,
245 G4ParticleDefinition* tParticle);
246
247 G4double CalcMandelstamS( const G4double mp ,
248 const G4double mt ,
249 const G4double Plab );
250
251 G4double GetProfileLambda(){return fProfileLambda;};
252
253 void SetProfileLambda(G4double pl) {fProfileLambda = pl;};
254 void SetProfileDelta(G4double pd) {fProfileDelta = pd;};
255 void SetProfileAlpha(G4double pa){fProfileAlpha = pa;};
256 void SetCofLambda(G4double pa){fCofLambda = pa;};
257 void SetCofAlpha(G4double pa){fCofAlpha = pa;};
258 void SetCofDelta(G4double pa){fCofDelta = pa;};
259 void SetCofPhase(G4double pa){fCofPhase = pa;};
260 void SetCofFar(G4double pa){fCofFar = pa;};
261 void SetEtaRatio(G4double pa){fEtaRatio = pa;};
262 void SetMaxL(G4int l){fMaxL = l;};
263
264private:
265
266
267 G4ParticleDefinition* theProton;
268 G4ParticleDefinition* theNeutron;
269 G4ParticleDefinition* theDeuteron;
270 G4ParticleDefinition* theAlpha;
271
272 const G4ParticleDefinition* thePionPlus;
273 const G4ParticleDefinition* thePionMinus;
274
275 G4double lowEnergyRecoilLimit;
276 G4double lowEnergyLimitHE;
277 G4double lowEnergyLimitQ;
278 G4double lowestEnergyLimit;
279 G4double plabLowLimit;
280
281 G4int fEnergyBin;
282 G4int fAngleBin;
283
284 G4PhysicsLogVector* fEnergyVector;
285 G4PhysicsTable* fAngleTable;
286 std::vector<G4PhysicsTable*> fAngleBank;
287
288 std::vector<G4double> fElementNumberVector;
289 std::vector<G4String> fElementNameVector;
290
291 const G4ParticleDefinition* fParticle;
292 G4double fWaveVector;
293 G4double fAtomicWeight;
294 G4double fAtomicNumber;
295
296 G4double fNuclearRadius1;
297 G4double fNuclearRadius2;
298 G4double fNuclearRadius;
299 G4double fNuclearRadiusSquare;
300
301 G4double fBeta;
302 G4double fZommerfeld;
303 G4double fAm;
304 G4bool fAddCoulomb;
305
306 G4double fCoulombPhase0;
307 G4double fHalfRutThetaTg;
308 G4double fHalfRutThetaTg2;
309 G4double fRutherfordTheta;
310
311 G4double fProfileLambda;
312 G4double fProfileDelta;
313 G4double fProfileAlpha;
314
315 G4double fCofLambda;
316 G4double fCofAlpha;
317 G4double fCofDelta;
318 G4double fCofPhase;
319 G4double fCofFar;
320
321 G4int fMaxL;
322 G4double fSumSigma;
323 G4double fEtaRatio;
324
325 G4double fReZ;
326
327};
328
329
330inline void G4NuclNuclDiffuseElastic::SetRecoilKinEnergyLimit(G4double value)
331{
332 lowEnergyRecoilLimit = value;
333}
334
335inline void G4NuclNuclDiffuseElastic::SetPlabLowLimit(G4double value)
336{
337 plabLowLimit = value;
338}
339
340inline void G4NuclNuclDiffuseElastic::SetHEModelLowLimit(G4double value)
341{
342 lowEnergyLimitHE = value;
343}
344
345inline void G4NuclNuclDiffuseElastic::SetQModelLowLimit(G4double value)
346{
347 lowEnergyLimitQ = value;
348}
349
350inline void G4NuclNuclDiffuseElastic::SetLowestEnergyLimit(G4double value)
351{
352 lowestEnergyLimit = value;
353}
354
355
356/////////////////////////////////////////////////////////////
357//
358// Bessel J0 function based on rational approximation from
359// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
360
361inline G4double G4NuclNuclDiffuseElastic::BesselJzero(G4double value)
362{
363 G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
364
365 modvalue = fabs(value);
366
367 if ( value < 8.0 && value > -8.0 )
368 {
369 value2 = value*value;
370
371 fact1 = 57568490574.0 + value2*(-13362590354.0
372 + value2*( 651619640.7
373 + value2*(-11214424.18
374 + value2*( 77392.33017
375 + value2*(-184.9052456 ) ) ) ) );
376
377 fact2 = 57568490411.0 + value2*( 1029532985.0
378 + value2*( 9494680.718
379 + value2*(59272.64853
380 + value2*(267.8532712
381 + value2*1.0 ) ) ) );
382
383 bessel = fact1/fact2;
384 }
385 else
386 {
387 arg = 8.0/modvalue;
388
389 value2 = arg*arg;
390
391 shift = modvalue-0.785398164;
392
393 fact1 = 1.0 + value2*(-0.1098628627e-2
394 + value2*(0.2734510407e-4
395 + value2*(-0.2073370639e-5
396 + value2*0.2093887211e-6 ) ) );
397
398 fact2 = -0.1562499995e-1 + value2*(0.1430488765e-3
399 + value2*(-0.6911147651e-5
400 + value2*(0.7621095161e-6
401 - value2*0.934945152e-7 ) ) );
402
403 bessel = sqrt(0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2 );
404 }
405 return bessel;
406}
407
408/////////////////////////////////////////////////////////////
409//
410// Bessel J1 function based on rational approximation from
411// J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
412
413inline G4double G4NuclNuclDiffuseElastic::BesselJone(G4double value)
414{
415 G4double modvalue, value2, fact1, fact2, arg, shift, bessel;
416
417 modvalue = fabs(value);
418
419 if ( modvalue < 8.0 )
420 {
421 value2 = value*value;
422
423 fact1 = value*(72362614232.0 + value2*(-7895059235.0
424 + value2*( 242396853.1
425 + value2*(-2972611.439
426 + value2*( 15704.48260
427 + value2*(-30.16036606 ) ) ) ) ) );
428
429 fact2 = 144725228442.0 + value2*(2300535178.0
430 + value2*(18583304.74
431 + value2*(99447.43394
432 + value2*(376.9991397
433 + value2*1.0 ) ) ) );
434 bessel = fact1/fact2;
435 }
436 else
437 {
438 arg = 8.0/modvalue;
439
440 value2 = arg*arg;
441
442 shift = modvalue - 2.356194491;
443
444 fact1 = 1.0 + value2*( 0.183105e-2
445 + value2*(-0.3516396496e-4
446 + value2*(0.2457520174e-5
447 + value2*(-0.240337019e-6 ) ) ) );
448
449 fact2 = 0.04687499995 + value2*(-0.2002690873e-3
450 + value2*( 0.8449199096e-5
451 + value2*(-0.88228987e-6
452 + value2*0.105787412e-6 ) ) );
453
454 bessel = sqrt( 0.636619772/modvalue)*(cos(shift)*fact1 - arg*sin(shift)*fact2);
455
456 if (value < 0.0) bessel = -bessel;
457 }
458 return bessel;
459}
460
461////////////////////////////////////////////////////////////////////
462//
463// damp factor in diffraction x/sh(x), x was already *pi
464
465inline G4double G4NuclNuclDiffuseElastic::DampFactor(G4double x)
466{
467 G4double df;
468 G4double f2 = 2., f3 = 6., f4 = 24.; // first factorials
469
470 // x *= pi;
471
472 if( std::fabs(x) < 0.01 )
473 {
474 df = 1./(1. + x/f2 + x*x/f3 + x*x*x/f4);
475 }
476 else
477 {
478 df = x/std::sinh(x);
479 }
480 return df;
481}
482
483
484////////////////////////////////////////////////////////////////////
485//
486// return J1(x)/x with special case for small x
487
488inline G4double G4NuclNuclDiffuseElastic::BesselOneByArg(G4double x)
489{
490 G4double x2, result;
491
492 if( std::fabs(x) < 0.01 )
493 {
494 x *= 0.5;
495 x2 = x*x;
496 result = 2. - x2 + x2*x2/6.;
497 }
498 else
499 {
500 result = BesselJone(x)/x;
501 }
502 return result;
503}
504
505////////////////////////////////////////////////////////////////////
506//
507// return particle beta
508
509inline G4double G4NuclNuclDiffuseElastic::CalculateParticleBeta( const G4ParticleDefinition* particle,
510 G4double momentum )
511{
512 G4double mass = particle->GetPDGMass();
513 G4double a = momentum/mass;
514 fBeta = a/std::sqrt(1+a*a);
515
516 return fBeta;
517}
518
519////////////////////////////////////////////////////////////////////
520//
521// return Zommerfeld parameter for Coulomb scattering
522
523inline G4double G4NuclNuclDiffuseElastic::CalculateZommerfeld( G4double beta, G4double Z1, G4double Z2 )
524{
525 fZommerfeld = fine_structure_const*Z1*Z2/beta;
526
527 return fZommerfeld;
528}
529
530////////////////////////////////////////////////////////////////////
531//
532// return Wentzel correction for Coulomb scattering
533
534inline G4double G4NuclNuclDiffuseElastic::CalculateAm( G4double momentum, G4double n, G4double Z)
535{
536 G4double k = momentum/hbarc;
537 G4double ch = 1.13 + 3.76*n*n;
538 G4double zn = 1.77*k*std::pow(Z,-1./3.)*Bohr_radius;
539 G4double zn2 = zn*zn;
540 fAm = ch/zn2;
541
542 return fAm;
543}
544
545////////////////////////////////////////////////////////////////////
546//
547// calculate nuclear radius for different atomic weights using different approximations
548
549inline G4double G4NuclNuclDiffuseElastic::CalculateNuclearRad( G4double A)
550{
551 G4double r0, radius;
552
553 if( A < 50. )
554 {
555 if( A > 10. ) r0 = 1.16*( 1 - std::pow(A, -2./3.) )*fermi; // 1.08*fermi;
556 else r0 = 1.1*fermi;
557
558 radius = r0*std::pow(A, 1./3.);
559 }
560 else
561 {
562 r0 = 1.7*fermi; // 1.7*fermi;
563
564 radius = r0*std::pow(A, 0.27); // 0.27);
565 }
566 return radius;
567}
568
569////////////////////////////////////////////////////////////////////
570//
571// return Coulomb scattering differential xsc with Wentzel correction
572
573inline G4double G4NuclNuclDiffuseElastic::GetCoulombElasticXsc( const G4ParticleDefinition* particle,
574 G4double theta,
575 G4double momentum,
576 G4double Z )
577{
578 G4double sinHalfTheta = std::sin(0.5*theta);
579 G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
580 G4double beta = CalculateParticleBeta( particle, momentum);
581 G4double z = particle->GetPDGCharge();
582 G4double n = CalculateZommerfeld( beta, z, Z );
583 G4double am = CalculateAm( momentum, n, Z);
584 G4double k = momentum/hbarc;
585 G4double ch = 0.5*n/k;
586 G4double ch2 = ch*ch;
587 G4double xsc = ch2/(sinHalfTheta2+am)/(sinHalfTheta2+am);
588
589 return xsc;
590}
591
592
593////////////////////////////////////////////////////////////////////
594//
595// return Coulomb scattering total xsc with Wentzel correction
596
597inline G4double G4NuclNuclDiffuseElastic::GetCoulombTotalXsc( const G4ParticleDefinition* particle,
598 G4double momentum, G4double Z )
599{
600 G4double beta = CalculateParticleBeta( particle, momentum);
601 G4cout<<"beta = "<<beta<<G4endl;
602 G4double z = particle->GetPDGCharge();
603 G4double n = CalculateZommerfeld( beta, z, Z );
604 G4cout<<"fZomerfeld = "<<n<<G4endl;
605 G4double am = CalculateAm( momentum, n, Z);
606 G4cout<<"cof Am = "<<am<<G4endl;
607 G4double k = momentum/hbarc;
608 G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl;
609 G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl;
610 G4double ch = n/k;
611 G4double ch2 = ch*ch;
612 G4double xsc = ch2*pi/(am +am*am);
613
614 return xsc;
615}
616
617////////////////////////////////////////////////////////////////////
618//
619// return Coulomb scattering xsc with Wentzel correction integrated between
620// theta1 and < theta2
621
622inline G4double G4NuclNuclDiffuseElastic::GetCoulombIntegralXsc( const G4ParticleDefinition* particle,
623 G4double momentum, G4double Z,
624 G4double theta1, G4double theta2 )
625{
626 G4double c1 = std::cos(theta1);
627 G4cout<<"c1 = "<<c1<<G4endl;
628 G4double c2 = std::cos(theta2);
629 G4cout<<"c2 = "<<c2<<G4endl;
630 G4double beta = CalculateParticleBeta( particle, momentum);
631 // G4cout<<"beta = "<<beta<<G4endl;
632 G4double z = particle->GetPDGCharge();
633 G4double n = CalculateZommerfeld( beta, z, Z );
634 // G4cout<<"fZomerfeld = "<<n<<G4endl;
635 G4double am = CalculateAm( momentum, n, Z);
636 // G4cout<<"cof Am = "<<am<<G4endl;
637 G4double k = momentum/hbarc;
638 // G4cout<<"k = "<<k*fermi<<" 1/fermi"<<G4endl;
639 // G4cout<<"k*Bohr_radius = "<<k*Bohr_radius<<G4endl;
640 G4double ch = n/k;
641 G4double ch2 = ch*ch;
642 am *= 2.;
643 G4double xsc = ch2*twopi*(c1-c2);
644 xsc /= (1 - c1 + am)*(1 - c2 + am);
645
646 return xsc;
647}
648
649///////////////////////////////////////////////////////////////////
650//
651// For the calculation of arg Gamma(z) one needs complex extension
652// of ln(Gamma(z))
653
654inline G4complex G4NuclNuclDiffuseElastic::GammaLogarithm(G4complex zz)
655{
656 static G4double cof[6] = { 76.18009172947146, -86.50532032941677,
657 24.01409824083091, -1.231739572450155,
658 0.1208650973866179e-2, -0.5395239384953e-5 } ;
659 register G4int j;
660 G4complex z = zz - 1.0;
661 G4complex tmp = z + 5.5;
662 tmp -= (z + 0.5) * std::log(tmp);
663 G4complex ser = G4complex(1.000000000190015,0.);
664
665 for ( j = 0; j <= 5; j++ )
666 {
667 z += 1.0;
668 ser += cof[j]/z;
669 }
670 return -tmp + std::log(2.5066282746310005*ser);
671}
672
673///////////////////////////////////////////////////////////////////
674//
675// For the calculation of arg Gamma(z) one needs complex extension
676// of ln(Gamma(z)) here is approximate algorithm
677
678inline G4complex G4NuclNuclDiffuseElastic::GammaLogB2n(G4complex z)
679{
680 G4complex z1 = 12.*z;
681 G4complex z2 = z*z;
682 G4complex z3 = z2*z;
683 G4complex z5 = z2*z3;
684 G4complex z7 = z2*z5;
685
686 z3 *= 360.;
687 z5 *= 1260.;
688 z7 *= 1680.;
689
690 G4complex result = (z-0.5)*std::log(z)-z+0.5*std::log(twopi);
691 result += 1./z1 - 1./z3 +1./z5 -1./z7;
692 return result;
693}
694
695/////////////////////////////////////////////////////////////////
696//
697//
698
699inline G4double G4NuclNuclDiffuseElastic::GetErf(G4double x)
700{
701 G4double t, z, tmp, result;
702
703 z = std::fabs(x);
704 t = 1.0/(1.0+0.5*z);
705
706 tmp = t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+
707 t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+
708 t*(-0.82215223+t*0.17087277)))))))));
709
710 if( x >= 0.) result = 1. - tmp;
711 else result = 1. + tmp;
712
713 return result;
714}
715
716/////////////////////////////////////////////////////////////////
717//
718//
719
720inline G4complex G4NuclNuclDiffuseElastic::GetErfcComp(G4complex z, G4int nMax)
721{
722 G4complex erfcz = 1. - GetErfComp( z, nMax);
723 return erfcz;
724}
725
726/////////////////////////////////////////////////////////////////
727//
728//
729
730inline G4complex G4NuclNuclDiffuseElastic::GetErfcSer(G4complex z, G4int nMax)
731{
732 G4complex erfcz = 1. - GetErfSer( z, nMax);
733 return erfcz;
734}
735
736/////////////////////////////////////////////////////////////////
737//
738//
739
740inline G4complex G4NuclNuclDiffuseElastic::GetErfcInt(G4complex z) // , G4int nMax)
741{
742 G4complex erfcz = 1. - GetErfInt( z); // , nMax);
743 return erfcz;
744}
745
746inline G4double G4NuclNuclDiffuseElastic::GetLegendrePol(G4int n, G4double theta)
747{
748 G4double legPol, epsilon = 1.e-6;
749 G4double x = std::cos(theta);
750
751 if ( n < 0 ) legPol = 0.;
752 else if( n == 0 ) legPol = 1.;
753 else if( n == 1 ) legPol = x;
754 else if( n == 2 ) legPol = (3.*x*x-1.)/2.;
755 else if( n == 3 ) legPol = (5.*x*x*x-3.*x)/2.;
756 else if( n == 4 ) legPol = (35.*x*x*x*x-30.*x*x+3.)/8.;
757 else if( n == 5 ) legPol = (63.*x*x*x*x*x-70.*x*x*x+15.*x)/8.;
758 else if( n == 6 ) legPol = (231.*x*x*x*x*x*x-315.*x*x*x*x+105.*x*x-5.)/16.;
759 else
760 {
761 // legPol = ( (2*n-1)*x*GetLegendrePol(n-1,x) - (n-1)*GetLegendrePol(n-2,x) )/n;
762
763 legPol = std::sqrt( 2./(n*pi*std::sin(theta+epsilon)) )*std::sin( (n+0.5)*theta+0.25*pi );
764 }
765 return legPol;
766}
767
768
769
770/////////////////////////////////////////////////////////////////
771//
772//
773
774inline G4complex G4NuclNuclDiffuseElastic::TestErfcComp(G4complex z, G4int nMax)
775{
776 G4complex miz = G4complex( z.imag(), -z.real() );
777 G4complex erfcz = 1. - GetErfComp( miz, nMax);
778 G4complex w = std::exp(-z*z)*erfcz;
779 return w;
780}
781
782/////////////////////////////////////////////////////////////////
783//
784//
785
786inline G4complex G4NuclNuclDiffuseElastic::TestErfcSer(G4complex z, G4int nMax)
787{
788 G4complex miz = G4complex( z.imag(), -z.real() );
789 G4complex erfcz = 1. - GetErfSer( miz, nMax);
790 G4complex w = std::exp(-z*z)*erfcz;
791 return w;
792}
793
794/////////////////////////////////////////////////////////////////
795//
796//
797
798inline G4complex G4NuclNuclDiffuseElastic::TestErfcInt(G4complex z) // , G4int nMax)
799{
800 G4complex miz = G4complex( z.imag(), -z.real() );
801 G4complex erfcz = 1. - GetErfInt( miz); // , nMax);
802 G4complex w = std::exp(-z*z)*erfcz;
803 return w;
804}
805
806/////////////////////////////////////////////////////////////////
807//
808//
809
810inline G4complex G4NuclNuclDiffuseElastic::GetErfComp(G4complex z, G4int nMax)
811{
812 G4int n;
813 G4double n2, cofn, shny, chny, fn, gn;
814
815 G4double x = z.real();
816 G4double y = z.imag();
817
818 G4double outRe = 0., outIm = 0.;
819
820 G4double twox = 2.*x;
821 G4double twoxy = twox*y;
822 G4double twox2 = twox*twox;
823
824 G4double cof1 = std::exp(-x*x)/pi;
825
826 G4double cos2xy = std::cos(twoxy);
827 G4double sin2xy = std::sin(twoxy);
828
829 G4double twoxcos2xy = twox*cos2xy;
830 G4double twoxsin2xy = twox*sin2xy;
831
832 for( n = 1; n <= nMax; n++)
833 {
834 n2 = n*n;
835
836 cofn = std::exp(-0.5*n2)/(n2+twox2); // /(n2+0.5*twox2);
837
838 chny = std::cosh(n*y);
839 shny = std::sinh(n*y);
840
841 fn = twox - twoxcos2xy*chny + n*sin2xy*shny;
842 gn = twoxsin2xy*chny + n*cos2xy*shny;
843
844 fn *= cofn;
845 gn *= cofn;
846
847 outRe += fn;
848 outIm += gn;
849 }
850 outRe *= 2*cof1;
851 outIm *= 2*cof1;
852
853 if(std::abs(x) < 0.0001)
854 {
855 outRe += GetErf(x);
856 outIm += cof1*y;
857 }
858 else
859 {
860 outRe += GetErf(x) + cof1*(1-cos2xy)/twox;
861 outIm += cof1*sin2xy/twox;
862 }
863 return G4complex(outRe, outIm);
864}
865
866/////////////////////////////////////////////////////////////////
867//
868//
869
870inline G4complex G4NuclNuclDiffuseElastic::GetErfSer(G4complex z, G4int nMax)
871{
872 G4int n;
873 G4double a =1., b = 1., tmp;
874 G4complex sum = z, d = z;
875
876 for( n = 1; n <= nMax; n++)
877 {
878 a *= 2.;
879 b *= 2.*n +1.;
880 d *= z*z;
881
882 tmp = a/b;
883
884 sum += tmp*d;
885 }
886 sum *= 2.*std::exp(-z*z)/std::sqrt(pi);
887
888 return sum;
889}
890
891/////////////////////////////////////////////////////////////////////
892
893inline G4double G4NuclNuclDiffuseElastic::GetExpCos(G4double x)
894{
895 G4double result;
896
897 result = std::exp(x*x-fReZ*fReZ);
898 result *= std::cos(2.*x*fReZ);
899 return result;
900}
901
902/////////////////////////////////////////////////////////////////////
903
904inline G4double G4NuclNuclDiffuseElastic::GetExpSin(G4double x)
905{
906 G4double result;
907
908 result = std::exp(x*x-fReZ*fReZ);
909 result *= std::sin(2.*x*fReZ);
910 return result;
911}
912
913
914
915/////////////////////////////////////////////////////////////////
916//
917//
918
919inline G4complex G4NuclNuclDiffuseElastic::GetErfInt(G4complex z) // , G4int nMax)
920{
921 G4double outRe, outIm;
922
923 G4double x = z.real();
924 G4double y = z.imag();
925 fReZ = x;
926
927 G4Integrator<G4NuclNuclDiffuseElastic,G4double(G4NuclNuclDiffuseElastic::*)(G4double)> integral;
928
929 outRe = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpSin, 0., y );
930 outIm = integral.Legendre96(this,&G4NuclNuclDiffuseElastic::GetExpCos, 0., y );
931
932 outRe *= 2./sqrt(pi);
933 outIm *= 2./sqrt(pi);
934
935 outRe += GetErf(x);
936
937 return G4complex(outRe, outIm);
938}
939
940
941/////////////////////////////////////////////////////////////////
942//
943//
944
945inline G4complex G4NuclNuclDiffuseElastic::CoulombAmplitude(G4double theta)
946{
947 G4complex ca;
948
949 G4double sinHalfTheta = std::sin(0.5*theta);
950 G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;
951 sinHalfTheta2 += fAm;
952
953 G4double order = 2.*fCoulombPhase0 - fZommerfeld*std::log(sinHalfTheta2);
954 G4complex z = G4complex(0., order);
955 ca = std::exp(z);
956
957 ca *= -fZommerfeld/(2.*fWaveVector*sinHalfTheta2);
958
959 return ca;
960}
961
962/////////////////////////////////////////////////////////////////
963//
964//
965
966
967inline void G4NuclNuclDiffuseElastic::CalculateCoulombPhaseZero()
968{
969 G4complex z = G4complex(1,fZommerfeld);
970 // G4complex gammalog = GammaLogarithm(z);
971 G4complex gammalog = GammaLogB2n(z);
972 fCoulombPhase0 = gammalog.imag();
973}
974
975/////////////////////////////////////////////////////////////////
976//
977//
978
979
980inline G4double G4NuclNuclDiffuseElastic::CalculateCoulombPhase(G4int n)
981{
982 G4complex z = G4complex(1. + n, fZommerfeld);
983 // G4complex gammalog = GammaLogarithm(z);
984 G4complex gammalog = GammaLogB2n(z);
985 return gammalog.imag();
986}
987
988
989/////////////////////////////////////////////////////////////////
990//
991//
992
993
994inline void G4NuclNuclDiffuseElastic::CalculateRutherfordAnglePar()
995{
996 fHalfRutThetaTg = fZommerfeld/fProfileLambda; // (fWaveVector*fNuclearRadius);
997 fRutherfordTheta = 2.*std::atan(fHalfRutThetaTg);
998 fHalfRutThetaTg2 = fHalfRutThetaTg*fHalfRutThetaTg;
999 G4cout<<"fRutherfordTheta = "<<fRutherfordTheta/degree<<" degree"<<G4endl;
1000
1001}
1002
1003/////////////////////////////////////////////////////////////////
1004//
1005//
1006
1007inline G4double G4NuclNuclDiffuseElastic::ProfileNear(G4double theta)
1008{
1009 G4double dTheta = fRutherfordTheta - theta;
1010 G4double result = 0., argument = 0.;
1011
1012 if(std::abs(dTheta) < 0.001) result = fProfileAlpha*fProfileDelta;
1013 else
1014 {
1015 argument = fProfileDelta*dTheta;
1016 result = pi*argument*std::exp(fProfileAlpha*argument);
1017 result /= std::sinh(pi*argument);
1018 result -= 1.;
1019 result /= dTheta;
1020 }
1021 return result;
1022}
1023
1024/////////////////////////////////////////////////////////////////
1025//
1026//
1027
1028inline G4double G4NuclNuclDiffuseElastic::ProfileFar(G4double theta)
1029{
1030 G4double dTheta = fRutherfordTheta + theta;
1031 G4double argument = fProfileDelta*dTheta;
1032
1033 G4double result = pi*argument*std::exp(fProfileAlpha*argument);
1034 result /= std::sinh(pi*argument);
1035 result /= dTheta;
1036
1037 return result;
1038}
1039
1040/////////////////////////////////////////////////////////////////
1041//
1042//
1043
1044inline G4complex G4NuclNuclDiffuseElastic::PhaseNear(G4double theta)
1045{
1046 G4double twosigma = 2.*fCoulombPhase0;
1047 twosigma -= fZommerfeld*std::log(fHalfRutThetaTg2/(1.+fHalfRutThetaTg2));
1048 twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi;
1049 twosigma -= fProfileLambda*theta - 0.25*pi;
1050
1051 twosigma *= fCofPhase;
1052
1053 G4complex z = G4complex(0., twosigma);
1054
1055 return std::exp(z);
1056}
1057
1058/////////////////////////////////////////////////////////////////
1059//
1060//
1061
1062inline G4complex G4NuclNuclDiffuseElastic::PhaseFar(G4double theta)
1063{
1064 G4double twosigma = 2.*fCoulombPhase0;
1065 twosigma -= fZommerfeld*std::log(fHalfRutThetaTg2/(1.+fHalfRutThetaTg2));
1066 twosigma += fRutherfordTheta*fZommerfeld/fHalfRutThetaTg - halfpi;
1067 twosigma += fProfileLambda*theta - 0.25*pi;
1068
1069 twosigma *= fCofPhase;
1070
1071 G4complex z = G4complex(0., twosigma);
1072
1073 return std::exp(z);
1074}
1075
1076/////////////////////////////////////////////////////////////////
1077//
1078//
1079
1080
1081inline G4complex G4NuclNuclDiffuseElastic::GammaLess(G4double theta)
1082{
1083 G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
1084 G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2);
1085
1086 G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
1087 G4double kappa = u/std::sqrt(pi);
1088 G4double dTheta = theta - fRutherfordTheta;
1089 u *= dTheta;
1090 G4double u2 = u*u;
1091 G4double u2m2p3 = u2*2./3.;
1092
1093 G4complex im = G4complex(0.,1.);
1094 G4complex order = G4complex(u,u);
1095 order /= std::sqrt(2.);
1096
1097 G4complex gamma = pi*kappa*GetErfcInt(-order)*std::exp(im*(u*u+0.25*pi));
1098 G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
1099 G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
1100 G4complex out = gamma*(1. - a1*dTheta) - a0;
1101
1102 return out;
1103}
1104
1105/////////////////////////////////////////////////////////////////
1106//
1107//
1108
1109inline G4complex G4NuclNuclDiffuseElastic::GammaMore(G4double theta)
1110{
1111 G4double sinThetaR = 2.*fHalfRutThetaTg/(1. + fHalfRutThetaTg2);
1112 G4double cosHalfThetaR2 = 1./(1. + fHalfRutThetaTg2);
1113
1114 G4double u = std::sqrt(0.5*fProfileLambda/sinThetaR);
1115 G4double kappa = u/std::sqrt(pi);
1116 G4double dTheta = theta - fRutherfordTheta;
1117 u *= dTheta;
1118 G4double u2 = u*u;
1119 G4double u2m2p3 = u2*2./3.;
1120
1121 G4complex im = G4complex(0.,1.);
1122 G4complex order = G4complex(u,u);
1123 order /= std::sqrt(2.);
1124 G4complex gamma = pi*kappa*GetErfcInt(order)*std::exp(im*(u*u+0.25*pi));
1125 G4complex a0 = 0.5*(1. + 4.*(1.+im*u2)*cosHalfThetaR2/3.)/sinThetaR;
1126 G4complex a1 = 0.5*(1. + 2.*(1.+im*u2m2p3)*cosHalfThetaR2)/sinThetaR;
1127 G4complex out = -gamma*(1. - a1*dTheta) - a0;
1128
1129 return out;
1130}
1131
1132/////////////////////////////////////////////////////////////////
1133//
1134//
1135
1136inline G4complex G4NuclNuclDiffuseElastic::AmplitudeNear(G4double theta)
1137{
1138 G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi);
1139 G4complex out = G4complex(kappa/fWaveVector,0.);
1140
1141 out *= PhaseNear(theta);
1142
1143 if( theta <= fRutherfordTheta )
1144 {
1145 out *= GammaLess(theta) + ProfileNear(theta);
1146 // out *= GammaMore(theta) + ProfileNear(theta);
1147 out += CoulombAmplitude(theta);
1148 }
1149 else
1150 {
1151 out *= GammaMore(theta) + ProfileNear(theta);
1152 // out *= GammaLess(theta) + ProfileNear(theta);
1153 }
1154 return out;
1155}
1156
1157/////////////////////////////////////////////////////////////////
1158//
1159//
1160
1161inline G4complex G4NuclNuclDiffuseElastic::AmplitudeFar(G4double theta)
1162{
1163 G4double kappa = std::sqrt(0.5*fProfileLambda/std::sin(theta)/pi);
1164 G4complex out = G4complex(kappa/fWaveVector,0.);
1165 out *= ProfileFar(theta);
1166 out *= PhaseFar(theta);
1167 return out;
1168}
1169
1170
1171/////////////////////////////////////////////////////////////////
1172//
1173//
1174
1175inline G4complex G4NuclNuclDiffuseElastic::Amplitude(G4double theta)
1176{
1177
1178 G4complex out = AmplitudeNear(theta) + fCofFar*AmplitudeFar(theta);
1179 // G4complex out = AmplitudeNear(theta);
1180 // G4complex out = AmplitudeFar(theta);
1181 return out;
1182}
1183
1184/////////////////////////////////////////////////////////////////
1185//
1186//
1187
1188inline G4double G4NuclNuclDiffuseElastic::AmplitudeMod2(G4double theta)
1189{
1190 G4complex out = Amplitude(theta);
1191 G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
1192 return mod2;
1193}
1194
1195/////////////////////////////////////////////////////////////////
1196//
1197//
1198
1199inline G4complex G4NuclNuclDiffuseElastic::AmplitudeGla(G4double theta)
1200{
1201 G4int n;
1202 G4double T12b, b, b2; // cosTheta = std::cos(theta);
1203 G4complex out = G4complex(0.,0.), shiftC, shiftN;
1204 G4complex im = G4complex(0.,1.);
1205
1206 for( n = 0; n < fMaxL; n++)
1207 {
1208 shiftC = std::exp( im*2.*CalculateCoulombPhase(n) );
1209 // b = ( fZommerfeld + std::sqrt( fZommerfeld*fZommerfeld + n*(n+1) ) )/fWaveVector;
1210 b = ( std::sqrt( G4double(n*(n+1)) ) )/fWaveVector;
1211 b2 = b*b;
1212 T12b = fSumSigma*std::exp(-b2/fNuclearRadiusSquare)/pi/fNuclearRadiusSquare;
1213 shiftN = std::exp( -0.5*(1.-im*fEtaRatio)*T12b ) - 1.;
1214 out += (2.*n+1.)*shiftC*shiftN*GetLegendrePol(n, theta);
1215 }
1216 out /= 2.*im*fWaveVector;
1217 out += CoulombAmplitude(theta);
1218 return out;
1219}
1220
1221/////////////////////////////////////////////////////////////////
1222//
1223//
1224
1225inline G4double G4NuclNuclDiffuseElastic::AmplitudeGlaMod2(G4double theta)
1226{
1227 G4complex out = AmplitudeGla(theta);
1228 G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
1229 return mod2;
1230}
1231
1232
1233/////////////////////////////////////////////////////////////////
1234//
1235//
1236
1237inline G4complex G4NuclNuclDiffuseElastic::AmplitudeGG(G4double theta)
1238{
1239 G4int n;
1240 G4double T12b, a, aTemp, b2, sinThetaH = std::sin(0.5*theta);
1241 G4double sinThetaH2 = sinThetaH*sinThetaH;
1242 G4complex out = G4complex(0.,0.);
1243 G4complex im = G4complex(0.,1.);
1244
1245 a = -fSumSigma/twopi/fNuclearRadiusSquare;
1246 b2 = fWaveVector*fWaveVector*fNuclearRadiusSquare*sinThetaH2;
1247
1248 aTemp = a;
1249
1250 for( n = 1; n < fMaxL; n++)
1251 {
1252 T12b = aTemp*std::exp(-b2/n)/n;
1253 aTemp *= a;
1254 out += T12b;
1255 G4cout<<"out = "<<out<<G4endl;
1256 }
1257 out *= -4.*im*fWaveVector/pi;
1258 out += CoulombAmplitude(theta);
1259 return out;
1260}
1261
1262/////////////////////////////////////////////////////////////////
1263//
1264//
1265
1266inline G4double G4NuclNuclDiffuseElastic::AmplitudeGGMod2(G4double theta)
1267{
1268 G4complex out = AmplitudeGG(theta);
1269 G4double mod2 = out.real()*out.real() + out.imag()*out.imag();
1270 return mod2;
1271}
1272
1273
1274///////////////////////////////////////////////////////////////////////////////
1275//
1276// Test for given particle and element table of momentum, angle probability.
1277// For the partMom in CMS.
1278
1279inline void G4NuclNuclDiffuseElastic::InitParameters(const G4ParticleDefinition* theParticle,
1280 G4double partMom, G4double Z, G4double A)
1281{
1282 fAtomicNumber = Z; // atomic number
1283 fAtomicWeight = A; // number of nucleons
1284
1285 fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight);
1286 G4double A1 = G4double( theParticle->GetBaryonNumber() );
1287 fNuclearRadius1 = CalculateNuclearRad(A1);
1288 // fNuclearRadius = std::sqrt(fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2);
1289 fNuclearRadius = fNuclearRadius1 + fNuclearRadius2;
1290
1291 G4double a = 0.;
1292 G4double z = theParticle->GetPDGCharge();
1293 G4double m1 = theParticle->GetPDGMass();
1294
1295 fWaveVector = partMom/hbarc;
1296
1297 G4double lambda = fCofLambda*fWaveVector*fNuclearRadius;
1298 G4cout<<"kR = "<<lambda<<G4endl;
1299
1300 if( z )
1301 {
1302 a = partMom/m1; // beta*gamma for m1
1303 fBeta = a/std::sqrt(1+a*a);
1304 fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
1305 fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
1306 }
1307 fProfileLambda = lambda*std::sqrt(1.-2*fZommerfeld/lambda);
1308 G4cout<<"fProfileLambda = "<<fProfileLambda<<G4endl;
1309 fProfileDelta = fCofDelta*fProfileLambda;
1310 fProfileAlpha = fCofAlpha*fProfileLambda;
1311
1312 CalculateCoulombPhaseZero();
1313 CalculateRutherfordAnglePar();
1314
1315 return;
1316}
1317
1318
1319///////////////////////////////////////////////////////////////////////////////
1320//
1321// Test for given particle and element table of momentum, angle probability.
1322// For the partMom in CMS.
1323
1324inline void G4NuclNuclDiffuseElastic::InitParametersGla(const G4DynamicParticle* aParticle,
1325 G4double partMom, G4double Z, G4double A)
1326{
1327 fAtomicNumber = Z; // target atomic number
1328 fAtomicWeight = A; // target number of nucleons
1329
1330 fNuclearRadius2 = CalculateNuclearRad(fAtomicWeight); // target nucleus radius
1331 G4double A1 = G4double( aParticle->GetDefinition()->GetBaryonNumber() );
1332 fNuclearRadius1 = CalculateNuclearRad(A1); // projectile nucleus radius
1333 fNuclearRadiusSquare = fNuclearRadius1*fNuclearRadius1+fNuclearRadius2*fNuclearRadius2;
1334
1335
1336 G4double a = 0., kR12;
1337 G4double z = aParticle->GetDefinition()->GetPDGCharge();
1338 G4double m1 = aParticle->GetDefinition()->GetPDGMass();
1339
1340 fWaveVector = partMom/hbarc;
1341
1342 G4double pN = A1 - z;
1343 if( pN < 0. ) pN = 0.;
1344
1345 G4double tN = A - Z;
1346 if( tN < 0. ) tN = 0.;
1347
1348 G4double pTkin = aParticle->GetKineticEnergy();
1349 pTkin /= A1;
1350
1351
1352 fSumSigma = (Z*z+pN*tN)*GetHadronNucleonXscNS(theProton, pTkin, theProton) +
1353 (z*tN+pN*Z)*GetHadronNucleonXscNS(theProton, pTkin, theNeutron);
1354
1355 G4cout<<"fSumSigma = "<<fSumSigma/millibarn<<" mb"<<G4endl;
1356 G4cout<<"pi*R2 = "<<pi*fNuclearRadiusSquare/millibarn<<" mb"<<G4endl;
1357 kR12 = fWaveVector*std::sqrt(fNuclearRadiusSquare);
1358 G4cout<<"k*sqrt(R2) = "<<kR12<<" "<<G4endl;
1359 fMaxL = (G4int(kR12)+1)*4;
1360 G4cout<<"fMaxL = "<<fMaxL<<" "<<G4endl;
1361
1362 if( z )
1363 {
1364 a = partMom/m1; // beta*gamma for m1
1365 fBeta = a/std::sqrt(1+a*a);
1366 fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
1367 fAm = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
1368 }
1369
1370 CalculateCoulombPhaseZero();
1371
1372
1373 return;
1374}
1375
1376
1377/////////////////////////////////////////////////////////////////////////////////////
1378//
1379// Returns nucleon-nucleon cross-section based on N. Starkov parametrisation of
1380// data from mainly http://wwwppds.ihep.su:8001/c5-6A.html database
1381// projectile nucleon is pParticle with pTkin shooting target nucleon tParticle
1382
1383inline G4double
1384G4NuclNuclDiffuseElastic::GetHadronNucleonXscNS( G4ParticleDefinition* pParticle,
1385 G4double pTkin,
1386 G4ParticleDefinition* tParticle)
1387{
1388 G4double xsection(0), Delta, A0, B0;
1389 G4double hpXsc(0);
1390 G4double hnXsc(0);
1391
1392
1393 G4double targ_mass = tParticle->GetPDGMass();
1394 G4double proj_mass = pParticle->GetPDGMass();
1395
1396 G4double proj_energy = proj_mass + pTkin;
1397 G4double proj_momentum = std::sqrt(pTkin*(pTkin+2*proj_mass));
1398
1399 G4double sMand = CalcMandelstamS ( proj_mass , targ_mass , proj_momentum );
1400
1401 sMand /= GeV*GeV; // in GeV for parametrisation
1402 proj_momentum /= GeV;
1403 proj_energy /= GeV;
1404 proj_mass /= GeV;
1405 G4double logS = std::log(sMand);
1406
1407 // General PDG fit constants
1408
1409
1410 // fEtaRatio=Re[f(0)]/Im[f(0)]
1411
1412 if( proj_momentum >= 1.2 )
1413 {
1414 fEtaRatio = 0.13*(logS - 5.8579332)*std::pow(sMand,-0.18);
1415 }
1416 else if( proj_momentum >= 0.6 )
1417 {
1418 fEtaRatio = -75.5*(std::pow(proj_momentum,0.25)-0.95)/
1419 (std::pow(3*proj_momentum,2.2)+1);
1420 }
1421 else
1422 {
1423 fEtaRatio = 15.5*proj_momentum/(27*proj_momentum*proj_momentum*proj_momentum+2);
1424 }
1425 G4cout<<"fEtaRatio = "<<fEtaRatio<<G4endl;
1426
1427 // xsc
1428
1429 if( proj_momentum >= 10. ) // high energy: pp = nn = np
1430 // if( proj_momentum >= 2.)
1431 {
1432 Delta = 1.;
1433
1434 if( proj_energy < 40. ) Delta = 0.916+0.0021*proj_energy;
1435
1436 if( proj_momentum >= 10.)
1437 {
1438 B0 = 7.5;
1439 A0 = 100. - B0*std::log(3.0e7);
1440
1441 xsection = A0 + B0*std::log(proj_energy) - 11
1442 + 103*std::pow(2*0.93827*proj_energy + proj_mass*proj_mass+
1443 0.93827*0.93827,-0.165); // mb
1444 }
1445 }
1446 else // low energy pp = nn != np
1447 {
1448 if(pParticle == tParticle) // pp or nn // nn to be pp
1449 {
1450 if( proj_momentum < 0.73 )
1451 {
1452 hnXsc = 23 + 50*( std::pow( std::log(0.73/proj_momentum), 3.5 ) );
1453 }
1454 else if( proj_momentum < 1.05 )
1455 {
1456 hnXsc = 23 + 40*(std::log(proj_momentum/0.73))*
1457 (std::log(proj_momentum/0.73));
1458 }
1459 else // if( proj_momentum < 10. )
1460 {
1461 hnXsc = 39.0 +
1462 75*(proj_momentum - 1.2)/(std::pow(proj_momentum,3.0) + 0.15);
1463 }
1464 xsection = hnXsc;
1465 }
1466 else // pn to be np
1467 {
1468 if( proj_momentum < 0.8 )
1469 {
1470 hpXsc = 33+30*std::pow(std::log(proj_momentum/1.3),4.0);
1471 }
1472 else if( proj_momentum < 1.4 )
1473 {
1474 hpXsc = 33+30*std::pow(std::log(proj_momentum/0.95),2.0);
1475 }
1476 else // if( proj_momentum < 10. )
1477 {
1478 hpXsc = 33.3+
1479 20.8*(std::pow(proj_momentum,2.0)-1.35)/
1480 (std::pow(proj_momentum,2.50)+0.95);
1481 }
1482 xsection = hpXsc;
1483 }
1484 }
1485 xsection *= millibarn; // parametrised in mb
1486 G4cout<<"xsection = "<<xsection/millibarn<<" mb"<<G4endl;
1487 return xsection;
1488}
1489
1490////////////////////////////////////////////////////////////////////////////////////
1491//
1492//
1493
1494inline G4double G4NuclNuclDiffuseElastic::CalcMandelstamS( const G4double mp ,
1495 const G4double mt ,
1496 const G4double Plab )
1497{
1498 G4double Elab = std::sqrt ( mp * mp + Plab * Plab );
1499 G4double sMand = mp*mp + mt*mt + 2*Elab*mt ;
1500
1501 return sMand;
1502}
1503
1504
1505
1506#endif
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