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G4ComponentGGHadronNucleusXsc.cc
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25 //
26 // author: V. Grichine
27 //
28 // 25.04.12 V. Grichine - first implementation
29 
31 
32 #include "G4PhysicalConstants.hh"
33 #include "G4SystemOfUnits.hh"
34 #include "G4ParticleTable.hh"
35 #include "G4IonTable.hh"
36 #include "G4ParticleDefinition.hh"
37 #include "G4DynamicParticle.hh"
38 #include "G4HadronNucleonXsc.hh"
39 
40 
42 //
43 
45  : G4VComponentCrossSection("Glauber-Gribov"),
46  fUpperLimit(100000*GeV), fLowerLimit(10.*MeV),// fLowerLimit(3*GeV),
47  fRadiusConst(1.08*fermi), // 1.1, 1.3 ?
48  fTotalXsc(0.0), fElasticXsc(0.0), fInelasticXsc(0.0), fProductionXsc(0.0),
49  fDiffractionXsc(0.0), fHadronNucleonXsc(0.0)
50 {
51  theGamma = G4Gamma::Gamma();
52  theProton = G4Proton::Proton();
53  theNeutron = G4Neutron::Neutron();
54  theAProton = G4AntiProton::AntiProton();
55  theANeutron = G4AntiNeutron::AntiNeutron();
56  thePiPlus = G4PionPlus::PionPlus();
57  thePiMinus = G4PionMinus::PionMinus();
58  thePiZero = G4PionZero::PionZero();
59  theKPlus = G4KaonPlus::KaonPlus();
60  theKMinus = G4KaonMinus::KaonMinus();
63  theL = G4Lambda::Lambda();
64  theAntiL = G4AntiLambda::AntiLambda();
65  theSPlus = G4SigmaPlus::SigmaPlus();
66  theASPlus = G4AntiSigmaPlus::AntiSigmaPlus();
67  theSMinus = G4SigmaMinus::SigmaMinus();
68  theASMinus = G4AntiSigmaMinus::AntiSigmaMinus();
69  theS0 = G4SigmaZero::SigmaZero();
71  theXiMinus = G4XiMinus::XiMinus();
72  theXi0 = G4XiZero::XiZero();
73  theAXiMinus = G4AntiXiMinus::AntiXiMinus();
74  theAXi0 = G4AntiXiZero::AntiXiZero();
75  theOmega = G4OmegaMinus::OmegaMinus();
77  theD = G4Deuteron::Deuteron();
78  theT = G4Triton::Triton();
79  theA = G4Alpha::Alpha();
80  theHe3 = G4He3::He3();
81 
82  hnXsc = new G4HadronNucleonXsc();
83 }
84 
86 //
87 //
88 
90 {
91  if (hnXsc) delete hnXsc;
92 }
93 
95 
97  G4double kinEnergy,
98  G4int Z, G4int A)
99 {
100  G4DynamicParticle* aDP = new G4DynamicParticle(aParticle,G4ParticleMomentum(1.,0.,0.),
101  kinEnergy);
102  fTotalXsc = GetIsoCrossSection(aDP, Z, A);
103  delete aDP;
104 
105  return fTotalXsc;
106 }
107 
109 
111  G4double kinEnergy,
112  G4int Z, G4double A)
113 {
114  G4DynamicParticle* aDP = new G4DynamicParticle(aParticle,G4ParticleMomentum(1.,0.,0.),
115  kinEnergy);
116  fTotalXsc = GetIsoCrossSection(aDP, Z, G4int(A));
117  delete aDP;
118 
119  return fTotalXsc;
120 }
121 
123 
125  G4double kinEnergy,
126  G4int Z, G4int A)
127 {
128  G4DynamicParticle* aDP = new G4DynamicParticle(aParticle,G4ParticleMomentum(1.,0.,0.),
129  kinEnergy);
130  fTotalXsc = GetIsoCrossSection(aDP, Z, A);
131  delete aDP;
132 
133  return fInelasticXsc;
134 }
135 
137 
139  G4double kinEnergy,
140  G4int Z, G4double A)
141 {
142  G4DynamicParticle* aDP = new G4DynamicParticle(aParticle,G4ParticleMomentum(1.,0.,0.),
143  kinEnergy);
144  fTotalXsc = GetIsoCrossSection(aDP, Z, G4int(A));
145  delete aDP;
146 
147  return fInelasticXsc;
148 }
149 
151 
153  G4double kinEnergy,
154  G4int Z, G4double A)
155 {
156  G4DynamicParticle* aDP = new G4DynamicParticle(aParticle,G4ParticleMomentum(1.,0.,0.),
157  kinEnergy);
158  fTotalXsc = GetIsoCrossSection(aDP, Z, G4int(A));
159  delete aDP;
160 
161  return fElasticXsc;
162 }
163 
165 
167  G4double kinEnergy,
168  G4int Z, G4int A)
169 {
170  G4DynamicParticle* aDP = new G4DynamicParticle(aParticle,G4ParticleMomentum(1.,0.,0.),
171  kinEnergy);
172  fTotalXsc = GetIsoCrossSection(aDP, Z, A);
173  delete aDP;
174 
175  return fElasticXsc;
176 }
177 
179 
181  G4double kinEnergy,
182  G4int Z, G4int A)
183 {
184  G4DynamicParticle* aDP = new G4DynamicParticle(aParticle,G4ParticleMomentum(1.,0.,0.),
185  kinEnergy);
186  fTotalXsc = GetIsoCrossSection(aDP, Z, A);
187  delete aDP;
188  G4double ratio = 0.;
189 
190  if(fInelasticXsc > 0.)
191  {
192  ratio = (fInelasticXsc - fProductionXsc)/fInelasticXsc;
193  if(ratio < 0.) ratio = 0.;
194  }
195  return ratio;
196 }
197 
198 
199 
200 
202 
203 G4bool
205  G4int Z, G4int /*A*/,
206  const G4Element*,
207  const G4Material*)
208 {
209  G4bool applicable = false;
210  // G4int baryonNumber = aDP->GetDefinition()->GetBaryonNumber();
211  G4double kineticEnergy = aDP->GetKineticEnergy();
212 
213  const G4ParticleDefinition* theParticle = aDP->GetDefinition();
214 
215  if ( ( kineticEnergy >= fLowerLimit &&
216  Z > 1 && // >= He
217  ( theParticle == theAProton ||
218  theParticle == theGamma ||
219  theParticle == theKPlus ||
220  theParticle == theKMinus ||
221  theParticle == theK0L ||
222  theParticle == theK0S ||
223  theParticle == theSMinus ||
224  theParticle == theProton ||
225  theParticle == theNeutron ||
226  theParticle == thePiPlus ||
227  theParticle == thePiMinus ) ) ) applicable = true;
228 
229  return applicable;
230 }
231 
233 //
234 // Calculates total and inelastic Xsc, derives elastic as total - inelastic accordong to
235 // Glauber model with Gribov correction calculated in the dipole approximation on
236 // light cone. Gaussian density of point-like nucleons helps to calculate rest integrals of the model.
237 // [1] B.Z. Kopeliovich, nucl-th/0306044 + simplification above
238 
239 G4double
241  G4int Z, G4int A,
242  const G4Isotope*,
243  const G4Element*,
244  const G4Material*)
245 {
246  G4double xsection, sigma, cofInelastic, cofTotal, nucleusSquare, ratio;
247  G4double hpInXsc(0.), hnInXsc(0.);
248  G4double R = GetNucleusRadius(A);
249 
250  G4int N = A - Z; // number of neutrons
251  if (N < 0) N = 0;
252 
253  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
254 
255  if( theParticle == theProton ||
256  theParticle == theNeutron ||
257  theParticle == thePiPlus ||
258  theParticle == thePiMinus )
259  {
260  // sigma = GetHadronNucleonXscNS(aParticle, A, Z);
261 
262  sigma = Z*hnXsc->GetHadronNucleonXscNS(aParticle, theProton);
263 
264  hpInXsc = hnXsc->GetInelasticHadronNucleonXsc();
265 
266  sigma += N*hnXsc->GetHadronNucleonXscNS(aParticle, theNeutron);
267 
268  hnInXsc = hnXsc->GetInelasticHadronNucleonXsc();
269 
270  cofInelastic = 2.4;
271  cofTotal = 2.0;
272  }
273  else if( theParticle == theKPlus ||
274  theParticle == theKMinus ||
275  theParticle == theK0S ||
276  theParticle == theK0L )
277  {
278  sigma = GetKaonNucleonXscVector(aParticle, A, Z);
279  cofInelastic = 2.2;
280  cofTotal = 2.0;
281  R = 1.3*fermi;
282  R *= std::pow(G4double(A), 0.3333);
283  }
284  else
285  {
286  sigma = GetHadronNucleonXscNS(aParticle, A, Z);
287  cofInelastic = 2.2;
288  cofTotal = 2.0;
289  }
290  // cofInelastic = 2.0;
291 
292  if( A > 1 )
293  {
294  nucleusSquare = cofTotal*pi*R*R; // basically 2piRR
295  ratio = sigma/nucleusSquare;
296 
297  xsection = nucleusSquare*std::log( 1. + ratio );
298 
299  xsection *= GetParticleBarCorTot(theParticle, Z);
300 
301  fTotalXsc = xsection;
302 
303 
304 
305  fInelasticXsc = nucleusSquare*std::log( 1. + cofInelastic*ratio )/cofInelastic;
306 
307  fInelasticXsc *= GetParticleBarCorIn(theParticle, Z);
308 
309  fElasticXsc = fTotalXsc - fInelasticXsc;
310 
311  if(fElasticXsc < 0.) fElasticXsc = 0.;
312 
313  G4double difratio = ratio/(1.+ratio);
314 
315  fDiffractionXsc = 0.5*nucleusSquare*( difratio - std::log( 1. + difratio ) );
316 
317 
318  // sigma = GetHNinelasticXsc(aParticle, A, Z);
319 
320  sigma = Z*hpInXsc + N*hnInXsc;
321 
322  ratio = sigma/nucleusSquare;
323 
324  fProductionXsc = nucleusSquare*std::log( 1. + cofInelastic*ratio )/cofInelastic;
325 
326  if (fElasticXsc < 0.) fElasticXsc = 0.;
327  }
328  else // H
329  {
330  fTotalXsc = sigma;
331  xsection = sigma;
332 
333  if ( theParticle != theAProton )
334  {
335  sigma = GetHNinelasticXsc(aParticle, A, Z);
336  fInelasticXsc = sigma;
337  fElasticXsc = fTotalXsc - fInelasticXsc;
338  }
339  else
340  {
341  fElasticXsc = fTotalXsc - fInelasticXsc;
342  }
343  if (fElasticXsc < 0.) fElasticXsc = 0.;
344 
345  }
346  return xsection;
347 }
348 
350 //
351 // Return single-diffraction/inelastic cross-section ratio
352 
354 GetRatioSD(const G4DynamicParticle* aParticle, G4int A, G4int Z)
355 {
356  G4double sigma, cofInelastic, cofTotal, nucleusSquare, ratio;
357  G4double R = GetNucleusRadius(A);
358 
359  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
360 
361  if( theParticle == theProton ||
362  theParticle == theNeutron ||
363  theParticle == thePiPlus ||
364  theParticle == thePiMinus )
365  {
366  sigma = GetHadronNucleonXscNS(aParticle, A, Z);
367  cofInelastic = 2.4;
368  cofTotal = 2.0;
369  }
370  else
371  {
372  sigma = GetHadronNucleonXscNS(aParticle, A, Z);
373  cofInelastic = 2.2;
374  cofTotal = 2.0;
375  }
376  nucleusSquare = cofTotal*pi*R*R; // basically 2piRR
377  ratio = sigma/nucleusSquare;
378 
379  fInelasticXsc = nucleusSquare*std::log( 1. + cofInelastic*ratio )/cofInelastic;
380 
381  G4double difratio = ratio/(1.+ratio);
382 
383  fDiffractionXsc = 0.5*nucleusSquare*( difratio - std::log( 1. + difratio ) );
384 
385  if (fInelasticXsc > 0.) ratio = fDiffractionXsc/fInelasticXsc;
386  else ratio = 0.;
387 
388  return ratio;
389 }
390 
392 //
393 // Return suasi-elastic/inelastic cross-section ratio
394 
396 GetRatioQE(const G4DynamicParticle* aParticle, G4int A, G4int Z)
397 {
398  G4double sigma, cofInelastic, cofTotal, nucleusSquare, ratio;
399  G4double R = GetNucleusRadius(A);
400 
401  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
402 
403  if( theParticle == theProton ||
404  theParticle == theNeutron ||
405  theParticle == thePiPlus ||
406  theParticle == thePiMinus )
407  {
408  sigma = GetHadronNucleonXscNS(aParticle, A, Z);
409  cofInelastic = 2.4;
410  cofTotal = 2.0;
411  }
412  else
413  {
414  sigma = GetHadronNucleonXscNS(aParticle, A, Z);
415  cofInelastic = 2.2;
416  cofTotal = 2.0;
417  }
418  nucleusSquare = cofTotal*pi*R*R; // basically 2piRR
419  ratio = sigma/nucleusSquare;
420 
421  fInelasticXsc = nucleusSquare*std::log( 1. + cofInelastic*ratio )/cofInelastic;
422 
423  sigma = GetHNinelasticXsc(aParticle, A, Z);
424  ratio = sigma/nucleusSquare;
425 
426  fProductionXsc = nucleusSquare*std::log( 1. + cofInelastic*ratio )/cofInelastic;
427 
428  if (fInelasticXsc > fProductionXsc) ratio = (fInelasticXsc-fProductionXsc)/fInelasticXsc;
429  else ratio = 0.;
430  if ( ratio < 0. ) ratio = 0.;
431 
432  return ratio;
433 }
434 
436 //
437 // Returns hadron-nucleon Xsc according to differnt parametrisations:
438 // [2] E. Levin, hep-ph/9710546
439 // [3] U. Dersch, et al, hep-ex/9910052
440 // [4] M.J. Longo, et al, Phys.Rev.Lett. 33 (1974) 725
441 
442 G4double
444  const G4Element* anElement)
445 {
446  G4int At = G4lrint(anElement->GetN()); // number of nucleons
447  G4int Zt = G4lrint(anElement->GetZ()); // number of protons
448 
449  return GetHadronNucleonXsc(aParticle, At, Zt);
450 }
451 
453 //
454 // Returns hadron-nucleon Xsc according to differnt parametrisations:
455 // [2] E. Levin, hep-ph/9710546
456 // [3] U. Dersch, et al, hep-ex/9910052
457 // [4] M.J. Longo, et al, Phys.Rev.Lett. 33 (1974) 725
458 
459 G4double
461  G4int At, G4int /*Zt*/)
462 {
463  G4double xsection;
464 
465  //G4double targ_mass = G4NucleiProperties::GetNuclearMass(At, Zt);
466 
467  G4double targ_mass = 0.939*GeV; // ~mean neutron and proton ???
468 
469  G4double proj_mass = aParticle->GetMass();
470  G4double proj_momentum = aParticle->GetMomentum().mag();
471  G4double sMand = CalcMandelstamS ( proj_mass , targ_mass , proj_momentum );
472 
473  sMand /= GeV*GeV; // in GeV for parametrisation
474  proj_momentum /= GeV;
475 
476  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
477 
478  G4double aa = At;
479 
480  if(theParticle == theGamma)
481  {
482  xsection = aa*(0.0677*std::pow(sMand,0.0808) + 0.129*std::pow(sMand,-0.4525));
483  }
484  else if(theParticle == theNeutron) // as proton ???
485  {
486  xsection = aa*(21.70*std::pow(sMand,0.0808) + 56.08*std::pow(sMand,-0.4525));
487  }
488  else if(theParticle == theProton)
489  {
490  xsection = aa*(21.70*std::pow(sMand,0.0808) + 56.08*std::pow(sMand,-0.4525));
491  // xsection = At*( 49.51*std::pow(sMand,-0.097) + 0.314*std::log(sMand)*std::log(sMand) );
492  // xsection = At*( 38.4 + 0.85*std::abs(std::pow(log(sMand),1.47)) );
493  }
494  else if(theParticle == theAProton)
495  {
496  xsection = aa*( 21.70*std::pow(sMand,0.0808) + 98.39*std::pow(sMand,-0.4525));
497  }
498  else if(theParticle == thePiPlus)
499  {
500  xsection = aa*(13.63*std::pow(sMand,0.0808) + 27.56*std::pow(sMand,-0.4525));
501  }
502  else if(theParticle == thePiMinus)
503  {
504  // xsection = At*( 55.2*std::pow(sMand,-0.255) + 0.346*std::log(sMand)*std::log(sMand) );
505  xsection = aa*(13.63*std::pow(sMand,0.0808) + 36.02*std::pow(sMand,-0.4525));
506  }
507  else if(theParticle == theKPlus)
508  {
509  xsection = aa*(11.82*std::pow(sMand,0.0808) + 8.15*std::pow(sMand,-0.4525));
510  }
511  else if(theParticle == theKMinus)
512  {
513  xsection = aa*(11.82*std::pow(sMand,0.0808) + 26.36*std::pow(sMand,-0.4525));
514  }
515  else // as proton ???
516  {
517  xsection = aa*(21.70*std::pow(sMand,0.0808) + 56.08*std::pow(sMand,-0.4525));
518  }
519  xsection *= millibarn;
520  return xsection;
521 }
522 
523 
525 //
526 // Returns hadron-nucleon Xsc according to PDG parametrisation (2005):
527 // http://pdg.lbl.gov/2006/reviews/hadronicrpp.pdf
528 
529 G4double
531  const G4Element* anElement)
532 {
533  G4int At = G4lrint(anElement->GetN()); // number of nucleons
534  G4int Zt = G4lrint(anElement->GetZ()); // number of protons
535 
536  return GetHadronNucleonXscPDG(aParticle, At, Zt);
537 }
538 
539 
540 
541 
543 //
544 // Returns hadron-nucleon Xsc according to PDG parametrisation (2005):
545 // http://pdg.lbl.gov/2006/reviews/hadronicrpp.pdf
546 // At = number of nucleons, Zt = number of protons
547 
548 G4double
550  G4int At, G4int Zt)
551 {
552  G4double xsection;
553 
554  G4int Nt = At-Zt; // number of neutrons
555  if (Nt < 0) Nt = 0;
556 
557  G4double zz = Zt;
558  G4double aa = At;
559  G4double nn = Nt;
560 
562  GetIonTable()->GetIonMass(Zt, At);
563 
564  targ_mass = 0.939*GeV; // ~mean neutron and proton ???
565 
566  G4double proj_mass = aParticle->GetMass();
567  G4double proj_momentum = aParticle->GetMomentum().mag();
568 
569  G4double sMand = CalcMandelstamS ( proj_mass , targ_mass , proj_momentum );
570 
571  sMand /= GeV*GeV; // in GeV for parametrisation
572 
573  // General PDG fit constants
574 
575  G4double s0 = 5.38*5.38; // in Gev^2
576  G4double eta1 = 0.458;
577  G4double eta2 = 0.458;
578  G4double B = 0.308;
579 
580 
581  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
582 
583 
584  if(theParticle == theNeutron) // proton-neutron fit
585  {
586  xsection = zz*( 35.80 + B*std::pow(std::log(sMand/s0),2.)
587  + 40.15*std::pow(sMand,-eta1) - 30.*std::pow(sMand,-eta2));
588  xsection += nn*( 35.45 + B*std::pow(std::log(sMand/s0),2.)
589  + 42.53*std::pow(sMand,-eta1) - 33.34*std::pow(sMand,-eta2)); // pp for nn
590  }
591  else if(theParticle == theProton)
592  {
593 
594  xsection = zz*( 35.45 + B*std::pow(std::log(sMand/s0),2.)
595  + 42.53*std::pow(sMand,-eta1) - 33.34*std::pow(sMand,-eta2));
596 
597  xsection += nn*( 35.80 + B*std::pow(std::log(sMand/s0),2.)
598  + 40.15*std::pow(sMand,-eta1) - 30.*std::pow(sMand,-eta2));
599  }
600  else if(theParticle == theAProton)
601  {
602  xsection = zz*( 35.45 + B*std::pow(std::log(sMand/s0),2.)
603  + 42.53*std::pow(sMand,-eta1) + 33.34*std::pow(sMand,-eta2));
604 
605  xsection += nn*( 35.80 + B*std::pow(std::log(sMand/s0),2.)
606  + 40.15*std::pow(sMand,-eta1) + 30.*std::pow(sMand,-eta2));
607  }
608  else if(theParticle == thePiPlus)
609  {
610  xsection = aa*( 20.86 + B*std::pow(std::log(sMand/s0),2.)
611  + 19.24*std::pow(sMand,-eta1) - 6.03*std::pow(sMand,-eta2));
612  }
613  else if(theParticle == thePiMinus)
614  {
615  xsection = aa*( 20.86 + B*std::pow(std::log(sMand/s0),2.)
616  + 19.24*std::pow(sMand,-eta1) + 6.03*std::pow(sMand,-eta2));
617  }
618  else if(theParticle == theKPlus || theParticle == theK0L )
619  {
620  xsection = zz*( 17.91 + B*std::pow(std::log(sMand/s0),2.)
621  + 7.14*std::pow(sMand,-eta1) - 13.45*std::pow(sMand,-eta2));
622 
623  xsection += nn*( 17.87 + B*std::pow(std::log(sMand/s0),2.)
624  + 5.17*std::pow(sMand,-eta1) - 7.23*std::pow(sMand,-eta2));
625  }
626  else if(theParticle == theKMinus || theParticle == theK0S )
627  {
628  xsection = zz*( 17.91 + B*std::pow(std::log(sMand/s0),2.)
629  + 7.14*std::pow(sMand,-eta1) + 13.45*std::pow(sMand,-eta2));
630 
631  xsection += nn*( 17.87 + B*std::pow(std::log(sMand/s0),2.)
632  + 5.17*std::pow(sMand,-eta1) + 7.23*std::pow(sMand,-eta2));
633  }
634  else if(theParticle == theSMinus)
635  {
636  xsection = aa*( 35.20 + B*std::pow(std::log(sMand/s0),2.)
637  - 199.*std::pow(sMand,-eta1) + 264.*std::pow(sMand,-eta2));
638  }
639  else if(theParticle == theGamma) // modify later on
640  {
641  xsection = aa*( 0.0 + B*std::pow(std::log(sMand/s0),2.)
642  + 0.032*std::pow(sMand,-eta1) - 0.0*std::pow(sMand,-eta2));
643 
644  }
645  else // as proton ???
646  {
647  xsection = zz*( 35.45 + B*std::pow(std::log(sMand/s0),2.)
648  + 42.53*std::pow(sMand,-eta1) - 33.34*std::pow(sMand,-eta2));
649 
650  xsection += nn*( 35.80 + B*std::pow(std::log(sMand/s0),2.)
651  + 40.15*std::pow(sMand,-eta1) - 30.*std::pow(sMand,-eta2));
652  }
653  xsection *= millibarn; // parametrised in mb
654  return xsection;
655 }
656 
657 
659 //
660 // Returns hadron-nucleon cross-section based on N. Starkov parametrisation of
661 // data from mainly http://wwwppds.ihep.su:8001/c5-6A.html database
662 
663 G4double
665  const G4Element* anElement)
666 {
667  G4int At = G4lrint(anElement->GetN()); // number of nucleons
668  G4int Zt = G4lrint(anElement->GetZ()); // number of protons
669 
670  return GetHadronNucleonXscNS(aParticle, At, Zt);
671 }
672 
673 
674 
675 
677 //
678 // Returns hadron-nucleon cross-section based on N. Starkov parametrisation of
679 // data from mainly http://wwwppds.ihep.su:8001/c5-6A.html database
680 
681 G4double
683  G4int At, G4int Zt)
684 {
685  G4double xsection(0);
686  // G4double Delta; DHW 19 May 2011: variable set but not used
687  G4double A0, B0;
688  G4double hpXscv(0);
689  G4double hnXscv(0);
690 
691  G4int Nt = At-Zt; // number of neutrons
692  if (Nt < 0) Nt = 0;
693 
694  G4double aa = At;
695  G4double zz = Zt;
696  G4double nn = Nt;
697 
699  GetIonTable()->GetIonMass(Zt, At);
700 
701  targ_mass = 0.939*GeV; // ~mean neutron and proton ???
702 
703  G4double proj_mass = aParticle->GetMass();
704  G4double proj_energy = aParticle->GetTotalEnergy();
705  G4double proj_momentum = aParticle->GetMomentum().mag();
706 
707  G4double sMand = CalcMandelstamS ( proj_mass , targ_mass , proj_momentum );
708 
709  sMand /= GeV*GeV; // in GeV for parametrisation
710  proj_momentum /= GeV;
711  proj_energy /= GeV;
712  proj_mass /= GeV;
713 
714  // General PDG fit constants
715 
716  G4double s0 = 5.38*5.38; // in Gev^2
717  G4double eta1 = 0.458;
718  G4double eta2 = 0.458;
719  G4double B = 0.308;
720 
721 
722  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
723 
724 
725  if(theParticle == theNeutron)
726  {
727  if( proj_momentum >= 373.)
728  {
729  return GetHadronNucleonXscPDG(aParticle,At,Zt);
730  }
731  else if( proj_momentum >= 10.)
732  // if( proj_momentum >= 2.)
733  {
734  // Delta = 1.; // DHW 19 May 2011: variable set but not used
735  // if( proj_energy < 40. ) Delta = 0.916+0.0021*proj_energy;
736 
737  if(proj_momentum >= 10.)
738  {
739  B0 = 7.5;
740  A0 = 100. - B0*std::log(3.0e7);
741 
742  xsection = A0 + B0*std::log(proj_energy) - 11
743  + 103*std::pow(2*0.93827*proj_energy + proj_mass*proj_mass+
744  0.93827*0.93827,-0.165); // mb
745  }
746  xsection *= zz + nn;
747  }
748  else
749  {
750  // nn to be pp
751 
752  if( proj_momentum < 0.73 )
753  {
754  hnXscv = 23 + 50*( std::pow( std::log(0.73/proj_momentum), 3.5 ) );
755  }
756  else if( proj_momentum < 1.05 )
757  {
758  hnXscv = 23 + 40*(std::log(proj_momentum/0.73))*
759  (std::log(proj_momentum/0.73));
760  }
761  else // if( proj_momentum < 10. )
762  {
763  hnXscv = 39.0+
764  75*(proj_momentum - 1.2)/(std::pow(proj_momentum,3.0) + 0.15);
765  }
766  // pn to be np
767 
768  if( proj_momentum < 0.8 )
769  {
770  hpXscv = 33+30*std::pow(std::log(proj_momentum/1.3),4.0);
771  }
772  else if( proj_momentum < 1.4 )
773  {
774  hpXscv = 33+30*std::pow(std::log(proj_momentum/0.95),2.0);
775  }
776  else // if( proj_momentum < 10. )
777  {
778  hpXscv = 33.3+
779  20.8*(std::pow(proj_momentum,2.0)-1.35)/
780  (std::pow(proj_momentum,2.50)+0.95);
781  }
782  xsection = hpXscv*zz + hnXscv*nn;
783  }
784  }
785  else if(theParticle == theProton)
786  {
787  if( proj_momentum >= 373.)
788  {
789  return GetHadronNucleonXscPDG(aParticle,At,Zt);
790  }
791  else if( proj_momentum >= 10.)
792  // if( proj_momentum >= 2.)
793  {
794  // Delta = 1.; DHW 19 May 2011: variable set but not used
795  // if( proj_energy < 40. ) Delta = 0.916+0.0021*proj_energy;
796 
797  if(proj_momentum >= 10.)
798  {
799  B0 = 7.5;
800  A0 = 100. - B0*std::log(3.0e7);
801 
802  xsection = A0 + B0*std::log(proj_energy) - 11
803  + 103*std::pow(2*0.93827*proj_energy + proj_mass*proj_mass+
804  0.93827*0.93827,-0.165); // mb
805  }
806  xsection *= zz + nn;
807  }
808  else
809  {
810  // pp
811 
812  if( proj_momentum < 0.73 )
813  {
814  hpXscv = 23 + 50*( std::pow( std::log(0.73/proj_momentum), 3.5 ) );
815  }
816  else if( proj_momentum < 1.05 )
817  {
818  hpXscv = 23 + 40*(std::log(proj_momentum/0.73))*
819  (std::log(proj_momentum/0.73));
820  }
821  else // if( proj_momentum < 10. )
822  {
823  hpXscv = 39.0+
824  75*(proj_momentum - 1.2)/(std::pow(proj_momentum,3.0) + 0.15);
825  }
826  // pn to be np
827 
828  if( proj_momentum < 0.8 )
829  {
830  hnXscv = 33+30*std::pow(std::log(proj_momentum/1.3),4.0);
831  }
832  else if( proj_momentum < 1.4 )
833  {
834  hnXscv = 33+30*std::pow(std::log(proj_momentum/0.95),2.0);
835  }
836  else // if( proj_momentum < 10. )
837  {
838  hnXscv = 33.3+
839  20.8*(std::pow(proj_momentum,2.0)-1.35)/
840  (std::pow(proj_momentum,2.50)+0.95);
841  }
842  xsection = hpXscv*zz + hnXscv*nn;
843  // xsection = hpXscv*(Zt + Nt);
844  // xsection = hnXscv*(Zt + Nt);
845  }
846  // xsection *= 0.95;
847  }
848  else if( theParticle == theAProton )
849  {
850  // xsection = Zt*( 35.45 + B*std::pow(std::log(sMand/s0),2.)
851  // + 42.53*std::pow(sMand,-eta1) + 33.34*std::pow(sMand,-eta2));
852 
853  // xsection += Nt*( 35.80 + B*std::pow(std::log(sMand/s0),2.)
854  // + 40.15*std::pow(sMand,-eta1) + 30.*std::pow(sMand,-eta2));
855 
856  G4double logP = std::log(proj_momentum);
857 
858  if( proj_momentum <= 1.0 )
859  {
860  xsection = zz*(65.55 + 53.84/(proj_momentum+1.e-6) );
861  }
862  else
863  {
864  xsection = zz*( 41.1 + 77.2*std::pow( proj_momentum, -0.68)
865  + 0.293*logP*logP - 1.82*logP );
866  }
867  if ( nn > 0.)
868  {
869  xsection += nn*( 41.9 + 96.2*std::pow( proj_momentum, -0.99) - 0.154*logP);
870  }
871  else // H
872  {
873  fInelasticXsc = 38.0 + 38.0*std::pow( proj_momentum, -0.96)
874  - 0.169*logP*logP;
875  fInelasticXsc *= millibarn;
876  }
877  }
878  else if( theParticle == thePiPlus )
879  {
880  if(proj_momentum < 0.4)
881  {
882  G4double Ex3 = 180*std::exp(-(proj_momentum-0.29)*(proj_momentum-0.29)/0.085/0.085);
883  hpXscv = Ex3+20.0;
884  }
885  else if( proj_momentum < 1.15 )
886  {
887  G4double Ex4 = 88*(std::log(proj_momentum/0.75))*(std::log(proj_momentum/0.75));
888  hpXscv = Ex4+14.0;
889  }
890  else if(proj_momentum < 3.5)
891  {
892  G4double Ex1 = 3.2*std::exp(-(proj_momentum-2.55)*(proj_momentum-2.55)/0.55/0.55);
893  G4double Ex2 = 12*std::exp(-(proj_momentum-1.47)*(proj_momentum-1.47)/0.225/0.225);
894  hpXscv = Ex1+Ex2+27.5;
895  }
896  else // if(proj_momentum > 3.5) // mb
897  {
898  hpXscv = 10.6+2.*std::log(proj_energy)+25*std::pow(proj_energy,-0.43);
899  }
900  // pi+n = pi-p??
901 
902  if(proj_momentum < 0.37)
903  {
904  hnXscv = 28.0 + 40*std::exp(-(proj_momentum-0.29)*(proj_momentum-0.29)/0.07/0.07);
905  }
906  else if(proj_momentum<0.65)
907  {
908  hnXscv = 26+110*(std::log(proj_momentum/0.48))*(std::log(proj_momentum/0.48));
909  }
910  else if(proj_momentum<1.3)
911  {
912  hnXscv = 36.1+
913  10*std::exp(-(proj_momentum-0.72)*(proj_momentum-0.72)/0.06/0.06)+
914  24*std::exp(-(proj_momentum-1.015)*(proj_momentum-1.015)/0.075/0.075);
915  }
916  else if(proj_momentum<3.0)
917  {
918  hnXscv = 36.1+0.079-4.313*std::log(proj_momentum)+
919  3*std::exp(-(proj_momentum-2.1)*(proj_momentum-2.1)/0.4/0.4)+
920  1.5*std::exp(-(proj_momentum-1.4)*(proj_momentum-1.4)/0.12/0.12);
921  }
922  else // mb
923  {
924  hnXscv = 10.6+2*std::log(proj_energy)+30*std::pow(proj_energy,-0.43);
925  }
926  xsection = hpXscv*zz + hnXscv*nn;
927  }
928  else if(theParticle == thePiMinus)
929  {
930  // pi-n = pi+p??
931 
932  if(proj_momentum < 0.4)
933  {
934  G4double Ex3 = 180*std::exp(-(proj_momentum-0.29)*(proj_momentum-0.29)/0.085/0.085);
935  hnXscv = Ex3+20.0;
936  }
937  else if(proj_momentum < 1.15)
938  {
939  G4double Ex4 = 88*(std::log(proj_momentum/0.75))*(std::log(proj_momentum/0.75));
940  hnXscv = Ex4+14.0;
941  }
942  else if(proj_momentum < 3.5)
943  {
944  G4double Ex1 = 3.2*std::exp(-(proj_momentum-2.55)*(proj_momentum-2.55)/0.55/0.55);
945  G4double Ex2 = 12*std::exp(-(proj_momentum-1.47)*(proj_momentum-1.47)/0.225/0.225);
946  hnXscv = Ex1+Ex2+27.5;
947  }
948  else // if(proj_momentum > 3.5) // mb
949  {
950  hnXscv = 10.6+2.*std::log(proj_energy)+25*std::pow(proj_energy,-0.43);
951  }
952  // pi-p
953 
954  if(proj_momentum < 0.37)
955  {
956  hpXscv = 28.0 + 40*std::exp(-(proj_momentum-0.29)*(proj_momentum-0.29)/0.07/0.07);
957  }
958  else if(proj_momentum<0.65)
959  {
960  hpXscv = 26+110*(std::log(proj_momentum/0.48))*(std::log(proj_momentum/0.48));
961  }
962  else if(proj_momentum<1.3)
963  {
964  hpXscv = 36.1+
965  10*std::exp(-(proj_momentum-0.72)*(proj_momentum-0.72)/0.06/0.06)+
966  24*std::exp(-(proj_momentum-1.015)*(proj_momentum-1.015)/0.075/0.075);
967  }
968  else if(proj_momentum<3.0)
969  {
970  hpXscv = 36.1+0.079-4.313*std::log(proj_momentum)+
971  3*std::exp(-(proj_momentum-2.1)*(proj_momentum-2.1)/0.4/0.4)+
972  1.5*std::exp(-(proj_momentum-1.4)*(proj_momentum-1.4)/0.12/0.12);
973  }
974  else // mb
975  {
976  hpXscv = 10.6+2*std::log(proj_energy)+30*std::pow(proj_energy,-0.43);
977  }
978  xsection = hpXscv*zz + hnXscv*nn;
979  }
980  else if(theParticle == theKPlus)
981  {
982  xsection = zz*( 17.91 + B*std::pow(std::log(sMand/s0),2.)
983  + 7.14*std::pow(sMand,-eta1) - 13.45*std::pow(sMand,-eta2));
984 
985  xsection += nn*( 17.87 + B*std::pow(std::log(sMand/s0),2.)
986  + 5.17*std::pow(sMand,-eta1) - 7.23*std::pow(sMand,-eta2));
987  }
988  else if(theParticle == theKMinus)
989  {
990  xsection = zz*( 17.91 + B*std::pow(std::log(sMand/s0),2.)
991  + 7.14*std::pow(sMand,-eta1) + 13.45*std::pow(sMand,-eta2));
992 
993  xsection += nn*( 17.87 + B*std::pow(std::log(sMand/s0),2.)
994  + 5.17*std::pow(sMand,-eta1) + 7.23*std::pow(sMand,-eta2));
995  }
996  else if(theParticle == theSMinus)
997  {
998  xsection = aa*( 35.20 + B*std::pow(std::log(sMand/s0),2.)
999  - 199.*std::pow(sMand,-eta1) + 264.*std::pow(sMand,-eta2));
1000  }
1001  else if(theParticle == theGamma) // modify later on
1002  {
1003  xsection = aa*( 0.0 + B*std::pow(std::log(sMand/s0),2.)
1004  + 0.032*std::pow(sMand,-eta1) - 0.0*std::pow(sMand,-eta2));
1005 
1006  }
1007  else // as proton ???
1008  {
1009  xsection = zz*( 35.45 + B*std::pow(std::log(sMand/s0),2.)
1010  + 42.53*std::pow(sMand,-eta1) - 33.34*std::pow(sMand,-eta2));
1011 
1012  xsection += nn*( 35.80 + B*std::pow(std::log(sMand/s0),2.)
1013  + 40.15*std::pow(sMand,-eta1) - 30.*std::pow(sMand,-eta2));
1014  }
1015  xsection *= millibarn; // parametrised in mb
1016  return xsection;
1017 }
1018 
1019 G4double
1021  G4int At, G4int Zt)
1022 {
1023  G4double Tkin, logTkin, xsc, xscP, xscN;
1024  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
1025 
1026  G4int Nt = At-Zt; // number of neutrons
1027  if (Nt < 0) Nt = 0;
1028 
1029  Tkin = aParticle->GetKineticEnergy(); // Tkin in MeV
1030 
1031  if( Tkin > 70*GeV ) return GetHadronNucleonXscPDG(aParticle,At,Zt);
1032 
1033  logTkin = std::log(Tkin); // Tkin in MeV!!!
1034 
1035  if( theParticle == theKPlus )
1036  {
1037  xscP = hnXsc->GetKpProtonTotXscVector(logTkin);
1038  xscN = hnXsc->GetKpNeutronTotXscVector(logTkin);
1039  }
1040  else if( theParticle == theKMinus )
1041  {
1042  xscP = hnXsc->GetKmProtonTotXscVector(logTkin);
1043  xscN = hnXsc->GetKmNeutronTotXscVector(logTkin);
1044  }
1045  else // K-zero as half of K+ and K-
1046  {
1047  xscP = (hnXsc->GetKpProtonTotXscVector(logTkin)+hnXsc->GetKmProtonTotXscVector(logTkin))*0.5;
1048  xscN = (hnXsc->GetKpNeutronTotXscVector(logTkin)+hnXsc->GetKmNeutronTotXscVector(logTkin))*0.5;
1049  }
1050  xsc = xscP*Zt + xscN*Nt;
1051  return xsc;
1052 }
1054 //
1055 // Returns hadron-nucleon inelastic cross-section based on proper parametrisation
1056 
1057 G4double
1059  const G4Element* anElement)
1060 {
1061  G4int At = G4lrint(anElement->GetN()); // number of nucleons
1062  G4int Zt = G4lrint(anElement->GetZ()); // number of protons
1063 
1064  return GetHNinelasticXsc(aParticle, At, Zt);
1065 }
1066 
1068 //
1069 // Returns hadron-nucleon inelastic cross-section based on FTF-parametrisation
1070 
1071 G4double
1073  G4int At, G4int Zt)
1074 {
1075  G4ParticleDefinition* hadron = aParticle->GetDefinition();
1076  G4double sumInelastic;
1077  G4int Nt = At - Zt;
1078  if(Nt < 0) Nt = 0;
1079 
1080  if( hadron == theKPlus )
1081  {
1082  sumInelastic = GetHNinelasticXscVU(aParticle, At, Zt);
1083  }
1084  else
1085  {
1086  //sumInelastic = Zt*GetHadronNucleonXscMK(aParticle, theProton);
1087  // sumInelastic += Nt*GetHadronNucleonXscMK(aParticle, theNeutron);
1088  sumInelastic = G4double(Zt)*GetHadronNucleonXscNS(aParticle, 1, 1);
1089  sumInelastic += G4double(Nt)*GetHadronNucleonXscNS(aParticle, 1, 0);
1090  }
1091  return sumInelastic;
1092 }
1093 
1094 
1096 //
1097 // Returns hadron-nucleon inelastic cross-section based on FTF-parametrisation
1098 
1099 G4double
1101  G4int At, G4int Zt)
1102 {
1103  G4int PDGcode = aParticle->GetDefinition()->GetPDGEncoding();
1104  G4int absPDGcode = std::abs(PDGcode);
1105 
1106  G4double Elab = aParticle->GetTotalEnergy();
1107  // (s - 2*0.88*GeV*GeV)/(2*0.939*GeV)/GeV;
1108  G4double Plab = aParticle->GetMomentum().mag();
1109  // std::sqrt(Elab * Elab - 0.88);
1110 
1111  Elab /= GeV;
1112  Plab /= GeV;
1113 
1114  G4double LogPlab = std::log( Plab );
1115  G4double sqrLogPlab = LogPlab * LogPlab;
1116 
1117  //G4cout<<"Plab = "<<Plab<<G4endl;
1118 
1119  G4double NumberOfTargetProtons = G4double(Zt);
1120  G4double NumberOfTargetNucleons = G4double(At);
1121  G4double NumberOfTargetNeutrons = NumberOfTargetNucleons - NumberOfTargetProtons;
1122 
1123  if(NumberOfTargetNeutrons < 0.0) NumberOfTargetNeutrons = 0.0;
1124 
1125  G4double Xtotal, Xelastic, Xinelastic;
1126 
1127  if( absPDGcode > 1000 ) //------Projectile is baryon --------
1128  {
1129  G4double XtotPP = 48.0 + 0. *std::pow(Plab, 0. ) +
1130  0.522*sqrLogPlab - 4.51*LogPlab;
1131 
1132  G4double XtotPN = 47.3 + 0. *std::pow(Plab, 0. ) +
1133  0.513*sqrLogPlab - 4.27*LogPlab;
1134 
1135  G4double XelPP = 11.9 + 26.9*std::pow(Plab,-1.21) +
1136  0.169*sqrLogPlab - 1.85*LogPlab;
1137 
1138  G4double XelPN = 11.9 + 26.9*std::pow(Plab,-1.21) +
1139  0.169*sqrLogPlab - 1.85*LogPlab;
1140 
1141  Xtotal = (NumberOfTargetProtons * XtotPP +
1142  NumberOfTargetNeutrons * XtotPN);
1143 
1144  Xelastic = (NumberOfTargetProtons * XelPP +
1145  NumberOfTargetNeutrons * XelPN);
1146  }
1147  else if( PDGcode == 211 ) //------Projectile is PionPlus -------
1148  {
1149  G4double XtotPiP = 16.4 + 19.3 *std::pow(Plab,-0.42) +
1150  0.19 *sqrLogPlab - 0.0 *LogPlab;
1151 
1152  G4double XtotPiN = 33.0 + 14.0 *std::pow(Plab,-1.36) +
1153  0.456*sqrLogPlab - 4.03*LogPlab;
1154 
1155  G4double XelPiP = 0.0 + 11.4*std::pow(Plab,-0.40) +
1156  0.079*sqrLogPlab - 0.0 *LogPlab;
1157 
1158  G4double XelPiN = 1.76 + 11.2*std::pow(Plab,-0.64) +
1159  0.043*sqrLogPlab - 0.0 *LogPlab;
1160 
1161  Xtotal = ( NumberOfTargetProtons * XtotPiP +
1162  NumberOfTargetNeutrons * XtotPiN );
1163 
1164  Xelastic = ( NumberOfTargetProtons * XelPiP +
1165  NumberOfTargetNeutrons * XelPiN );
1166  }
1167  else if( PDGcode == -211 ) //------Projectile is PionMinus -------
1168  {
1169  G4double XtotPiP = 33.0 + 14.0 *std::pow(Plab,-1.36) +
1170  0.456*sqrLogPlab - 4.03*LogPlab;
1171 
1172  G4double XtotPiN = 16.4 + 19.3 *std::pow(Plab,-0.42) +
1173  0.19 *sqrLogPlab - 0.0 *LogPlab;
1174 
1175  G4double XelPiP = 1.76 + 11.2*std::pow(Plab,-0.64) +
1176  0.043*sqrLogPlab - 0.0 *LogPlab;
1177 
1178  G4double XelPiN = 0.0 + 11.4*std::pow(Plab,-0.40) +
1179  0.079*sqrLogPlab - 0.0 *LogPlab;
1180 
1181  Xtotal = ( NumberOfTargetProtons * XtotPiP +
1182  NumberOfTargetNeutrons * XtotPiN );
1183 
1184  Xelastic = ( NumberOfTargetProtons * XelPiP +
1185  NumberOfTargetNeutrons * XelPiN );
1186  }
1187  else if( PDGcode == 111 ) //------Projectile is PionZero -------
1188  {
1189  G4double XtotPiP =(16.4 + 19.3 *std::pow(Plab,-0.42) +
1190  0.19 *sqrLogPlab - 0.0 *LogPlab + //Pi+
1191  33.0 + 14.0 *std::pow(Plab,-1.36) +
1192  0.456*sqrLogPlab - 4.03*LogPlab)/2; //Pi-
1193 
1194  G4double XtotPiN =(33.0 + 14.0 *std::pow(Plab,-1.36) +
1195  0.456*sqrLogPlab - 4.03*LogPlab + //Pi+
1196  16.4 + 19.3 *std::pow(Plab,-0.42) +
1197  0.19 *sqrLogPlab - 0.0 *LogPlab)/2; //Pi-
1198 
1199  G4double XelPiP =( 0.0 + 11.4*std::pow(Plab,-0.40) +
1200  0.079*sqrLogPlab - 0.0 *LogPlab + //Pi+
1201  1.76 + 11.2*std::pow(Plab,-0.64) +
1202  0.043*sqrLogPlab - 0.0 *LogPlab)/2; //Pi-
1203 
1204  G4double XelPiN =( 1.76 + 11.2*std::pow(Plab,-0.64) +
1205  0.043*sqrLogPlab - 0.0 *LogPlab + //Pi+
1206  0.0 + 11.4*std::pow(Plab,-0.40) +
1207  0.079*sqrLogPlab - 0.0 *LogPlab)/2; //Pi-
1208 
1209  Xtotal = ( NumberOfTargetProtons * XtotPiP +
1210  NumberOfTargetNeutrons * XtotPiN );
1211 
1212  Xelastic = ( NumberOfTargetProtons * XelPiP +
1213  NumberOfTargetNeutrons * XelPiN );
1214  }
1215  else if( PDGcode == 321 ) //------Projectile is KaonPlus -------
1216  {
1217  G4double XtotKP = 18.1 + 0. *std::pow(Plab, 0. ) +
1218  0.26 *sqrLogPlab - 1.0 *LogPlab;
1219  G4double XtotKN = 18.7 + 0. *std::pow(Plab, 0. ) +
1220  0.21 *sqrLogPlab - 0.89*LogPlab;
1221 
1222  G4double XelKP = 5.0 + 8.1*std::pow(Plab,-1.8 ) +
1223  0.16 *sqrLogPlab - 1.3 *LogPlab;
1224 
1225  G4double XelKN = 7.3 + 0. *std::pow(Plab,-0. ) +
1226  0.29 *sqrLogPlab - 2.4 *LogPlab;
1227 
1228  Xtotal = ( NumberOfTargetProtons * XtotKP +
1229  NumberOfTargetNeutrons * XtotKN );
1230 
1231  Xelastic = ( NumberOfTargetProtons * XelKP +
1232  NumberOfTargetNeutrons * XelKN );
1233  }
1234  else if( PDGcode ==-321 ) //------Projectile is KaonMinus ------
1235  {
1236  G4double XtotKP = 32.1 + 0. *std::pow(Plab, 0. ) +
1237  0.66 *sqrLogPlab - 5.6 *LogPlab;
1238  G4double XtotKN = 25.2 + 0. *std::pow(Plab, 0. ) +
1239  0.38 *sqrLogPlab - 2.9 *LogPlab;
1240 
1241  G4double XelKP = 7.3 + 0. *std::pow(Plab,-0. ) +
1242  0.29 *sqrLogPlab - 2.4 *LogPlab;
1243 
1244  G4double XelKN = 5.0 + 8.1*std::pow(Plab,-1.8 ) +
1245  0.16 *sqrLogPlab - 1.3 *LogPlab;
1246 
1247  Xtotal = ( NumberOfTargetProtons * XtotKP +
1248  NumberOfTargetNeutrons * XtotKN );
1249 
1250  Xelastic = ( NumberOfTargetProtons * XelKP +
1251  NumberOfTargetNeutrons * XelKN );
1252  }
1253  else if( PDGcode == 311 ) //------Projectile is KaonZero ------
1254  {
1255  G4double XtotKP = ( 18.1 + 0. *std::pow(Plab, 0. ) +
1256  0.26 *sqrLogPlab - 1.0 *LogPlab + //K+
1257  32.1 + 0. *std::pow(Plab, 0. ) +
1258  0.66 *sqrLogPlab - 5.6 *LogPlab)/2; //K-
1259 
1260  G4double XtotKN = ( 18.7 + 0. *std::pow(Plab, 0. ) +
1261  0.21 *sqrLogPlab - 0.89*LogPlab + //K+
1262  25.2 + 0. *std::pow(Plab, 0. ) +
1263  0.38 *sqrLogPlab - 2.9 *LogPlab)/2; //K-
1264 
1265  G4double XelKP = ( 5.0 + 8.1*std::pow(Plab,-1.8 )
1266  + 0.16 *sqrLogPlab - 1.3 *LogPlab + //K+
1267  7.3 + 0. *std::pow(Plab,-0. ) +
1268  0.29 *sqrLogPlab - 2.4 *LogPlab)/2; //K-
1269 
1270  G4double XelKN = ( 7.3 + 0. *std::pow(Plab,-0. ) +
1271  0.29 *sqrLogPlab - 2.4 *LogPlab + //K+
1272  5.0 + 8.1*std::pow(Plab,-1.8 ) +
1273  0.16 *sqrLogPlab - 1.3 *LogPlab)/2; //K-
1274 
1275  Xtotal = ( NumberOfTargetProtons * XtotKP +
1276  NumberOfTargetNeutrons * XtotKN );
1277 
1278  Xelastic = ( NumberOfTargetProtons * XelKP +
1279  NumberOfTargetNeutrons * XelKN );
1280  }
1281  else //------Projectile is undefined, Nucleon assumed
1282  {
1283  G4double XtotPP = 48.0 + 0. *std::pow(Plab, 0. ) +
1284  0.522*sqrLogPlab - 4.51*LogPlab;
1285 
1286  G4double XtotPN = 47.3 + 0. *std::pow(Plab, 0. ) +
1287  0.513*sqrLogPlab - 4.27*LogPlab;
1288 
1289  G4double XelPP = 11.9 + 26.9*std::pow(Plab,-1.21) +
1290  0.169*sqrLogPlab - 1.85*LogPlab;
1291  G4double XelPN = 11.9 + 26.9*std::pow(Plab,-1.21) +
1292  0.169*sqrLogPlab - 1.85*LogPlab;
1293 
1294  Xtotal = ( NumberOfTargetProtons * XtotPP +
1295  NumberOfTargetNeutrons * XtotPN );
1296 
1297  Xelastic = ( NumberOfTargetProtons * XelPP +
1298  NumberOfTargetNeutrons * XelPN );
1299  }
1300  Xinelastic = Xtotal - Xelastic;
1301 
1302  if( Xinelastic < 0.) Xinelastic = 0.;
1303 
1304  return Xinelastic*= millibarn;
1305 }
1306 
1308 //
1309 //
1310 
1311 G4double
1313  const G4Element* anElement)
1314 {
1315  G4int At = G4lrint(anElement->GetN());
1316  G4double oneThird = 1.0/3.0;
1317  G4double cubicrAt = std::pow(G4double(At), oneThird);
1318 
1319  G4double R; // = fRadiusConst*cubicrAt;
1320  /*
1321  G4double tmp = std::pow( cubicrAt-1., 3.);
1322  tmp += At;
1323  tmp *= 0.5;
1324 
1325  if (At > 20.) // 20.
1326  {
1327  R = fRadiusConst*std::pow (tmp, oneThird);
1328  }
1329  else
1330  {
1331  R = fRadiusConst*cubicrAt;
1332  }
1333  */
1334 
1335  R = fRadiusConst*cubicrAt;
1336 
1337  G4double meanA = 21.;
1338 
1339  G4double tauA1 = 40.;
1340  G4double tauA2 = 10.;
1341  G4double tauA3 = 5.;
1342 
1343  G4double a1 = 0.85;
1344  G4double b1 = 1. - a1;
1345 
1346  G4double b2 = 0.3;
1347  G4double b3 = 4.;
1348 
1349  if (At > 20) // 20.
1350  {
1351  R *= ( a1 + b1*std::exp( -(At - meanA)/tauA1) );
1352  }
1353  else if (At > 3)
1354  {
1355  R *= ( 1.0 + b2*( 1. - std::exp( (At - meanA)/tauA2) ) );
1356  }
1357  else
1358  {
1359  R *= ( 1.0 + b3*( 1. - std::exp( (At - meanA)/tauA3) ) );
1360  }
1361  return R;
1362 
1363 }
1365 //
1366 //
1367 
1368 G4double
1370 {
1371  G4double oneThird = 1.0/3.0;
1372  G4double cubicrAt = std::pow(G4double(At), oneThird);
1373 
1374  G4double R; // = fRadiusConst*cubicrAt;
1375 
1376  /*
1377  G4double tmp = std::pow( cubicrAt-1., 3.);
1378  tmp += At;
1379  tmp *= 0.5;
1380 
1381  if (At > 20.)
1382  {
1383  R = fRadiusConst*std::pow (tmp, oneThird);
1384  }
1385  else
1386  {
1387  R = fRadiusConst*cubicrAt;
1388  }
1389  */
1390 
1391  R = fRadiusConst*cubicrAt;
1392 
1393  G4double meanA = 20.;
1394  G4double tauA = 20.;
1395 
1396  if (At > 20) // 20.
1397  {
1398  R *= ( 0.8 + 0.2*std::exp( -(G4double(At) - meanA)/tauA) );
1399  }
1400  else
1401  {
1402  R *= ( 1.0 + 0.1*( 1. - std::exp( (G4double(At) - meanA)/tauA) ) );
1403  }
1404 
1405  return R;
1406 }
1407 
1409 //
1410 //
1411 
1413  const G4double mt ,
1414  const G4double Plab )
1415 {
1416  G4double Elab = std::sqrt ( mp * mp + Plab * Plab );
1417  G4double Ecm = std::sqrt ( mp * mp + mt * mt + 2 * Elab * mt );
1418  // G4double Pcm = Plab * mt / Ecm;
1419  // G4double KEcm = std::sqrt ( Pcm * Pcm + mp * mp ) - mp;
1420 
1421  return Ecm ; // KEcm;
1422 }
1423 
1425 //
1426 //
1427 
1429  const G4double mt ,
1430  const G4double Plab )
1431 {
1432  G4double Elab = std::sqrt ( mp * mp + Plab * Plab );
1433  G4double sMand = mp*mp + mt*mt + 2*Elab*mt ;
1434 
1435  return sMand;
1436 }
1437 
1439 //
1440 //
1441 
1443 {
1444  outFile << "G4ComponentGGHadronNucleusXsc calculates total, inelastic and\n"
1445  << "elastic cross sections for hadron-nucleus cross sections using\n"
1446  << "the Glauber model with Gribov corrections. It is valid for all\n"
1447  << "targets except hydrogen, and for incident p, pbar, n, sigma-,\n"
1448  << "pi+, pi-, K+, K- and gammas with energies above 3 GeV. This is\n"
1449  << "a cross section component which is to be used to build a cross\n"
1450  << "data set.\n";
1451 }
1452 
1453 
1455 //
1456 // Correction arrays for GG <-> Bar changea at ~ 90 GeV
1457 
1458 const G4double G4ComponentGGHadronNucleusXsc::fNeutronBarCorrectionTot[93] = {
1459 
1460 1.0, 1.0, 1.118517e+00, 1.082002e+00, 1.116171e+00, 1.078747e+00, 1.061315e+00,
1461 1.058205e+00, 1.082663e+00, 1.068500e+00, 1.076912e+00, 1.083475e+00, 1.079117e+00,
1462 1.071856e+00, 1.071990e+00, 1.073774e+00, 1.079356e+00, 1.081314e+00, 1.082056e+00,
1463 1.090772e+00, 1.096776e+00, 1.095828e+00, 1.097678e+00, 1.099157e+00, 1.103677e+00,
1464 1.105132e+00, 1.109806e+00, 1.110816e+00, 1.117378e+00, 1.115165e+00, 1.115710e+00,
1465 1.111855e+00, 1.110482e+00, 1.110112e+00, 1.106676e+00, 1.108706e+00, 1.105549e+00,
1466 1.106318e+00, 1.106242e+00, 1.107672e+00, 1.107342e+00, 1.108119e+00, 1.106655e+00,
1467 1.102588e+00, 1.096657e+00, 1.092920e+00, 1.086629e+00, 1.083592e+00, 1.076030e+00,
1468 1.083777e+00, 1.089460e+00, 1.086545e+00, 1.079924e+00, 1.082218e+00, 1.077798e+00,
1469 1.077062e+00, 1.072825e+00, 1.072241e+00, 1.072104e+00, 1.072490e+00, 1.069829e+00,
1470 1.070398e+00, 1.065458e+00, 1.064968e+00, 1.060524e+00, 1.060048e+00, 1.057620e+00,
1471 1.056428e+00, 1.055366e+00, 1.055017e+00, 1.052304e+00, 1.051767e+00, 1.049728e+00,
1472 1.048745e+00, 1.047399e+00, 1.045876e+00, 1.042972e+00, 1.041824e+00, 1.039993e+00,
1473 1.039021e+00, 1.036627e+00, 1.034176e+00, 1.032526e+00, 1.033633e+00, 1.036107e+00,
1474 1.037803e+00, 1.031266e+00, 1.032991e+00, 1.033284e+00, 1.035015e+00, 1.033945e+00,
1475 1.037075e+00, 1.034721e+00
1476 
1477 };
1478 
1479 const G4double G4ComponentGGHadronNucleusXsc::fNeutronBarCorrectionIn[93] = {
1480 
1481 1.0, 1.0, 1.167421e+00, 1.156250e+00, 1.205364e+00, 1.154225e+00, 1.120391e+00,
1482 1.124632e+00, 1.129460e+00, 1.107863e+00, 1.102152e+00, 1.104593e+00, 1.100285e+00,
1483 1.098450e+00, 1.092677e+00, 1.101124e+00, 1.106461e+00, 1.115049e+00, 1.123903e+00,
1484 1.126661e+00, 1.131259e+00, 1.133949e+00, 1.134185e+00, 1.133767e+00, 1.132813e+00,
1485 1.131515e+00, 1.130338e+00, 1.134171e+00, 1.139206e+00, 1.141474e+00, 1.142189e+00,
1486 1.140725e+00, 1.140100e+00, 1.139848e+00, 1.137674e+00, 1.138645e+00, 1.136339e+00,
1487 1.136439e+00, 1.135946e+00, 1.136431e+00, 1.135702e+00, 1.135703e+00, 1.134113e+00,
1488 1.131935e+00, 1.128381e+00, 1.126373e+00, 1.122453e+00, 1.120908e+00, 1.115953e+00,
1489 1.115947e+00, 1.114426e+00, 1.111749e+00, 1.106207e+00, 1.107494e+00, 1.103622e+00,
1490 1.102576e+00, 1.098816e+00, 1.097889e+00, 1.097306e+00, 1.097130e+00, 1.094578e+00,
1491 1.094552e+00, 1.090222e+00, 1.089358e+00, 1.085409e+00, 1.084560e+00, 1.082182e+00,
1492 1.080773e+00, 1.079464e+00, 1.078724e+00, 1.076121e+00, 1.075235e+00, 1.073159e+00,
1493 1.071920e+00, 1.070395e+00, 1.069503e+00, 1.067525e+00, 1.066919e+00, 1.065779e+00,
1494 1.065319e+00, 1.063730e+00, 1.062092e+00, 1.061085e+00, 1.059908e+00, 1.059815e+00,
1495 1.059109e+00, 1.051920e+00, 1.051258e+00, 1.049473e+00, 1.048823e+00, 1.045984e+00,
1496 1.046435e+00, 1.042614e+00
1497 
1498 };
1499 
1500 const G4double G4ComponentGGHadronNucleusXsc::fProtonBarCorrectionTot[93] = {
1501 
1502 1.0, 1.0,
1503 1.118515e+00, 1.082000e+00, 1.116169e+00, 1.078745e+00, 1.061313e+00, 1.058203e+00,
1504 1.082661e+00, 1.068498e+00, 1.076910e+00, 1.083474e+00, 1.079115e+00, 1.071854e+00,
1505 1.071988e+00, 1.073772e+00, 1.079355e+00, 1.081312e+00, 1.082054e+00, 1.090770e+00,
1506 1.096774e+00, 1.095827e+00, 1.097677e+00, 1.099156e+00, 1.103676e+00, 1.105130e+00,
1507 1.109805e+00, 1.110814e+00, 1.117377e+00, 1.115163e+00, 1.115708e+00, 1.111853e+00,
1508 1.110480e+00, 1.110111e+00, 1.106674e+00, 1.108705e+00, 1.105548e+00, 1.106317e+00,
1509 1.106241e+00, 1.107671e+00, 1.107341e+00, 1.108118e+00, 1.106654e+00, 1.102586e+00,
1510 1.096655e+00, 1.092918e+00, 1.086628e+00, 1.083590e+00, 1.076028e+00, 1.083776e+00,
1511 1.089458e+00, 1.086543e+00, 1.079923e+00, 1.082216e+00, 1.077797e+00, 1.077061e+00,
1512 1.072824e+00, 1.072239e+00, 1.072103e+00, 1.072488e+00, 1.069828e+00, 1.070396e+00,
1513 1.065456e+00, 1.064966e+00, 1.060523e+00, 1.060047e+00, 1.057618e+00, 1.056427e+00,
1514 1.055365e+00, 1.055016e+00, 1.052303e+00, 1.051766e+00, 1.049727e+00, 1.048743e+00,
1515 1.047397e+00, 1.045875e+00, 1.042971e+00, 1.041823e+00, 1.039992e+00, 1.039019e+00,
1516 1.036626e+00, 1.034175e+00, 1.032525e+00, 1.033632e+00, 1.036106e+00, 1.037802e+00,
1517 1.031265e+00, 1.032990e+00, 1.033283e+00, 1.035014e+00, 1.033944e+00, 1.037074e+00,
1518 1.034720e+00
1519 
1520 };
1521 
1522 const G4double G4ComponentGGHadronNucleusXsc::fProtonBarCorrectionIn[93] = {
1523 
1524 1.0, 1.0,
1525 1.167419e+00, 1.156248e+00, 1.205362e+00, 1.154224e+00, 1.120390e+00, 1.124630e+00,
1526 1.129459e+00, 1.107861e+00, 1.102151e+00, 1.104591e+00, 1.100284e+00, 1.098449e+00,
1527 1.092675e+00, 1.101122e+00, 1.106460e+00, 1.115048e+00, 1.123902e+00, 1.126659e+00,
1528 1.131258e+00, 1.133948e+00, 1.134183e+00, 1.133766e+00, 1.132812e+00, 1.131514e+00,
1529 1.130337e+00, 1.134170e+00, 1.139205e+00, 1.141472e+00, 1.142188e+00, 1.140724e+00,
1530 1.140099e+00, 1.139847e+00, 1.137672e+00, 1.138644e+00, 1.136338e+00, 1.136438e+00,
1531 1.135945e+00, 1.136429e+00, 1.135701e+00, 1.135702e+00, 1.134112e+00, 1.131934e+00,
1532 1.128380e+00, 1.126371e+00, 1.122452e+00, 1.120907e+00, 1.115952e+00, 1.115946e+00,
1533 1.114425e+00, 1.111748e+00, 1.106205e+00, 1.107493e+00, 1.103621e+00, 1.102575e+00,
1534 1.098815e+00, 1.097888e+00, 1.097305e+00, 1.097129e+00, 1.094577e+00, 1.094551e+00,
1535 1.090221e+00, 1.089357e+00, 1.085408e+00, 1.084559e+00, 1.082181e+00, 1.080772e+00,
1536 1.079463e+00, 1.078723e+00, 1.076120e+00, 1.075234e+00, 1.073158e+00, 1.071919e+00,
1537 1.070394e+00, 1.069502e+00, 1.067524e+00, 1.066918e+00, 1.065778e+00, 1.065318e+00,
1538 1.063729e+00, 1.062091e+00, 1.061084e+00, 1.059907e+00, 1.059814e+00, 1.059108e+00,
1539 1.051919e+00, 1.051257e+00, 1.049472e+00, 1.048822e+00, 1.045983e+00, 1.046434e+00,
1540 1.042613e+00
1541 
1542 };
1543 
1544 
1545 const G4double G4ComponentGGHadronNucleusXsc::fPionPlusBarCorrectionTot[93] = {
1546 
1547 1.0, 1.0,
1548 1.075927e+00, 1.074407e+00, 1.126098e+00, 1.100127e+00, 1.089742e+00, 1.083536e+00,
1549 1.089988e+00, 1.103566e+00, 1.096922e+00, 1.126573e+00, 1.132734e+00, 1.136512e+00,
1550 1.136629e+00, 1.133086e+00, 1.132428e+00, 1.129299e+00, 1.125622e+00, 1.126992e+00,
1551 1.127840e+00, 1.162670e+00, 1.160392e+00, 1.157864e+00, 1.157227e+00, 1.154627e+00,
1552 1.192555e+00, 1.197243e+00, 1.197911e+00, 1.200326e+00, 1.220053e+00, 1.215019e+00,
1553 1.211703e+00, 1.209080e+00, 1.204248e+00, 1.203328e+00, 1.198671e+00, 1.196840e+00,
1554 1.194392e+00, 1.193037e+00, 1.190408e+00, 1.188583e+00, 1.206127e+00, 1.210028e+00,
1555 1.206434e+00, 1.204456e+00, 1.200547e+00, 1.199058e+00, 1.200174e+00, 1.200276e+00,
1556 1.198912e+00, 1.213048e+00, 1.207160e+00, 1.208020e+00, 1.203814e+00, 1.202380e+00,
1557 1.198306e+00, 1.197002e+00, 1.196027e+00, 1.195449e+00, 1.192563e+00, 1.192135e+00,
1558 1.187556e+00, 1.186308e+00, 1.182124e+00, 1.180900e+00, 1.178224e+00, 1.176471e+00,
1559 1.174811e+00, 1.173702e+00, 1.170827e+00, 1.169581e+00, 1.167205e+00, 1.165626e+00,
1560 1.180244e+00, 1.177626e+00, 1.175121e+00, 1.173903e+00, 1.172192e+00, 1.171128e+00,
1561 1.168997e+00, 1.166826e+00, 1.164130e+00, 1.165412e+00, 1.165504e+00, 1.165020e+00,
1562 1.158462e+00, 1.158014e+00, 1.156519e+00, 1.156081e+00, 1.153602e+00, 1.154190e+00,
1563 1.152974e+00
1564 
1565 };
1566 
1567 const G4double G4ComponentGGHadronNucleusXsc::fPionPlusBarCorrectionIn[93] = {
1568 
1569 1.0, 1.0,
1570 1.140246e+00, 1.097872e+00, 1.104301e+00, 1.068722e+00, 1.044495e+00, 1.062622e+00,
1571 1.047987e+00, 1.037032e+00, 1.035686e+00, 1.042870e+00, 1.052222e+00, 1.065100e+00,
1572 1.070480e+00, 1.078286e+00, 1.081488e+00, 1.089713e+00, 1.099105e+00, 1.098003e+00,
1573 1.102175e+00, 1.117707e+00, 1.121734e+00, 1.125229e+00, 1.126457e+00, 1.128905e+00,
1574 1.137312e+00, 1.126263e+00, 1.126459e+00, 1.115191e+00, 1.116986e+00, 1.117184e+00,
1575 1.117037e+00, 1.116777e+00, 1.115858e+00, 1.115745e+00, 1.114489e+00, 1.113993e+00,
1576 1.113226e+00, 1.112818e+00, 1.111890e+00, 1.111238e+00, 1.111209e+00, 1.111775e+00,
1577 1.110256e+00, 1.109414e+00, 1.107647e+00, 1.106980e+00, 1.106096e+00, 1.107331e+00,
1578 1.107849e+00, 1.106407e+00, 1.103426e+00, 1.103896e+00, 1.101756e+00, 1.101031e+00,
1579 1.098915e+00, 1.098260e+00, 1.097768e+00, 1.097487e+00, 1.095964e+00, 1.095773e+00,
1580 1.093348e+00, 1.092687e+00, 1.090465e+00, 1.089821e+00, 1.088394e+00, 1.087462e+00,
1581 1.086571e+00, 1.085997e+00, 1.084451e+00, 1.083798e+00, 1.082513e+00, 1.081670e+00,
1582 1.080735e+00, 1.075659e+00, 1.074341e+00, 1.073689e+00, 1.072787e+00, 1.072237e+00,
1583 1.071107e+00, 1.069955e+00, 1.064856e+00, 1.065873e+00, 1.065938e+00, 1.065694e+00,
1584 1.062192e+00, 1.061967e+00, 1.061180e+00, 1.060960e+00, 1.059646e+00, 1.059975e+00,
1585 1.059658e+00
1586 
1587 };
1588 
1589 
1590 const G4double G4ComponentGGHadronNucleusXsc::fPionMinusBarCorrectionTot[93] = {
1591 
1592 1.0, 1.0,
1593 1.075927e+00, 1.077959e+00, 1.129145e+00, 1.102088e+00, 1.089765e+00, 1.083542e+00,
1594 1.089995e+00, 1.104895e+00, 1.097154e+00, 1.127663e+00, 1.133063e+00, 1.137425e+00,
1595 1.136724e+00, 1.133859e+00, 1.132498e+00, 1.130276e+00, 1.127896e+00, 1.127656e+00,
1596 1.127905e+00, 1.164210e+00, 1.162259e+00, 1.160075e+00, 1.158978e+00, 1.156649e+00,
1597 1.194157e+00, 1.199177e+00, 1.198983e+00, 1.202325e+00, 1.221967e+00, 1.217548e+00,
1598 1.214389e+00, 1.211760e+00, 1.207335e+00, 1.206081e+00, 1.201766e+00, 1.199779e+00,
1599 1.197283e+00, 1.195706e+00, 1.193071e+00, 1.191115e+00, 1.208838e+00, 1.212681e+00,
1600 1.209235e+00, 1.207163e+00, 1.203451e+00, 1.201807e+00, 1.203283e+00, 1.203388e+00,
1601 1.202244e+00, 1.216509e+00, 1.211066e+00, 1.211504e+00, 1.207539e+00, 1.205991e+00,
1602 1.202143e+00, 1.200724e+00, 1.199595e+00, 1.198815e+00, 1.196025e+00, 1.195390e+00,
1603 1.191137e+00, 1.189791e+00, 1.185888e+00, 1.184575e+00, 1.181996e+00, 1.180229e+00,
1604 1.178545e+00, 1.177355e+00, 1.174616e+00, 1.173312e+00, 1.171016e+00, 1.169424e+00,
1605 1.184120e+00, 1.181478e+00, 1.179085e+00, 1.177817e+00, 1.176124e+00, 1.175003e+00,
1606 1.172947e+00, 1.170858e+00, 1.168170e+00, 1.169397e+00, 1.169304e+00, 1.168706e+00,
1607 1.162774e+00, 1.162217e+00, 1.160740e+00, 1.160196e+00, 1.157857e+00, 1.158220e+00,
1608 1.157267e+00
1609 };
1610 
1611 
1612 const G4double G4ComponentGGHadronNucleusXsc::fPionMinusBarCorrectionIn[93] = {
1613 
1614 1.0, 1.0,
1615 1.140246e+00, 1.100898e+00, 1.106773e+00, 1.070289e+00, 1.044514e+00, 1.062628e+00,
1616 1.047992e+00, 1.038041e+00, 1.035862e+00, 1.043679e+00, 1.052466e+00, 1.065780e+00,
1617 1.070551e+00, 1.078869e+00, 1.081541e+00, 1.090455e+00, 1.100847e+00, 1.098511e+00,
1618 1.102226e+00, 1.118865e+00, 1.123143e+00, 1.126904e+00, 1.127785e+00, 1.130444e+00,
1619 1.138502e+00, 1.127678e+00, 1.127244e+00, 1.116634e+00, 1.118347e+00, 1.118988e+00,
1620 1.118957e+00, 1.118696e+00, 1.118074e+00, 1.117722e+00, 1.116717e+00, 1.116111e+00,
1621 1.115311e+00, 1.114745e+00, 1.113814e+00, 1.113069e+00, 1.113141e+00, 1.113660e+00,
1622 1.112249e+00, 1.111343e+00, 1.109718e+00, 1.108942e+00, 1.108310e+00, 1.109549e+00,
1623 1.110227e+00, 1.108846e+00, 1.106183e+00, 1.106354e+00, 1.104388e+00, 1.103583e+00,
1624 1.101632e+00, 1.100896e+00, 1.100296e+00, 1.099873e+00, 1.098420e+00, 1.098082e+00,
1625 1.095892e+00, 1.095162e+00, 1.093144e+00, 1.092438e+00, 1.091083e+00, 1.090142e+00,
1626 1.089236e+00, 1.088604e+00, 1.087159e+00, 1.086465e+00, 1.085239e+00, 1.084388e+00,
1627 1.083473e+00, 1.078373e+00, 1.077136e+00, 1.076450e+00, 1.075561e+00, 1.074973e+00,
1628 1.073898e+00, 1.072806e+00, 1.067706e+00, 1.068684e+00, 1.068618e+00, 1.068294e+00,
1629 1.065241e+00, 1.064939e+00, 1.064166e+00, 1.063872e+00, 1.062659e+00, 1.062828e+00,
1630 1.062699e+00
1631 
1632 };
1633 
1634 
1635 //
1636 //