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G4AtimaEnergyLossModel.cc
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25 //
26 // GEANT4 Class header file
27 //
28 //
29 // File name: G4AtimaEnergyLossModel
30 //
31 // Author: Jose Luis Rodriguez Sanchez on base of ATIMA code
32 //
33 // Creation date: 16.01.2018
34 //
35 // Modifications:
36 // 09/10/2018: Solved bug in the determination of the material atomic number
37 //
38 // Class Description:
39 //
40 // This model calculates the stopping power of ions according
41 // to the ATIMA code developed at GSI, Darmstadt, Germany.
42 // For details: http://web-docs.gsi.de/~weick/atima/
43 //
44 // Helmut Weick, GSI (responsible for fortran version)
45 // Andrej Prochazka, GSI (responsible for C version)
46 // Christoph Scheidenberger, GSI (project coordination)
47 //
48 // -------------------------------------------------------------------
49 //
50 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
51 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
52 
53 #include "G4AtimaEnergyLossModel.hh"
54 #include "Randomize.hh"
55 #include "G4PhysicalConstants.hh"
56 #include "G4SystemOfUnits.hh"
57 #include "G4Electron.hh"
58 #include "G4GenericIon.hh"
59 #include "G4LossTableManager.hh"
60 #include "G4EmCorrections.hh"
61 #include "G4ParticleChangeForLoss.hh"
62 #include "G4DeltaAngle.hh"
63 #include "G4Log.hh"
64 #include "G4Exp.hh"
65 #include "G4Pow.hh"
66 
67 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
68 
69 using namespace std;
70 
71 G4double G4AtimaEnergyLossModel::stepE = 0.0;
72 G4double G4AtimaEnergyLossModel::tableE[] = {0.0};
73 
74 G4AtimaEnergyLossModel::G4AtimaEnergyLossModel(const G4ParticleDefinition*,
75  const G4String& nam)
76  : G4VEmModel(nam),
77  particle(nullptr),
78  tlimit(DBL_MAX),
79  isIon(false)
80 {
81  g4calc = G4Pow::GetInstance();
82  fParticleChange = nullptr;
83  theElectron = G4Electron::Electron();
84  SetParticle(theElectron);
85  corr = G4LossTableManager::Instance()->EmCorrections();
86  nist = G4NistManager::Instance();
87  SetLowEnergyLimit(2.0*MeV);
88  MLN10 = 2.30258509299;
89  atomic_mass_unit = 931.4940954; // MeV/c^2
90  dedx_constant = 0.3070749187; //4*pi*Na*me*c^2*r_e^2 //MeV cm^2
91  electron_mass = 0.510998928; // MeV/c^2
92  fine_structure = 1.0/137.035999139;
93  domega2dx_constant = dedx_constant*electron_mass; //4*pi*Na*me*c^2*r_e^2 //MeV^2 cm^2
94  if(tableE[0] == 0.0) {
95  G4double logmin = 0.;
96  G4double logmax = 5.;
97  stepE = (logmax-logmin)/199.;
98  for(G4int i=0; i<200; ++i){
99  tableE[i] = G4Exp(MLN10*(logmin + ((G4double)i)*stepE));
100  }
101  }
102 }
103 
104 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
105 
106 G4AtimaEnergyLossModel::~G4AtimaEnergyLossModel()
107 {}
108 
109 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
110 
111 void G4AtimaEnergyLossModel::Initialise(const G4ParticleDefinition* p,
112  const G4DataVector&)
113 {
114  SetGenericIon(p);
115  SetParticle(p);
116 
117  //G4cout << "G4AtimaEnergyLossModel::Initialise for " << p->GetParticleName()
118  // << " isIon= " << isIon
119  // << G4endl;
120 
121  // always false before the run
122  SetDeexcitationFlag(false);
123 
124  if(nullptr == fParticleChange) {
125  fParticleChange = GetParticleChangeForLoss();
126  if(UseAngularGeneratorFlag() && !GetAngularDistribution()) {
127  SetAngularDistribution(new G4DeltaAngle());
128  }
129  }
130 }
131 
132 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
133 
134 G4double G4AtimaEnergyLossModel::GetChargeSquareRatio(const G4ParticleDefinition* p,
135  const G4Material* mat,
136  G4double kineticEnergy)
137 {
138  // this method is called only for ions
139  G4double q2 = corr->EffectiveChargeSquareRatio(p,mat,kineticEnergy);
140  corrFactor = q2*corr->EffectiveChargeCorrection(p,mat,kineticEnergy);
141  return corrFactor;
142 }
143 
144 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
145 
146 G4double G4AtimaEnergyLossModel::GetParticleCharge(const G4ParticleDefinition* p,
147  const G4Material* mat,
148  G4double kineticEnergy)
149 {
150  //G4cout<<"G4AtimaEnergyLossModel::GetParticleCharge e= "<<kineticEnergy <<
151  // " q= " << corr->GetParticleCharge(p,mat,kineticEnergy) <<G4endl;
152  // this method is called only for ions, so no check if it is an ion
153  return corr->GetParticleCharge(p,mat,kineticEnergy);
154 }
155 
156 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
157 
158 void G4AtimaEnergyLossModel::SetupParameters()
159 {
160  mass = particle->GetPDGMass();
161  spin = particle->GetPDGSpin();
162  G4double q = particle->GetPDGCharge()/eplus;
163  chargeSquare = q*q;
164  corrFactor = chargeSquare;
165  ratio = electron_mass_c2/mass;
166  static const G4double aMag = 1./(0.5*eplus*hbar_Planck*c_squared);
167  G4double magmom = particle->GetPDGMagneticMoment()*mass*aMag;
168  magMoment2 = magmom*magmom - 1.0;
169  formfact = 0.0;
170  tlimit = DBL_MAX;
171  if(particle->GetLeptonNumber() == 0) {
172  G4int iz = G4lrint(q);
173  if(iz <= 1) {
174  formfact = (spin == 0.0 && mass < GeV) ? 1.181e-6 : 1.548e-6;
175  } else {
176  G4double x = nist->GetA27(iz);
177  formfact = 3.969e-6*x*x;
178  }
179  tlimit = std::sqrt(0.414/formfact +
180  electron_mass_c2*electron_mass_c2) - electron_mass_c2;
181  }
182 }
183 
184 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
185 
186 G4double G4AtimaEnergyLossModel::MinEnergyCut(const G4ParticleDefinition*,
187  const G4MaterialCutsCouple* couple)
188 {
189  return couple->GetMaterial()->GetIonisation()->GetMeanExcitationEnergy();
190 }
191 
192 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
193 
194 G4double
195 G4AtimaEnergyLossModel::ComputeCrossSectionPerElectron(const G4ParticleDefinition* p,
196  G4double kineticEnergy,
197  G4double cutEnergy,
198  G4double maxKinEnergy)
199 {
200  G4double cross = 0.0;
201  G4double tmax = MaxSecondaryEnergy(p, kineticEnergy);
202  G4double maxEnergy = std::min(tmax,maxKinEnergy);
203  if(cutEnergy < maxEnergy) {
204 
205  G4double totEnergy = kineticEnergy + mass;
206  G4double energy2 = totEnergy*totEnergy;
207  G4double beta2 = kineticEnergy*(kineticEnergy + 2.0*mass)/energy2;
208 
209  cross = (maxEnergy - cutEnergy)/(cutEnergy*maxEnergy)
210  - beta2*G4Log(maxEnergy/cutEnergy)/tmax;
211 
212  // +term for spin=1/2 particle
213  if( 0.0 < spin ) { cross += 0.5*(maxEnergy - cutEnergy)/energy2; }
214 
215  cross *= twopi_mc2_rcl2*chargeSquare/beta2;
216  }
217 
218  // G4cout << "BB: e= " << kineticEnergy << " tmin= " << cutEnergy
219  // << " tmax= " << tmax << " cross= " << cross << G4endl;
220 
221  return cross;
222 }
223 
224 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
225 
226 G4double G4AtimaEnergyLossModel::ComputeCrossSectionPerAtom(
227  const G4ParticleDefinition* p,
228  G4double kineticEnergy,
229  G4double Z, G4double,
230  G4double cutEnergy,
231  G4double maxEnergy)
232 {
233  G4double cross = Z*ComputeCrossSectionPerElectron
234  (p,kineticEnergy,cutEnergy,maxEnergy);
235  return cross;
236 }
237 
238 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
239 
240 G4double G4AtimaEnergyLossModel::CrossSectionPerVolume(
241  const G4Material* material,
242  const G4ParticleDefinition* p,
243  G4double kineticEnergy,
244  G4double cutEnergy,
245  G4double maxEnergy)
246 {
247  G4double eDensity = material->GetElectronDensity();
248  G4double cross = eDensity*ComputeCrossSectionPerElectron
249  (p,kineticEnergy,cutEnergy,maxEnergy);
250  return cross;
251 }
252 
253 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
254 
255 G4double G4AtimaEnergyLossModel::ComputeDEDXPerVolume(const G4Material* material,
256  const G4ParticleDefinition* p,
257  G4double kineticEnergy,
258  G4double)
259 {
260  //Call to ATIMA Stopping Power function
261  G4double zt = material->GetIonisation()->GetZeffective();
262  zt = std::min(zt,93.);
263  G4double at = nist->GetAtomicMassAmu(G4lrint(zt));
264  G4double dedx = StoppingPower(p->GetPDGMass(), p->GetPDGCharge(),
265  kineticEnergy/(MeV), at, zt) *material->GetDensity()/(g/cm3);
266  dedx = std::max(dedx, 0.0);
267 
268  // G4cout << "E(MeV)= " << kineticEnergy/MeV << " dedx= " << dedx
269  // << " " << material->GetName() << G4endl;
270  return dedx;
271 }
272 
273 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
274 
275 void G4AtimaEnergyLossModel::CorrectionsAlongStep(const G4MaterialCutsCouple* couple,
276  const G4DynamicParticle* dp,
277  G4double& eloss,
278  G4double&,
279  G4double length)
280 {
281  if(isIon) {
282  const G4ParticleDefinition* p = dp->GetDefinition();
283  const G4Material* mat = couple->GetMaterial();
284  G4double cutEnergy = DBL_MAX;
285  GetModelOfFluctuations()->SetParticleAndCharge(p, p->GetPDGCharge());
286  G4double kineticEnergy = dp->GetKineticEnergy();
287  eloss = ComputeDEDXPerVolume(mat, p, kineticEnergy, cutEnergy)*length/(cm);
288  }
289 
290 }
291 
292 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
293 
294 void G4AtimaEnergyLossModel::SampleSecondaries(vector<G4DynamicParticle*>* vdp,
295  const G4MaterialCutsCouple* couple,
296  const G4DynamicParticle* dp,
297  G4double minKinEnergy,
298  G4double maxEnergy)
299 {
300  G4double kineticEnergy = dp->GetKineticEnergy();
301  G4double tmax = MaxSecondaryEnergy(dp->GetDefinition(),kineticEnergy);
302 
303  G4double maxKinEnergy = std::min(maxEnergy,tmax);
304  if(minKinEnergy >= maxKinEnergy) { return; }
305 
306  //G4cout << "G4AtimaEnergyLossModel::SampleSecondaries Emin= " << minKinEnergy
307  // << " Emax= " << maxKinEnergy << G4endl;
308 
309  G4double totEnergy = kineticEnergy + mass;
310  G4double etot2 = totEnergy*totEnergy;
311  G4double beta2 = kineticEnergy*(kineticEnergy + 2.0*mass)/etot2;
312 
313  G4double deltaKinEnergy, f;
314  G4double f1 = 0.0;
315  G4double fmax = 1.0;
316  if( 0.0 < spin ) { fmax += 0.5*maxKinEnergy*maxKinEnergy/etot2; }
317 
318  CLHEP::HepRandomEngine* rndmEngineMod = G4Random::getTheEngine();
319  G4double rndm[2];
320 
321  // sampling without nuclear size effect
322  do {
323  rndmEngineMod->flatArray(2, rndm);
324  deltaKinEnergy = minKinEnergy*maxKinEnergy
325  /(minKinEnergy*(1.0 - rndm[0]) + maxKinEnergy*rndm[0]);
326 
327  f = 1.0 - beta2*deltaKinEnergy/tmax;
328  if( 0.0 < spin ) {
329  f1 = 0.5*deltaKinEnergy*deltaKinEnergy/etot2;
330  f += f1;
331  }
332 
333  // Loop checking, 03-Aug-2015, Vladimir Ivanchenko
334  } while( fmax*rndm[1] > f);
335 
336  // projectile formfactor - suppresion of high energy
337  // delta-electron production at high energy
338 
339  G4double x = formfact*deltaKinEnergy*(deltaKinEnergy + 2*electron_mass_c2);
340  if(x > 1.e-6) {
341 
342  G4double x10 = 1.0 + x;
343  G4double grej = 1.0/(x10*x10);
344  if( 0.0 < spin ) {
345  G4double x2 = 0.5*electron_mass_c2*deltaKinEnergy/(mass*mass);
346  grej *= (1.0 + magMoment2*(x2 - f1/f)/(1.0 + x2));
347  }
348  if(grej > 1.1) {
349  G4cout << "### G4AtimaEnergyLossModel WARNING: grej= " << grej
350  << " " << dp->GetDefinition()->GetParticleName()
351  << " Ekin(MeV)= " << kineticEnergy
352  << " delEkin(MeV)= " << deltaKinEnergy
353  << G4endl;
354  }
355  if(rndmEngineMod->flat() > grej) { return; }
356  }
357 
358  G4ThreeVector deltaDirection;
359 
360  if(UseAngularGeneratorFlag()) {
361 
362  const G4Material* mat = couple->GetMaterial();
363  G4int Z = SelectRandomAtomNumber(mat);
364 
365  deltaDirection =
366  GetAngularDistribution()->SampleDirection(dp, deltaKinEnergy, Z, mat);
367 
368  } else {
369 
370  G4double deltaMomentum =
371  std::sqrt(deltaKinEnergy * (deltaKinEnergy + 2.0*electron_mass_c2));
372  G4double cost = deltaKinEnergy * (totEnergy + electron_mass_c2) /
373  (deltaMomentum * dp->GetTotalMomentum());
374  if(cost > 1.0) { cost = 1.0; }
375  G4double sint = std::sqrt((1.0 - cost)*(1.0 + cost));
376 
377  G4double phi = twopi*rndmEngineMod->flat();
378 
379  deltaDirection.set(sint*cos(phi),sint*sin(phi), cost) ;
380  deltaDirection.rotateUz(dp->GetMomentumDirection());
381  }
382  /*
383  G4cout << "### G4AtimaEnergyLossModel "
384  << dp->GetDefinition()->GetParticleName()
385  << " Ekin(MeV)= " << kineticEnergy
386  << " delEkin(MeV)= " << deltaKinEnergy
387  << " tmin(MeV)= " << minKinEnergy
388  << " tmax(MeV)= " << maxKinEnergy
389  << " dir= " << dp->GetMomentumDirection()
390  << " dirDelta= " << deltaDirection
391  << G4endl;
392  */
393  // create G4DynamicParticle object for delta ray
394  G4DynamicParticle* delta =
395  new G4DynamicParticle(theElectron,deltaDirection,deltaKinEnergy);
396 
397  vdp->push_back(delta);
398 
399  // Change kinematics of primary particle
400  kineticEnergy -= deltaKinEnergy;
401  G4ThreeVector finalP = dp->GetMomentum() - delta->GetMomentum();
402  finalP = finalP.unit();
403 
404  fParticleChange->SetProposedKineticEnergy(kineticEnergy);
405  fParticleChange->SetProposedMomentumDirection(finalP);
406 }
407 
408 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
409 
410 G4double G4AtimaEnergyLossModel::MaxSecondaryEnergy(const G4ParticleDefinition* pd,
411  G4double kinEnergy)
412 {
413  // here particle type is checked for any method
414  SetParticle(pd);
415  G4double tau = kinEnergy/mass;
416  G4double tmax = 2.0*electron_mass_c2*tau*(tau + 2.) /
417  (1. + 2.0*(tau + 1.)*ratio + ratio*ratio);
418  return std::min(tmax,tlimit);
419 }
420 
421 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
422 
423 G4double G4AtimaEnergyLossModel::StoppingPower(G4double ap, G4double zp,
424  G4double ep, G4double at, G4double zt){
425  //
426  if(ep==0)return 0.0;
427  ap=ap/atomic_mass_unit;
428  ep=ep/ap;
429  G4double se = 0.0;
430  // ep in MeV
431  if(ep<=10.){
432  se = sezi_dedx_e(zp, ep, at, zt);
433  }
434  else if(ep>10. && ep<30.){
435  G4double factor = 0.05 * ( ep - 10.0 );
436  se = (1.0-factor)*sezi_dedx_e(zp, ep, at, zt) + factor*Bethek_dedx_e(ap, zp, ep, at, zt);
437  }
438  else {
439  se = Bethek_dedx_e(ap, zp, ep, at, zt);
440  }
441  return se + dedx_n(ap, zp, ep, at, zt);
442 }
443 
444 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
445 
446 G4double G4AtimaEnergyLossModel::dedx_n(const G4double ap, const G4double zp,
447  const G4double ep, const G4double at, const G4double zt){
448 
449  G4double zpowers = g4calc->powA(zp,0.23)+g4calc->powA(zt,0.23);
450  G4double asum = ap + at;
451  G4double epsilon = 32.53*at*1000.*ep*ap/(zp*zt*asum*zpowers); //projectile energy is converted from MeV/u to keV
452  G4double sn=0.;
453 
454  if(epsilon<=30.0){
455  sn = G4Log(1.+(1.1383*epsilon))/ (2.*(epsilon + 0.01321*g4calc->powA(epsilon,0.21226) + 0.19593*sqrt(epsilon)));
456  }
457  else{
458  sn = G4Log(epsilon)/(2.*epsilon);
459  }
460  sn = 100.*8.4621*zp*zt*ap*sn*Avogadro/1.e+23/(asum*zpowers*at);
461  return sn;
462 }
463 
464 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
465 
466 G4double G4AtimaEnergyLossModel::sezi_dedx_e(const G4double zp, const G4double ep, const G4double at, const G4double zt){
467  G4double e = ep*1000.; // e in keV/u
468  G4double se = 0.;
469 
470  // heavy ion Z > 2
471  G4double h1,h4;
472  G4double a,q,b;
473  G4double l1,l0,l;
474  G4double YRmin = 0.130; // YRmin = VR / ZP**0.67 <= 0.13 OR VR <= 1.0
475  G4double VRmin = 1.0;
476  G4double vfermi = atima_vfermi[(G4int)zt-1];
477  G4double yr=0;
478  G4double zeta = 0;
479 
480  G4double v = std::sqrt(e/25.0)/vfermi;
481  G4double v2= v*v;
482 
483  G4double vr = (v >= 1)? v*vfermi*(1.+ 1./(5.*v2)) : 3.0*vfermi/4.0*(1.0+v2*(2.0/3.0-v2/15.0));
484 
485  h1= 1./g4calc->powA(zp,0.6667);
486  yr = std::max(YRmin,vr*h1);
487  yr = std::max(yr, VRmin*h1);
488 
489  //-- CALCULATE ZEFF
490  a = -0.803*g4calc->powA(yr,0.3) + 1.3167*g4calc->powA(yr,0.6) + 0.38157*yr + 0.008983*yr*yr;
491  q = std::min(1.0, std::max(0.0 , (1.0 - G4Exp(-std::min(a, 50.0))))); //-- Q = IONIZATION LEVEL OF THE ION AT RELATIVE VELOCITY YR
492 
493  //-- IONIZATION LEVEL TO EFFECTIVE CHARGE
494  h1 = 1./g4calc->powA(zp,0.3333);
495 
496  b = (std::min(0.43, std::max(0.32,0.12 + 0.025*zp)))*h1;
497  l0 = (0.8 - q * std::min(1.2,0.6 +zp/30.0))*h1;
498  if(q < 0.2){
499  l1 = 0;
500  }
501  else{
502  if (q < std::max(0.0,0.9-0.025*zp)){
503  l1 = b*(q-0.2)/std::abs(std::max(0.0,0.9-0.025*zp)-0.2000001);
504  }
505  else{
506  if(q < std::max(0.0,1.0 - 0.025*std::min(16.,zp))) l1 = b;
507  else l1 = b*(1.0 - q)/(0.025*std::min(16.,zp));
508  }
509  }
510  // calculate screening
511  l = std::max(l1,l0*atima_lambda_screening[(G4int)zp-1]);
512  h1 =4.0*l*vfermi/1.919;
513  zeta = q + (1./(2.*(vfermi*vfermi)))*(1. - q)* G4Log(1. + h1*h1);
514 
515  // ZP**3 EFFECT AS IN REF. 779?
516  a = 7.6 - std::max(0.0, G4Log(e));
517  zeta = zeta*(1. + (1./(zp*zp))*(0.18 + .0015*zt)*G4Exp(-a*a));
518 
519  h1= 1./g4calc->powA(zp,0.6667);
520  if (yr <= ( std::max(YRmin, VRmin*h1))){
521  VRmin=std::max(VRmin, YRmin/h1);
522  //--C ..CALCULATE VELOCITY STOPPING FOR YR < YRmin
523  G4double vmin =.5*(VRmin + std::sqrt(std::max(0.0,VRmin*VRmin - 0.8*vfermi*vfermi)));
524  G4double eee = 25.0*vmin*vmin;
525  G4double eval = 1.0;
526  if((zt == 6) || (((zt == 14) || (zt == 32)) && (zp <= 19))) eval = 0.35;
527  else eval = 0.5;
528 
529  h1 = zeta *zp;
530  h4 = g4calc->powA(e / eee,eval);
531  se = sezi_p_se(eee*0.001,at,zt) * h1*h1*h4;
532  return se;
533  }
534  else {
535  se = sezi_p_se(ep,at,zt)*g4calc->powA(zeta*zp,2.0);
536  return se;
537  }
538 
539  return se;
540 }
541 
542 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
543 
544 G4double G4AtimaEnergyLossModel::sezi_p_se(const G4double energy, const G4double at, const G4double zt){
545  G4double sp = 0.;
546  G4double e = 1000*energy; //e in keV/u
547  G4int i = zt - 1;
548 
549  if(e<=25)e=25;
550  G4double sl = (proton_stopping_coef[i][0]*g4calc->powA(e,proton_stopping_coef[i][1])) + (proton_stopping_coef[i][2]*g4calc->powA(e,proton_stopping_coef[i][3]));
551  G4double sh = proton_stopping_coef[i][4]/g4calc->powA(e,proton_stopping_coef[i][5]) * G4Log( (proton_stopping_coef[i][6]/e) + (proton_stopping_coef[i][7]*e));
552  sp = sl*sh/(sl+sh);
553  e=1000*energy;
554  if(e<=25){
555  sp *=(zt>6)?g4calc->powA(e/25.,0.45):g4calc->powA(e/25.,0.25);
556  }
557  return 100.*sp*Avogadro/1.e+23/at;
558 }
559 
560 
561 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
562 
563 G4double G4AtimaEnergyLossModel::Bethek_dedx_e(G4double ap, G4double zp, G4double ep, G4double at, G4double zt){
564 //
565 // According to C. Scheidenberger et al., Phys. Rev. Lett. 73, 50 (1994).
566 //
567  G4double gamma=1.0 + ep/atomic_mass_unit;
568  G4double beta2=1.0-1.0/(gamma*gamma);
569  //
570  G4double beta = std::sqrt(beta2);
571  G4double zp_eff = zp*(1.0-G4Exp(-0.95/fine_structure*beta/g4calc->A23(zp)));
572  G4int zi = std::min(std::max((G4int)zt, 1), 120);
573  G4double Ipot = ionisation_potentials_z[zi];
574  G4double f1 = dedx_constant*g4calc->powA(zp_eff,2.)*zt/(beta2*at);
575 
576  //
577  G4double f2 = G4Log(2.0*electron_mass*1000000*beta2/Ipot);
578  G4double eta = beta*gamma;
579 
580  if(!(eta>=0.13)){ //shell corrections
581  G4double cor = (+0.422377*g4calc->powA(eta,-2.)
582  +0.0304043*g4calc->powA(eta,-4.)
583  -0.00038106*g4calc->powA(eta,-6.))*1e-6*g4calc->powA(Ipot,2.)
584  +(+3.858019*g4calc->powA(eta,-2.)
585  -0.1667989*(g4calc->powA(eta,-4.))
586  +0.00157955*(g4calc->powA(eta,-6.)))*1.0e-9*g4calc->powA(Ipot,3.);
587  f2 = f2 -cor/zt;
588  }
589 
590  f2+=2*G4Log(gamma) -beta2;
591 
592  //Barkas correction
593  G4double barkas=1.0;
594  G4double V2FVA[4]={0.33,0.30,0.26,0.23};
595  G4double VA[4]={1.,2.,3.,4.};
596  G4double v1 = eta/(fine_structure*std::sqrt(zt));
597  G4double v2fv;
598  if(v1 >= 4.){
599  v2fv = 0.45 / std::sqrt(v1);
600  }
601  else if(v1 > 1. && v1 < 4.){//VALUES FROM THE JACKSON MC CARTHY FUNCTION //PHYS. REV. B 6 4131
602  G4int i=1;
603  for(; i<4; i++){
604  if(VA[i] >= v1) break;
605  }
606  i = std::min(i, 3);
607  v2fv = V2FVA[i-1]+(v1-VA[i-1])*(V2FVA[i]-V2FVA[i-1])/(VA[i]-VA[i-1]);
608  }
609  else{
610  v2fv=0;
611  }
612  barkas= 1.0+2.0 * zp_eff * v2fv /(v1*v1*std::sqrt(zt));
613 
614  //Fermi-density effect for relativistic velocities
615  gamma = 1./std::sqrt(1-(beta*beta));
616  G4double x = G4Log(beta * gamma) / 2.302585;
617  G4int i = std::min(std::max(zi-1,0), 91);
618  G4double del = 0.;
619 
620  if (x < x0[i] ){
621  if(del_0[i] > 0.)del = del_0[i] * g4calc->powA(10.0,(2.*(x-x0[i])));
622  }
623  else {
624  del = 4.6052 * x - c[i];
625  if ( x0[i]<= x && x <= x1[i] ) del += afermi[i] * g4calc->powA((x1[i] - x),m0[i]);
626  }
627 
628  //Precalculated lindhard correction
629  G4double LS = 0.;
630  G4int z = G4lrint(zp);
631  if(z>109)z=109;
632  if(ep<tableE[0])ep=tableE[0];
633 
634  G4double da = (ap - element_atomic_weights[z])/element_atomic_weights[z];
635  z = z-1;
636 
637  G4double v3 = EnergyTable_interpolate(ep,ls_coefficients_a[z]);
638  G4double v4 = EnergyTable_interpolate(ep,ls_coefficients_ahi[z]);
639  G4double dif = v4 - v3;
640  LS = v3+(dif*da/0.05);
641 
642  //Final stopping power
643  G4double result = (f2)*barkas + LS - del/2.;
644  result *=f1;
645 
646  return result;
647 }
648 
649 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
650 
651 G4double G4AtimaEnergyLossModel::EnergyTable_interpolate(G4double xval,const G4double* y){
652  G4double r;
653  G4int num=200;
654  G4double lxval = G4Log(xval)/MLN10;
655  if(xval<tableE[0] || xval>tableE[num-1])return 0.0;
656  if(xval==tableE[num-1])return y[num-1];
657  G4int i = (G4int)(lxval/stepE);
658  i = std::min(std::max(i, 0), num-2);
659  G4double linstep = tableE[i+1] - tableE[i];
660  G4double x = 1.0 - ((xval - tableE[i])/linstep);
661  r = (x*y[i]) + ((1-x)*y[i+1]);
662  return r;
663 }
664 
665 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
666 
667 const G4double G4AtimaEnergyLossModel::proton_stopping_coef[92][8] = { // proton in material stopping coefficient
668 { .0091827, .0053496, .69741, .48493, 316.07,1.0143, 9329.3, .0539890}, //H
669 { .11393, .0051984, 1.0822, .39252, 1081.0, 1.0645, 4068.5, .0176990}, //He
670 { .85837, .0050147, 1.6044, .38844, 1337.3, 1.0470, 2659.2, .01898},
671 { .8781, .0051049, 5.4232, .2032, 1200.6, 1.0211, 1401.8, .0385290},
672 { 1.4608, .0048836, 2.338, .44249, 1801.3, 1.0352, 1784.1, .02024},
673 { 3.2579, .0049148, 2.7156, .36473, 2092.2, 1.0291, 2643.6, .0182370}, //C
674 { .59674, .0050837, 4.2073, .30612, 2394.2, 1.0255, 4892.1, .0160060},
675 { .75253, .0050314, 4.0824, .30067, 2455.8, 1.0181, 5069.7, .0174260}, //O
676 { 1.226, .0051385, 3.2246, .32703, 2525.0, 1.0142, 7563.6, .0194690},
677 { 1.0332, .0051645, 3.004, .33889, 2338.6, .99997, 6991.2, .0217990}, //Ne
678 { 6.0972, .0044292, 3.1929, .45763, 1363.3, .95182, 2380.6, .0818350},
679 {14.013, .0043646, 2.2641, .36326, 2187.4, .99098, 6264.8, .0462},
680 { .039001, .0045415, 5.5463, .39562, 1589.2, .95316, 816.16, .0474840},
681 { 2.072, .0044516, 3.5585, .53933, 1515.2, .93161, 1790.3, .0351980},
682 {17.575, .0038346, .078694, 1.2388,2806.0, .97284, 1037.6, .0128790},
683 {16.126, .0038315, .054164, 1.3104,2813.3, .96587, 1251.4, .0118470},
684 { 3.217, .0044579, 3.6696, .5091, 2734.6, .96253, 2187.5, .0169070},
685 { 2.0379, .0044775, 3.0743, .54773, 3505.0, .97575, 1714.00, .0117010},
686 { .74171, .0043051, 1.1515, .95083, 917.21, .8782, 389.93, .18926},
687 { 9.1316, .0043809, 5.4611, .31327, 3891.8, .97933, 6267.9, .0151960}, //Ca
688 { 7.2247, .0043718, 6.1017, .37511, 2829.2, .95218, 6376.1, .0203980},
689 { .147, .0048456, 6.3485, .41057, 2164.1, .94028, 5292.6, .0502630},
690 { 5.0611, .0039867, 2.6174, .57957, 2218.9, .92361, 6323.00, .0256690},
691 { .53267, .0042968, .39005, 1.2725, 1872.7, .90776, 64.166, .0301070},
692 { .47697, .0043038, .31452, 1.3289, 1920.5, .90649, 45.576, .0274690},
693 { .027426, .0035443, .031563, 2.1755, 1919.5, .90099, 23.902, .0253630},
694 { .16383, .0043042, .073454, 1.8592, 1918.4, .89678, 27.61, .0231840},
695 { 4.2562, .0043737, 1.5606, .72067, 1546.8, .87958, 302.02, .0409440}, //Ni
696 { 2.3508, .0043237, 2.882, .50113, 1837.7, .89992, 2377.00, .04965},
697 { 3.1095, .0038455, .11477, 1.5037, 2184.7, .89309, 67.306, .0165880},
698 {15.322, .0040306, .65391, .67668, 3001.7, .92484, 3344.2, .0163660},
699 { 3.6932, .0044813, 8.608, .27638, 2982.7, .9276, 3166.6, .0308740},
700 { 7.1373, .0043134, 9.4247, .27937, 2725.8, .91597, 3166.1, .0250080},
701 { 4.8979, .0042937, 3.7793, .50004, 2824.5, .91028, 1282.4, .0170610},
702 { 1.3683, .0043024, 2.5679, .60822, 6907.8, .9817, 628.01, .0068055},
703 { 1.8301, .0042983, 2.9057, .6038, 4744.6, .94722, 936.64, .0092242},
704 { .42056, .0041169, .01695, 2.3616, 2252.7, .89192, 39.752, .0277570},
705 {30.78, .0037736, .55813, .76816, 7113.2, .97697, 1604.4, .0065268},
706 {11.576, .0042119, 7.0244, .37764, 4713.5, .94264, 2493.2, .01127},
707 { 6.2406, .0041916, 5.2701, .49453, 4234.6, .93232, 2063.9, .0118440},
708 { .33073, .0041243, 1.7246, 1.1062, 1930.2, .86907, 27.416, .0382080},
709 { .017747, .0041715, .14586, 1.7305,1803.6, .86315, 29.669, .0321230},
710 { 3.7229, .0041768, 4.6286, .56769, 1678.0, .86202, 3094.00, .06244},
711 { .13998, .0041329, .25573, 1.4241, 1919.3, .86326, 72.797, .0322350},
712 { .2859, .0041386, .31301, 1.3424, 1954.8, .86175, 115.18, .0293420},
713 { .76, .0042179, 3.386, .76285, 1867.4, .85805, 69.994, .0364480},
714 { 6.3957, .0041935, 5.4689, .41378, 1712.6, .85397,18493.00, .0564710},
715 { 3.4717, .0041344, 3.2337, .63788, 1116.4, .81959, 4766.0, .1179},
716 { 2.5265, .0042282, 4.532, .53562, 1030.8, .81652,16252.0, .19722},
717 { 7.3683, .0041007, 4.6791, .51428, 1160.0, .82454,17965.0, .13316},
718 { 7.7197, .004388, 3.242, .68434, 1428.1, .83398, 1786.7, .0665120},
719 {16.78, .0041918, 9.3198, .29568, 3370.9, .90289, 7431.7, .02616},
720 { 4.2132, .0042098, 4.6753, .57945, 3503.9, .89261, 1468.9, .0143590},
721 { 4.0818, .004214, 4.4425, .58393, 3945.3, .90281, 1340.5, .0134140}, //Xe
722 {.18517, .0036215, .00058788,3.5315, 2931.3, .88936, 26.18, .0263930},
723 { 4.8248, .0041458, 6.0934, .57026, 2300.1, .86359, 2980.7, .0386790},
724 { .49857, .0041054, 1.9775, .95877, 786.55, .78509, 806.6, .40882},
725 { 3.2754, .0042177, 5.768, .54054, 6631.3, .94282, 744.07, .0083026},
726 { 2.9978, .0040901, 4.5299, .62025, 2161.2, .85669, 1268.6, .0430310},
727 { 2.8701, .004096, 4.2568, .6138, 2130.4, .85235, 1704.1, .0393850},
728 {10.853, .0041149, 5.8907, .46834, 2857.2, .8755, 3654.2, .0299550},
729 { 3.6407, .0041782, 4.8742, .57861, 1267.7, .82211, 3508.2, .24174},
730 {17.645, .0040992, 6.5855, .32734, 3931.3, .90754, 5156.7, .0362780},
731 { 7.5309, .0040814, 4.9389, .50679, 2519.7, .85819, 3314.6, .0305140},
732 { 5.4742, .0040829, 4.897, .51113, 2340.1, .85296, 2342.7, .0356620},
733 { 4.2661, .0040667, 4.5032, .55257, 2076.4, .84151, 1666.6, .0408010},
734 { 6.8313, .0040486, 4.3987, .51675, 2003.0, .83437, 1410.4, .03478},
735 { 1.2707, .0040553, 4.6295, .57428, 1626.3, .81858, 995.68, .0553190},
736 { 5.7561, .0040491, 4.357, .52496, 2207.3, .83796, 1579.5, .0271650},
737 {14.127, .0040596, 5.8304, .37755, 3645.9, .87823, 3411.8, .0163920},
738 { 6.6948, .0040603, 4.9361, .47961, 2719.0, .85249, 1885.8, .0197130},
739 { 3.0619, .0040511, 3.5803, .59082, 2346.1, .83713, 1222.0, .0200720},
740 {10.811, .0033008, 1.3767, .76512, 2003.7, .82269, 1110.6, .0249580},
741 { 2.7101, .0040961, 1.2289, .98598, 1232.4, .79066, 155.42, .0472940},
742 { .52345, .0040244, 1.4038, .8551, 1461.4, .79677, 503.34, .0367890},
743 { .4616, .0040203, 1.3014, .87043, 1473.5, .79687, 443.09, .0363010},
744 { .97814, .0040374, 2.0127, .7225, 1890.8, .81747, 930.7, .02769},
745 { 3.2086, .004051, 3.6658, .53618, 3091.2, .85602, 1508.1, .0154010},
746 { 2.0035, .0040431, 7.4882, .3561, 4464.3, .88836, 3966.5, .0128390},
747 {15.43, .0039432, 1.1237, .70703, 4595.7, .88437, 1576.5, .0088534},
748 { 3.1512, .0040524, 4.0996, .5425, 3246.3, .85772, 1691.8, .0150580},
749 { 7.1896, .0040588, 8.6927, .35842, 4760.6, .88833, 2888.3, .0110290}, //Pb
750 { 9.3209, .004054, 11.543, .32027, 4866.2, .89124, 3213.4, .0119350},
751 {29.242, .0036195, .16864, 1.1226, 5688.0, .89812, 1033.3, .0071303},
752 { 1.8522, .0039973, 3.1556, .65096, 3755.0, .86383, 1602.0, .0120420},
753 { 3.222, .0040041, 5.9024, .52678, 4040.2, .86804, 1658.4, .0117470},
754 { 9.3412, .0039661, 7.921, .42977, 5180.9, .88773, 2173.2, .0092007},
755 {36.183, .0036003, .58341, .86747, 6990.2, .91082, 1417.1, .0062187},
756 { 5.9284, .0039695, 6.4082, .52122, 4619.5, .88083, 2323.5, .0116270},
757 { 5.2454, .0039744, 6.7969, .48542, 4586.3, .87794, 2481.5, .0112820},
758 {33.702, .0036901, .47257, .89235, 5295.7, .8893, 2053.3, .0091908},
759 {2.7589, .0039806, 3.2092, .66122, 2505.4, .82863, 2065.1, .0228160} //U
760 };
761 
762 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
763 
764 const G4double G4AtimaEnergyLossModel::atima_vfermi[92] = {
765 1.0309,
766 0.15976,
767 0.59782,
768 1.0781,
769 1.0486,
770 1.00,
771 1.058,
772 0.93942,
773 0.74562,
774 0.3424,
775 0.45259,
776 0.71074,
777 0.90519,
778 0.97411,
779 0.97184,
780 0.89852,
781 0.70827,
782 0.39816,
783 0.36552,
784 0.62712,
785 0.81707,
786 0.9943,
787 1.1423,
788 1.2381,
789 1.1222,
790 0.92705,
791 1.0047,
792 1.2,
793 1.0661,
794 0.97411,
795 0.84912,
796 0.95,
797 1.0903,
798 1.0429,
799 0.49715,
800 0.37755,
801 0.35211,
802 0.57801,
803 0.77773,
804 1.0207,
805 1.029,
806 1.2542,
807 1.122,
808 1.1241,
809 1.0882,
810 1.2709,
811 1.2542,
812 0.90094,
813 0.74093,
814 0.86054,
815 0.93155,
816 1.0047,
817 0.55379,
818 0.43289,
819 0.32636,
820 0.5131,
821 0.6950,
822 0.72591,
823 0.71202,
824 0.67413,
825 0.71418,
826 0.71453,
827 0.5911,
828 0.70263,
829 0.68049,
830 0.68203,
831 0.68121,
832 0.68532,
833 0.68715,
834 0.61884,
835 0.71801,
836 0.83048,
837 1.1222,
838 1.2381,
839 1.045,
840 1.0733,
841 1.0953,
842 1.2381,
843 1.2879,
844 0.78654,
845 0.66401,
846 0.84912,
847 0.88433,
848 0.80746,
849 0.43357,
850 0.41923,
851 0.43638,
852 0.51464,
853 0.73087,
854 0.81065,
855 1.9578,
856 1.0257
857 };
858 
859 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
860 
861 const G4double G4AtimaEnergyLossModel::atima_lambda_screening[92]= {
862  1.00,
863  1.00,
864  1.10,
865  1.06,
866  1.01,
867  1.03,
868  1.04,
869  0.99,
870  0.95,
871  0.90,
872  0.82,
873  0.81,
874  0.83,
875  0.88,
876  1.00,
877  0.95,
878  0.97,
879  0.99,
880  0.98,
881  0.97,
882  0.98,
883  0.97,
884  0.96,
885  0.93,
886  0.91,
887  0.9,
888  0.88,
889  0.9,
890  0.9,
891  0.9,
892  0.9,
893  0.85,
894  0.9,
895  0.9,
896  0.91,
897  0.92,
898  0.9,
899  0.9,
900  0.9,
901  0.9,
902  0.9,
903  0.88,
904  0.9,
905  0.88,
906  0.88,
907  0.9,
908  0.9,
909  0.88,
910  0.9,
911  0.9,
912  0.9,
913  0.9,
914  0.96,
915  1.2,
916  0.9,
917  0.88,
918  0.88,
919  0.85,
920  0.90,
921  0.90,
922  0.92,
923  0.95,
924  0.99,
925  1.03,
926  1.05,
927  1.07,
928  1.08,
929  1.10,
930  1.08,
931  1.08,
932  1.08,
933  1.08,
934  1.09,
935  1.09,
936  1.10,
937  1.11,
938  1.12,
939  1.13,
940  1.14,
941  1.15,
942  1.17,
943  1.20,
944  1.18,
945  1.17,
946  1.17,
947  1.16,
948  1.16,
949  1.16,
950  1.16,
951  1.16,
952  1.16,
953  1.16
954 };
955 
956 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
957 
958 const G4double G4AtimaEnergyLossModel::element_atomic_weights[110]={
959  0.0,
960  1.00794, //H
961  4.0026, //He
962  6.941, //Li
963  9.01218, //Be
964  10.811, //B
965  12.0107, //C
966  14.0067, //N
967  15.9994, //O
968  18.9984, //F
969  20.1797, //Ne
970  22.9898, //Na
971  24.305, //Mg
972  26.9815, //Al
973  28.0855, //Si
974  30.9738, //P
975  32.065, //S
976  35.453, //Cl
977  39.948, //Ar
978  39.0983, //K
979  40.078, //Ca
980  44.9559, //Sc
981  47.867, //Ti
982  50.9415, //V
983  51.9961, //Cr
984  54.938, //Mn
985  55.845, //Fe
986  58.9332, //Co
987  58.6934, //Ni
988  63.546, //Cu
989  65.409, //Zn
990  69.723, //Ga
991  72.64, //Ge
992  74.9216, //As
993  78.96, //Se
994  79.904, //Br
995  83.798, //Kr
996  85.4678, //Rb
997  87.62, //Sr
998  88.9059, //Y
999  91.224, //Zr
1000  92.9064, //Nb
1001  95.94, //Mo
1002  97.9072, //Tc
1003  101.07, //Ru
1004  102.906, //Rh
1005  106.42, //Pd
1006  107.868, //Ag
1007  112.411, //Cd
1008  114.818, //In
1009  118.71, //Sn
1010  121.76, //Sb
1011  127.6, //Te
1012  126.904, //I
1013  131.293, //Xe
1014  132.905, //Cs
1015  137.327, //Ba
1016  138.905, //La
1017  140.116, //Ce
1018  140.908, //Pr
1019  144.24, //Nd
1020  144.913, //Pm
1021  150.36, //Sm
1022  151.964, //Eu
1023  157.25, //Gd
1024  158.925, //Tb
1025  162.5, //Dy
1026  164.93, //Ho
1027  167.259, //Er
1028  168.934, //Tm
1029  173.04, //Yb
1030  174.967, //Lu
1031  178.49, //Hf
1032  180.948, //Ta
1033  183.84, //W
1034  186.207, //Re
1035  190.23, //Os
1036  192.217, //Ir
1037  195.078, //Pt
1038  196.967, //Au
1039  200.59, //Hg
1040  204.383, //Tl
1041  207.2, //Pb
1042  208.98, //Bi
1043  208.982, //Po
1044  209.987, //At
1045  222.018, //Rn
1046  223.02, //Fr
1047  226.025, //Ra
1048  227.028, //Ac
1049  232.038, //Th
1050  231.036, //Pa
1051  238.029, //U
1052  237.048, //Np
1053  244.064, //Pu
1054  243.061, //Am
1055  247.07, //Cm
1056  247.07, //Bk
1057  251.08, //Cf
1058  252.083, //Es
1059  257.095, //Fm
1060  258.098, //Md
1061  259.101, //No
1062  262.11, //Lr
1063  261.109, //Rf
1064  262.114, //Db
1065  266.122, //Sg
1066  264.125, //Bh
1067  269.134, //Hs
1068  268.139 //Mt
1069 };
1070 
1071 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1072 
1073 //LS coefficient for A=atomic weight
1074 const G4double G4AtimaEnergyLossModel::ls_coefficients_a[110][200]=
1075 { {-0.0286005,-0.0269762,-0.0254384,-0.0239826,-0.0226044,-0.0212998,-0.0200648,-0.0188958,-0.0177891,-0.0167414,-0.0157495,-0.0148105,-0.0139213,-0.0130793,-0.0122818,-0.0115265,-0.0108109,-0.0101329,-0.00949027,-0.00888115,-0.0083036,-0.00775583,-0.00723615,-0.00674295,-0.0062747,-0.00582996,-0.00540738,-0.00500564,-0.00462353,-0.00425989,-0.00391361,-0.00358365,-0.00326903,-0.0029688,-0.00268208,-0.00240803,-0.00214586,-0.00189481,-0.00165416,-0.00142324,-0.0012014,-0.000988038,-0.000782569,-0.000584449,-0.000393155,-0.000208196,-2.91012e-05,0.000144572,0.000313247,0.000477324,0.000637183,0.000793185,0.000945673,0.00109497,0.0012414,0.00138523,0.00152676,0.00166625,0.00180395,0.00194009,0.0020749,0.0022086,0.00234139,0.00247346,0.00260498,0.00273612,0.00286706,0.00299792,0.00312886,0.00325999,0.00339145,0.00352333,0.00365574,0.00378876,0.00392249,0.00405698,0.00419229,0.00432849,0.0044656,0.00460367,0.0047427,0.00488271,0.00502369,0.00516564,0.00530853,0.00545232,0.00559697,0.00574243,0.00588862,0.00603547,0.00618289,0.00633076,0.00647899,0.00662745,0.006776,0.00692451,0.00707282,0.00722077,0.00736819,0.00751491,0.00766074,0.0078055,0.007949,0.00809104,0.00823143,0.00836998,0.00850649,0.00864077,0.00877264,0.0089019,0.0090284,0.00915196,0.00927243,0.00938966,0.00950352,0.00961389,0.00972066,0.00982374,0.00992306,0.0100185,0.0101102,0.0101979,0.0102817,0.0103616,0.0104376,0.0105097,0.010578,0.0106425,0.0107033,0.0107605,0.0108141,0.0108643,0.0109111,0.0109547,0.0109951,0.0110324,0.0110669,0.0110984,0.0111273,0.0111535,0.0111772,0.0111984,0.0112173,0.0112339,0.0112483,0.0112605,0.0112705,0.0112785,0.0112844,0.0112882,0.0112899,0.0112895,0.0112869,0.0112821,0.0112749,0.0112652,0.011253,0.011238,0.01122,0.0111988,0.011174,0.0111455,0.0111127,0.0110753,0.0110328,0.0109847,0.0109303,0.0108689,0.0107998,0.010722,0.0106346,0.0105364,0.0104261,0.0103024,0.0101636,0.0100079,0.00983338,0.00963767,0.00941827,0.0091723,0.0088966,0.00858758,0.00824121,0.00785299,0.00741787,0.0069302,0.00638364,0.00577111,0.00508464,0.00431533,0.00345395,0.00248834,0.00140654,0.000194686,-0.00116268,-0.00268283,-0.00438502,-0.00629005,-0.00842259,-0.0108087},
1076  {-0.108683,-0.102922,-0.097437,-0.0922162,-0.0872489,-0.0825243,-0.0780321,-0.073762,-0.0697043,-0.0658493,-0.0621879,-0.0587109,-0.0554098,-0.0522762,-0.049302,-0.0464796,-0.0438014,-0.0412604,-0.0388496,-0.0365626,-0.0343929,-0.0323346,-0.0303819,-0.0285294,-0.0267717,-0.0251038,-0.023521,-0.0220186,-0.0205924,-0.0192382,-0.017952,-0.0167301,-0.015569,-0.0144651,-0.0134154,-0.0124167,-0.011466,-0.0105607,-0.00969814,-0.00887572,-0.00809112,-0.00734207,-0.00662644,-0.00594219,-0.00528738,-0.00466019,-0.00405889,-0.00348181,-0.00292739,-0.00239414,-0.00188067,-0.00138562,-0.000907732,-0.000445801,1.31405e-06,0.000434696,0.000855371,0.00126431,0.00166244,0.00205062,0.0024297,0.00280044,0.00316359,0.00351985,0.00386987,0.00421428,0.00455367,0.00488858,0.00521953,0.00554701,0.00587147,0.00619333,0.00651298,0.00683078,0.00714706,0.00746212,0.00777624,0.00808966,0.00840259,0.00871523,0.00902774,0.00934025,0.00965286,0.00996565,0.0102787,0.010592,0.0109055,0.0112192,0.0115331,0.0118471,0.012161,0.0124748,0.0127882,0.013101,0.0134132,0.0137243,0.0140342,0.0143426,0.0146492,0.0149537,0.0152557,0.015555,0.0158511,0.0161438,0.0164326,0.0167172,0.0169973,0.0172725,0.0175424,0.0178067,0.0180651,0.0183173,0.0185629,0.0188017,0.0190335,0.019258,0.019475,0.0196843,0.0198859,0.0200796,0.0202654,0.0204431,0.0206127,0.0207744,0.020928,0.0210737,0.0212116,0.0213417,0.0214643,0.0215794,0.0216873,0.021788,0.0218819,0.0219691,0.0220498,0.0221242,0.0221925,0.022255,0.0223118,0.0223631,0.0224091,0.0224499,0.0224857,0.0225167,0.0225428,0.0225643,0.0225811,0.0225932,0.0226007,0.0226036,0.0226016,0.0225948,0.0225828,0.0225656,0.0225427,0.022514,0.0224789,0.022437,0.0223877,0.0223304,0.0222644,0.0221887,0.0221025,0.0220046,0.0218937,0.0217684,0.0216273,0.0214683,0.0212895,0.0210887,0.0208632,0.0206101,0.0203263,0.020008,0.0196512,0.0192513,0.0188031,0.018301,0.0177384,0.0171081,0.0164021,0.0156115,0.0147258,0.0137341,0.0126235,0.0113801,0.00998803,0.00842986,0.00668603,0.00473508,0.00255242,0.000111379,-0.00261781,-0.0056681,-0.00907593,-0.0128834,-0.0171323,-0.0218726,-0.0271577,-0.0330461},
1077  {-0.223884,-0.213009,-0.202568,-0.192553,-0.182953,-0.173755,-0.16495,-0.156525,-0.148469,-0.140769,-0.133415,-0.126394,-0.119694,-0.113303,-0.10721,-0.101404,-0.0958714,-0.0906027,-0.0855866,-0.0808123,-0.0762693,-0.0719475,-0.0678369,-0.063928,-0.0602115,-0.0566782,-0.0533196,-0.0501272,-0.0470929,-0.0442089,-0.0414678,-0.0388623,-0.0363856,-0.034031,-0.0317921,-0.029663,-0.0276377,-0.0257108,-0.0238769,-0.0221309,-0.0204681,-0.0188837,-0.0173734,-0.0159331,-0.0145586,-0.0132462,-0.0119923,-0.0107934,-0.00964627,-0.00854773,-0.00749484,-0.00648478,-0.00551487,-0.00458256,-0.00368542,-0.00282117,-0.00198762,-0.0011827,-0.000404448,0.000348997,0.0010794,0.00178843,0.00247768,0.00314864,0.00380272,0.00444127,0.00506554,0.00567674,0.00627597,0.00686428,0.00744268,0.00801208,0.00857334,0.00912727,0.00967462,0.0102161,0.0107522,0.0112837,0.011811,0.0123347,0.012855,0.0133725,0.0138873,0.0143999,0.0149103,0.0154188,0.0159254,0.0164303,0.0169335,0.017435,0.0179346,0.0184323,0.018928,0.0194213,0.0199121,0.0204002,0.0208851,0.0213666,0.0218443,0.0223178,0.0227866,0.0232502,0.0237084,0.0241604,0.024606,0.0250444,0.0254754,0.0258983,0.0263127,0.0267181,0.027114,0.0275001,0.0278758,0.0282409,0.028595,0.0289377,0.0292689,0.0295882,0.0298954,0.0301905,0.0304734,0.0307439,0.0310021,0.031248,0.0314816,0.0317031,0.0319127,0.0321105,0.0322967,0.0324716,0.0326355,0.0327885,0.0329311,0.0330635,0.0331861,0.0332991,0.033403,0.0334979,0.0335842,0.0336623,0.0337323,0.0337945,0.0338491,0.0338964,0.0339365,0.0339694,0.0339954,0.0340144,0.0340265,0.0340315,0.0340294,0.0340199,0.0340028,0.0339778,0.0339445,0.0339023,0.0338507,0.033789,0.0337163,0.0336318,0.0335342,0.0334224,0.0332949,0.03315,0.032986,0.0328007,0.0325918,0.0323567,0.0320922,0.0317951,0.0314616,0.0310874,0.0306677,0.0301973,0.02967,0.0290791,0.0284172,0.0276758,0.0268457,0.025916,0.0248751,0.0237098,0.0224056,0.0209459,0.0193125,0.0174852,0.0154416,0.0131562,0.0106012,0.00774588,0.00455597,0.000993742,-0.00298393,-0.00742085,-0.0123683,-0.0178814,-0.0240203,-0.030853,-0.0384474,-0.0468817},
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1179  {-3.37618,-3.34687,-3.31754,-3.28818,-3.2588,-3.22939,-3.19995,-3.17049,-3.14099,-3.11146,-3.0819,-3.0523,-3.02266,-2.99298,-2.96325,-2.93349,-2.90367,-2.8738,-2.84388,-2.8139,-2.78386,-2.75376,-2.72359,-2.69335,-2.66304,-2.63264,-2.60217,-2.57161,-2.54095,-2.5102,-2.47935,-2.44839,-2.41732,-2.38612,-2.3548,-2.32335,-2.29176,-2.26003,-2.22814,-2.19608,-2.16386,-2.13146,-2.09887,-2.06608,-2.03309,-1.99988,-1.96644,-1.93277,-1.89884,-1.86466,-1.8302,-1.79546,-1.76042,-1.72507,-1.6894,-1.6534,-1.61704,-1.58032,-1.54323,-1.50574,-1.46785,-1.42954,-1.3908,-1.35162,-1.31198,-1.27186,-1.23127,-1.19018,-1.14858,-1.10647,-1.06384,-1.02067,-0.976964,-0.932717,-0.887923,-0.842581,-0.796691,-0.750256,-0.703282,-0.655775,-0.607746,-0.559209,-0.51018,-0.460678,-0.410726,-0.360352,-0.309585,-0.258459,-0.207013,-0.155288,-0.103329,-0.0511866,0.00108674,0.0534343,0.105796,0.158109,0.210306,0.262319,0.314078,0.365508,0.416536,0.467087,0.517085,0.566455,0.615121,0.66301,0.710049,0.756168,0.801301,0.845383,0.888354,0.930156,0.970739,1.01006,1.04806,1.08472,1.12001,1.15388,1.18634,1.21735,1.24692,1.27502,1.30168,1.32688,1.35065,1.37299,1.39392,1.41346,1.43164,1.44848,1.46401,1.47826,1.49126,1.50304,1.51363,1.52308,1.5314,1.53862,1.54479,1.54992,1.55404,1.55718,1.55936,1.56059,1.56089,1.56028,1.55876,1.55634,1.55303,1.54883,1.54373,1.53773,1.53081,1.52296,1.51417,1.50442,1.49367,1.4819,1.46909,1.45519,1.44017,1.42399,1.40661,1.38798,1.36805,1.34678,1.32411,1.3,1.2744,1.24724,1.21849,1.1881,1.15603,1.12223,1.08668,1.04934,1.01021,0.969266,0.926519,0.88198,0.835678,0.787657,0.73797,0.686693,0.63391,0.579718,0.524232,0.467569,0.409857,0.35122,0.291788,0.231675,0.170992,0.109833,0.0482752,-0.0136167,-0.0757989,-0.138235,-0.2009,-0.263772},
1180  {-3.38571,-3.3564,-3.32707,-3.29772,-3.26834,-3.23893,-3.2095,-3.18004,-3.15055,-3.12102,-3.09146,-3.06187,-3.03223,-3.00256,-2.97284,-2.94308,-2.91327,-2.88341,-2.85349,-2.82352,-2.79349,-2.76339,-2.73323,-2.703,-2.6727,-2.64232,-2.61185,-2.5813,-2.55066,-2.51992,-2.48908,-2.45814,-2.42708,-2.3959,-2.3646,-2.33316,-2.30159,-2.26987,-2.23799,-2.20596,-2.17376,-2.14137,-2.1088,-2.07604,-2.04307,-2.00988,-1.97646,-1.94281,-1.90891,-1.87475,-1.84031,-1.8056,-1.77058,-1.73526,-1.69961,-1.66362,-1.62729,-1.59059,-1.55352,-1.51605,-1.47817,-1.43988,-1.40115,-1.36198,-1.32234,-1.28223,-1.24163,-1.20053,-1.15893,-1.1168,-1.07414,-1.03095,-0.987206,-0.942914,-0.898067,-0.852663,-0.806701,-0.760184,-0.713116,-0.665503,-0.617356,-0.568687,-0.519511,-0.469848,-0.41972,-0.369154,-0.318178,-0.266826,-0.215136,-0.163149,-0.11091,-0.058469,-0.0058782,0.0468055,0.099522,0.152208,0.204796,0.257218,0.309402,0.361274,0.412759,0.463781,0.514262,0.564127,0.613298,0.6617,0.70926,0.755905,0.801567,0.84618,0.889681,0.932012,0.973119,1.01295,1.05147,1.08863,1.12441,1.15876,1.19168,1.22315,1.25314,1.28167,1.30872,1.3343,1.35843,1.38111,1.40235,1.42219,1.44065,1.45774,1.4735,1.48796,1.50116,1.51311,1.52386,1.53343,1.54186,1.54918,1.55542,1.56061,1.56477,1.56794,1.57012,1.57134,1.57162,1.57097,1.5694,1.56691,1.56352,1.55923,1.55402,1.5479,1.54085,1.53286,1.52391,1.51398,1.50305,1.49109,1.47807,1.46396,1.44871,1.43229,1.41465,1.39576,1.37555,1.35399,1.33102,1.30659,1.28065,1.25316,1.22406,1.19331,1.16086,1.12668,1.09074,1.05301,1.01347,0.972123,0.92897,0.884027,0.837326,0.788912,0.738842,0.687194,0.634056,0.579527,0.523722,0.466763,0.408776,0.349887,0.290223,0.2299,0.169024,0.107687,0.0459644,-0.016083,-0.0784135,-0.140991,-0.203796,-0.266801},
1181  {-3.39515,-3.36584,-3.33652,-3.30717,-3.27779,-3.24839,-3.21896,-3.18951,-3.16002,-3.1305,-3.10094,-3.07135,-3.04172,-3.01205,-2.98234,-2.95259,-2.92278,-2.89293,-2.86302,-2.83306,-2.80303,-2.77295,-2.7428,-2.71258,-2.68228,-2.65191,-2.62146,-2.59092,-2.56029,-2.52957,-2.49874,-2.46781,-2.43676,-2.4056,-2.37431,-2.34289,-2.31134,-2.27964,-2.24778,-2.21577,-2.18358,-2.15122,-2.11868,-2.08593,-2.05298,-2.01982,-1.98643,-1.9528,-1.91893,-1.88479,-1.85038,-1.81569,-1.78071,-1.74541,-1.70979,-1.67383,-1.63752,-1.60085,-1.56379,-1.52635,-1.4885,-1.45022,-1.41151,-1.37235,-1.33273,-1.29262,-1.25203,-1.21094,-1.16933,-1.12719,-1.08452,-1.0413,-0.997534,-0.953207,-0.908317,-0.86286,-0.816837,-0.770248,-0.723097,-0.67539,-0.627135,-0.578346,-0.529036,-0.479225,-0.428933,-0.378186,-0.327014,-0.275449,-0.223528,-0.171292,-0.118785,-0.066058,-0.0131622,0.0398454,0.0929047,0.145952,0.19892,0.25174,0.304339,0.356642,0.408575,0.460059,0.511016,0.561369,0.611039,0.659949,0.708025,0.755193,0.801382,0.846524,0.890555,0.933415,0.975048,1.0154,1.05444,1.09211,1.12838,1.16322,1.19661,1.22853,1.25898,1.28793,1.31539,1.34137,1.36587,1.3889,1.41049,1.43065,1.4494,1.46677,1.48279,1.49749,1.51091,1.52306,1.534,1.54374,1.55232,1.55978,1.56614,1.57143,1.57568,1.57892,1.58116,1.58243,1.58275,1.58212,1.58057,1.5781,1.5747,1.5704,1.56517,1.55902,1.55194,1.5439,1.53491,1.52493,1.51394,1.50192,1.48883,1.47463,1.45931,1.4428,1.42507,1.40607,1.38577,1.3641,1.34102,1.31647,1.29041,1.26279,1.23356,1.20267,1.17008,1.13576,1.09966,1.06178,1.02208,0.980574,0.937256,0.892146,0.845276,0.796693,0.746455,0.69464,0.641336,0.586645,0.530683,0.473569,0.415434,0.356401,0.296599,0.236142,0.175137,0.113675,0.0518299,-0.0103368,-0.0727844,-0.135477,-0.198395,-0.261512},
1182  {-3.4045,-3.3752,-3.34588,-3.31653,-3.28716,-3.25776,-3.22834,-3.19889,-3.1694,-3.13989,-3.11034,-3.08075,-3.05113,-3.02147,-2.99176,-2.96201,-2.93221,-2.90237,-2.87247,-2.84251,-2.8125,-2.78242,-2.75228,-2.72207,-2.69179,-2.66143,-2.63099,-2.60046,-2.56984,-2.53913,-2.50832,-2.4774,-2.44637,-2.41523,-2.38395,-2.35255,-2.32102,-2.28934,-2.2575,-2.22551,-2.19335,-2.16101,-2.12848,-2.09577,-2.06284,-2.0297,-1.99634,-1.96274,-1.92889,-1.89479,-1.86041,-1.82575,-1.79079,-1.75552,-1.71993,-1.684,-1.64772,-1.61108,-1.57405,-1.53664,-1.49881,-1.46056,-1.42187,-1.38274,-1.34313,-1.30305,-1.26247,-1.22138,-1.17977,-1.13764,-1.09496,-1.05174,-1.00795,-0.963599,-0.918677,-0.873181,-0.827108,-0.78046,-0.733239,-0.685452,-0.637105,-0.58821,-0.538782,-0.488838,-0.438399,-0.387489,-0.336138,-0.284378,-0.232244,-0.179777,-0.127023,-0.0740292,-0.0208483,0.032463,0.0858444,0.139232,0.192559,0.245756,0.298749,0.351463,0.403821,0.455746,0.507158,0.557977,0.608125,0.657524,0.706095,0.753764,0.800459,0.84611,0.890651,0.934021,0.976161,1.01702,1.05655,1.0947,1.13145,1.16676,1.20061,1.23297,1.26384,1.2932,1.32106,1.34741,1.37226,1.39563,1.41753,1.43798,1.45701,1.47464,1.4909,1.50581,1.51942,1.53175,1.54284,1.55271,1.56141,1.56897,1.57541,1.58076,1.58506,1.58833,1.59059,1.59186,1.59217,1.59151,1.58992,1.58739,1.58392,1.57953,1.57421,1.56795,1.56075,1.55258,1.54344,1.53331,1.52215,1.50994,1.49665,1.48225,1.4667,1.44996,1.43198,1.41273,1.39215,1.37019,1.3468,1.32194,1.29555,1.26759,1.238,1.20674,1.17377,1.13905,1.10255,1.06426,1.02414,0.982214,0.938474,0.892944,0.845658,0.796665,0.746028,0.693828,0.640156,0.585116,0.528826,0.471409,0.412992,0.353702,0.293666,0.232996,0.171797,0.110157,0.0481464,-0.0141762,-0.0767727,-0.139609,-0.202666,-0.265917}
1183 };
1184 
1185 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1186 
1187 //LS coefficient for A=atomic weight * 1.05
1188 const G4double G4AtimaEnergyLossModel::ls_coefficients_ahi[110][200]=
1189 {
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1295  {-3.38571,-3.3564,-3.32707,-3.29772,-3.26834,-3.23893,-3.2095,-3.18004,-3.15055,-3.12102,-3.09146,-3.06187,-3.03223,-3.00256,-2.97284,-2.94308,-2.91327,-2.8834,-2.85349,-2.82352,-2.79349,-2.76339,-2.73323,-2.703,-2.6727,-2.64232,-2.61185,-2.5813,-2.55066,-2.51992,-2.48908,-2.45813,-2.42707,-2.3959,-2.36459,-2.33316,-2.30158,-2.26986,-2.23799,-2.20595,-2.17375,-2.14137,-2.1088,-2.07603,-2.04306,-2.00987,-1.97646,-1.9428,-1.9089,-1.87474,-1.84031,-1.80559,-1.77057,-1.73525,-1.6996,-1.66362,-1.62728,-1.59058,-1.55351,-1.51604,-1.47817,-1.43987,-1.40114,-1.36197,-1.32233,-1.28222,-1.24162,-1.20053,-1.15892,-1.1168,-1.07414,-1.03094,-0.987204,-0.942913,-0.898068,-0.852665,-0.806705,-0.760189,-0.713123,-0.665513,-0.617368,-0.568702,-0.519529,-0.469869,-0.419745,-0.369182,-0.31821,-0.266863,-0.215178,-0.163197,-0.110964,-0.058529,-0.00594485,0.0467317,0.0994405,0.152118,0.204698,0.257111,0.309285,0.361146,0.41262,0.46363,0.5141,0.563951,0.613109,0.661497,0.709042,0.755671,0.801317,0.845912,0.889394,0.931706,0.972793,1.01261,1.0511,1.08824,1.12399,1.15832,1.19121,1.22265,1.25261,1.28111,1.30813,1.33367,1.35776,1.3804,1.40161,1.4214,1.43981,1.45685,1.47257,1.48697,1.50011,1.512,1.52268,1.53219,1.54055,1.54779,1.55395,1.55905,1.56312,1.56618,1.56826,1.56937,1.56954,1.56876,1.56706,1.56444,1.5609,1.55645,1.55107,1.54477,1.53754,1.52935,1.52019,1.51005,1.49888,1.48668,1.4734,1.45901,1.44347,1.42674,1.40879,1.38955,1.36899,1.34706,1.32371,1.29888,1.27253,1.2446,1.21506,1.18385,1.15093,1.11627,1.07984,1.04162,1.00158,0.959738,0.916092,0.870663,0.823487,0.774613,0.724104,0.672041,0.618514,0.563627,0.507499,0.450252,0.392011,0.332905,0.273059,0.212583,0.151582,0.0901431,0.0283351,-0.0337836,-0.0961764,-0.158809,-0.221663,-0.284712},
1296  {-3.39515,-3.36584,-3.33652,-3.30717,-3.27779,-3.24839,-3.21896,-3.1895,-3.16002,-3.1305,-3.10094,-3.07135,-3.04172,-3.01205,-2.98234,-2.95258,-2.92278,-2.89293,-2.86302,-2.83306,-2.80303,-2.77295,-2.7428,-2.71258,-2.68228,-2.65191,-2.62146,-2.59092,-2.56029,-2.52956,-2.49874,-2.4678,-2.43676,-2.4056,-2.37431,-2.34289,-2.31133,-2.27963,-2.24778,-2.21576,-2.18358,-2.15122,-2.11867,-2.08593,-2.05298,-2.01981,-1.98642,-1.9528,-1.91892,-1.88478,-1.85038,-1.81569,-1.7807,-1.7454,-1.70978,-1.67382,-1.63751,-1.60084,-1.56378,-1.52634,-1.48849,-1.45021,-1.4115,-1.37234,-1.33272,-1.29262,-1.25202,-1.21093,-1.16932,-1.12718,-1.08451,-1.0413,-0.99753,-0.953204,-0.908315,-0.86286,-0.816838,-0.770251,-0.723102,-0.675397,-0.627145,-0.578358,-0.529052,-0.479243,-0.428955,-0.378212,-0.327044,-0.275484,-0.223567,-0.171337,-0.118837,-0.0661154,-0.0132264,0.039774,0.0928255,0.145864,0.198824,0.251634,0.304223,0.356516,0.408437,0.459909,0.510854,0.561194,0.61085,0.659746,0.707806,0.754958,0.801129,0.846253,0.890266,0.933106,0.974719,1.01505,1.05406,1.09171,1.12795,1.16277,1.19613,1.22803,1.25844,1.28736,1.31479,1.34073,1.36519,1.38819,1.40973,1.42984,1.44855,1.46587,1.48184,1.49649,1.50984,1.52194,1.53281,1.54248,1.55099,1.55837,1.56464,1.56985,1.57401,1.57715,1.57929,1.58045,1.58065,1.5799,1.57821,1.5756,1.57206,1.56759,1.5622,1.55587,1.5486,1.54037,1.53117,1.52097,1.50974,1.49747,1.48412,1.46965,1.45403,1.43722,1.41917,1.39984,1.37918,1.35714,1.33367,1.30873,1.28225,1.2542,1.22452,1.19317,1.16011,1.12531,1.08872,1.05034,1.01015,0.968141,0.924329,0.878733,0.831389,0.782345,0.731669,0.679438,0.625747,0.5707,0.514415,0.457015,0.398628,0.339379,0.279396,0.218788,0.157659,0.0960955,0.0341663,-0.0280709,-0.0905801,-0.153327,-0.216294,-0.279454},
1297  {-3.4045,-3.3752,-3.34588,-3.31653,-3.28716,-3.25776,-3.22834,-3.19888,-3.1694,-3.13989,-3.11034,-3.08075,-3.05113,-3.02146,-2.99176,-2.96201,-2.93221,-2.90236,-2.87246,-2.84251,-2.8125,-2.78242,-2.75228,-2.72207,-2.69178,-2.66142,-2.63098,-2.60046,-2.56984,-2.53913,-2.50832,-2.4774,-2.44637,-2.41522,-2.38395,-2.35255,-2.32101,-2.28933,-2.2575,-2.2255,-2.19334,-2.161,-2.12848,-2.09576,-2.06283,-2.0297,-1.99633,-1.96273,-1.92888,-1.89478,-1.8604,-1.82574,-1.79078,-1.75551,-1.71992,-1.68399,-1.64771,-1.61107,-1.57404,-1.53663,-1.4988,-1.46055,-1.42186,-1.38273,-1.34312,-1.30303,-1.26246,-1.22137,-1.17977,-1.13763,-1.09495,-1.05173,-1.00794,-0.963594,-0.918673,-0.873177,-0.827106,-0.78046,-0.733241,-0.685456,-0.637111,-0.58822,-0.538794,-0.488854,-0.438418,-0.387512,-0.336165,-0.284409,-0.232281,-0.17982,-0.127072,-0.074084,-0.02091,0.0323938,0.0857674,0.139147,0.192465,0.245652,0.298634,0.351337,0.403684,0.455597,0.506996,0.557802,0.607936,0.657319,0.705874,0.753527,0.800204,0.845837,0.890358,0.933707,0.975826,1.01666,1.05617,1.0943,1.13102,1.1663,1.20012,1.23246,1.26329,1.29262,1.32044,1.34675,1.37157,1.3949,1.41676,1.43716,1.45614,1.47372,1.48992,1.50478,1.51833,1.5306,1.54162,1.55143,1.56005,1.56753,1.57389,1.57915,1.58336,1.58653,1.58868,1.58984,1.59002,1.58925,1.58752,1.58484,1.58123,1.57668,1.57119,1.56475,1.55736,1.549,1.53964,1.52928,1.51789,1.50543,1.49188,1.4772,1.46136,1.4443,1.426,1.40641,1.38547,1.36314,1.33936,1.3141,1.28729,1.25889,1.22885,1.19713,1.16368,1.12848,1.09149,1.0527,1.01209,0.969659,0.925425,0.87941,0.831651,0.782201,0.731129,0.678519,0.624464,0.569074,0.512468,0.454771,0.39611,0.336611,0.2764,0.215585,0.154267,0.0925296,0.0304376,-0.0319538,-0.0946098,-0.1575,-0.220604,-0.283896}
1298 };
1299 
1300 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1301 
1302 const G4double G4AtimaEnergyLossModel::ionisation_potentials_z[121] = {
1303  9999999, // 0
1304  19.2, // H
1305  41.8, // He
1306  40.0,
1307  63.7,
1308  76.0,
1309  78.0, // C
1310  82.0,
1311  95.0,
1312  115.0,
1313  137.0,
1314  149.0,
1315  156.0,
1316  166.0,
1317  173.0,
1318  173.0,
1319  180.0,
1320  174.0,
1321  188.0,
1322  190.0,
1323  191.0, //Ca (20)
1324  216.0,
1325  233.0,
1326  245.0,
1327  257.0,
1328  272.0,
1329  286.0, //Fe 26
1330  297.0,
1331  311.0,
1332  322.0,
1333  330.0,
1334  334.0,
1335  350.0,
1336  347.0,
1337  348.0,
1338  343.0,
1339  352.0,
1340  363.0,
1341  366.0,
1342  379.0,
1343  393.0,
1344  417.0,
1345  424.0,
1346  428.0,
1347  441.0,
1348  449.0,
1349  470.0,
1350  470.0,
1351  469.0,
1352  488.0,
1353  488.0, //Sn 50
1354  487.0,
1355  485.0,
1356  491.0,
1357  482.0, // Xe 54
1358  488.0,
1359  491.0,
1360  501.0,
1361  523.0,
1362  535.0,
1363  546.0,
1364  560.0,
1365  574.0,
1366  580.0,
1367  591.0,
1368  614.0,
1369  628.0,
1370  650.0,
1371  658.0,
1372  674.0,
1373  684.0,
1374  694.0,
1375  705.0,
1376  718.0,
1377  727.0,
1378  736.0,
1379  746.0,
1380  757.0,
1381  790.0,
1382  790.0, // Au 79
1383  800.0,
1384  810.0,
1385  823.0, //Pb 82
1386  823.0,
1387  830.0,
1388  825.0,
1389  794.0,
1390  827.0,
1391  826.0,
1392  841.0,
1393  847.0,
1394  878.0,
1395  890.0, // U 92
1396  900.0,
1397  910.0,
1398  920.0,
1399  930.0,
1400  940.0,
1401  950.0,
1402  960.0,
1403  970.0,
1404  980.0,
1405  990.0,
1406  1000.0,
1407  1010.0,
1408  1020.0,
1409  1030.0,
1410  1040.0,
1411  1050.0,
1412  1060.0,
1413  1070.0,
1414  1080.0,
1415  1090.0,
1416  1100.0,
1417  1110.0,
1418  1120.0,
1419  1130.0,
1420  1140.0,
1421  1150.0,
1422  1160.0,
1423  1170.0,
1424  };
1425 
1426 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1427 
1428 const G4double G4AtimaEnergyLossModel::x0[92]= {
1429 1.8639, 2.2017, 0.1304, 0.0592, 0.0305, -.0178, 1.7378, 1.7541, 1.8433, 2.0735,
1430 0.2880, 0.1499, 0.1708, 0.2014, 0.1696, 0.1580, 1.5555, 1.7635, 0.3851, 0.3228,
1431 0.1640, 0.0957, 0.0691, 0.0340, 0.0447, -.0012, -.0187, -.0566, -.0254, 0.0049,
1432 0.2267, 0.3376, 0.1767, 0.2258, 1.5262, 1.7158, 0.5737, 0.4585, 0.3608, 0.2957,
1433 0.1785, 0.2267, 0.0949, 0.0599, 0.0576, 0.0563, 0.0657, 0.1281, 0.2406, 0.2879,
1434 0.3189, 0.3296, 0.0549, 1.5630, 0.5473, 0.4190, 0.3161, 0.2713, 0.2333, 0.1984,
1435 0.1627, 0.1520, 0.1888, 0.1058, 0.0947, 0.0822, 0.0761, 0.0648, 0.0812, 0.1199,
1436 0.1560, 0.1965, 0.2117, 0.2167, 0.0559, 0.0891, 0.0819, 0.1484, 0.2021, 0.2756,
1437 0.3491, 0.3776, 0.4152, 0.4267, 0.4300, 1.5368, 0.6000, 0.5991, 0.4559, 0.4202,
1438 0.3144, 0.2260 };
1439 
1440 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1441 
1442 const G4double G4AtimaEnergyLossModel::x1[92]= {
1443 3.2718, 3.6122, 1.6397, 1.6922, 1.9688, 2.3415, 4.1323, 4.3213, 4.4096, 4.6421,
1444 3.1962, 3.0668, 3.0127, 2.8715, 2.7815, 2.7159, 4.2994, 4.4855, 3.1724, 3.1191,
1445 3.0593, 3.0386, 3.0322, 3.0451, 3.1074, 3.1531, 3.1790, 3.1851, 3.2792, 3.3668,
1446 3.5434, 3.6096, 3.5702, 3.6264, 4.9899, 5.0748, 3.7995, 3.6778, 3.5542, 3.4890,
1447 3.2201, 3.2784, 3.1253, 3.0834, 3.1069, 3.0555, 3.1074, 3.1667, 3.2032, 3.2959,
1448 3.3489, 3.4418, 3.2596, 4.7371, 3.5914, 3.4547, 3.3293, 3.3432, 3.2773, 3.3063,
1449 3.3199, 3.3460, 3.4633, 3.3932, 3.4224, 3.4474, 3.4782, 3.4922, 3.5085, 3.6246,
1450 3.5218, 3.4337, 3.4805, 3.4960, 3.4845, 3.5414, 3.5480, 3.6212, 3.6979, 3.7275,
1451 3.8044, 3.8073, 3.8248, 3.8293, 4.0000, 4.9889, 4.0000, 3.9428, 3.7966, 3.7681,
1452 3.5079, 3.3721 };
1453 
1454 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1455 
1456 const G4double G4AtimaEnergyLossModel::afermi[92]= {
1457  0.14092, 0.13443, 0.95136, 0.80392, 0.56224, 0.26142, 0.15349, 0.11778, 0.11083, .08064,
1458  0.07772, 0.08163, 0.08024, 0.14921, 0.23610, 0.33992, 0.19849, 0.19714, 0.19827, .15643,
1459  0.15754, 0.15662, 0.15436, 0.15419, 0.14973, 0.14680, 0.14474, 0.16496, 0.14339, .14714,
1460  0.09440, 0.07188, 0.06633, 0.06568, 0.06335, 0.07446, 0.07261, 0.07165, 0.07138, .07177,
1461  0.13883, 0.10525, 0.16572, 0.19342, 0.19205, 0.24178, 0.24585, 0.24609, 0.23879, .18689,
1462  0.16652, 0.13815, 0.23766, 0.23314, 0.18233, 0.18268, 0.18591, 0.18885, 0.23265, .23530,
1463  0.24280, 0.24698, 0.24448, 0.25109, 0.24453, 0.24665, 0.24638, 0.24823, 0.24889, .25295,
1464  0.24033, 0.22918, 0.17798, 0.15509, 0.15184, 0.12751, 0.12690, 0.11128, 0.09756, .11014,
1465  0.09455, 0.09359, 0.09410, 0.09282, 0.09000, 0.20798, 0.08000, 0.08804, 0.08567, 0.08655,
1466  0.14770, 0.19677 };
1467 
1468 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1469 
1470 const G4double G4AtimaEnergyLossModel::c[92]= {
1471 9.5835, 11.1393, 3.1221, 2.7847, 2.8477, 2.8680, 10.5400, 10.7004, 10.9653, 11.9041,
1472 5.0526, 4.5297, 4.2395, 4.4351, 4.5214, 4.6659, 11.1421, 11.9480, 5.6423, 5.0396,
1473 4.6949, 4.4450, 4.2659, 4.1781, 4.2702, 4.2911, 4.2601, 4.3115, 4.4190, 4.6906,
1474 4.9353, 5.1411, 5.0510, 5.3210, 11.7307,12.5115,6.4776, 5.9867, 5.4801 , 5.1774,
1475 5.0141, 4.8793, 4.7769, 4.7694, 4.8008, 4.9358, 5.0630, 5.2727, 5.5211, 5.5340,
1476 5.6241, 5.7131, 5.9488, 12.7281, 6.9135, 6.3153, 5.7850, 5.7837, 5.8096, 5.8290,
1477 5.8224, 5.8597, 6.2278, 5.8738, 5.9045, 5.9183, 5.9587, 5.9521, 5.9677, 6.3325,
1478 5.9785, 5.7139, 5.5262, 5.4059, 5.3445, 5.3083, 5.3418, 5.4732, 5.5747, 5.9605,
1479 6.1365, 6.2018, 6.3505, 6.4003, 6.4, 13.2839, 7., 7.0452, 6.3742, 6.2473,
1480 6.0327, 5.8694 };
1481 
1482 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1483 
1484 const G4double G4AtimaEnergyLossModel::m0[92]= {
1485 5.7273, 5.8347, 2.4993, 2.4339, 2.4512, 2.8697, 3.2125, 3.2913, 3.2962, 3.5771,
1486 3.6452, 3.6166, 3.6345, 3.2546, 2.9158, 2.6456, 2.9702, 2.9618, 2.9233, 3.0745,
1487 3.0517, 3.0302, 3.0163, 2.9896, 2.9796, 2.9632, 2.9502, 2.8430, 2.9044, 2.8652,
1488 3.1314, 3.3306, 3.4176, 3.4317, 3.4670, 3.4051, 3.4177, 3.4435, 3.4585, 3.4533,
1489 3.0930, 3.2549, 2.9738, 2.8707, 2.8633, 2.7239, 2.6899, 2.6772, 2.7144, 2.8576,
1490 2.9319, 3.0354, 2.7276, 2.7414, 2.8866, 2.8906, 2.8828, 2.8592, 2.7331, 2.7050,
1491 2.6674, 2.6403, 2.6245, 2.5977, 2.6056, 2.5849, 2.5726, 2.5573, 2.5469, 2.5141,
1492 2.5643, 2.6155, 2.7623, 2.8447, 2.8627, 2.9608, 2.9658, 3.0417, 3.1101, 3.0519,
1493 3.1450, 3.1608, 3.1671, 3.1830, 1.1111, 2.7409, 1.1111, 3.2454, 3.2683, 3.2610,
1494 2.9845, 2.8171 };
1495 
1496 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1497 
1498 const G4double G4AtimaEnergyLossModel::del_0[92]= {
1499 0.0, 0.00, 0.14, 0.14, 0.14, 0.12, 0.00, 0.00, 0.00, 0.00,
1500 0.08, 0.08, 0.12, 0.14, 0.14, 0.14, 0.00, 0.00, 0.10, 0.14,
1501 0.10, 0.12, 0.14, 0.14, 0.14, 0.12, 0.12, 0.10, 0.08, 0.08,
1502 0.14, 0.14, 0.08, 0.10, 0.00, 0.00, 0.14, 0.14, 0.14, 0.14,
1503 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
1504 0.14, 0.14, 0.00, 0.00, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
1505 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
1506 0.14, 0.14, 0.14, 0.14, 0.08, 0.10, 0.10, 0.12, 0.14, 0.14,
1507 0.14, 0.14, 0.14, 0.14, 0.00, 0.00, 0.00, 0.14, 0.14, 0.14,
1508 0.14, 0.14 };
1509 
1510 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......