Geant4_10
G4QAOLowEnergyLoss.cc
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28 // GEANT 4 class implementation file
29 //
30 // History: New Implementation
31 //
32 // ---------- G4QAOLowEnergyLoss physics process -------
33 // by Stephane Chauvie, 5 May 2000
34 // Modified:
35 //
36 // 24/05/2000 MGP Modified to remove compilation warnings on Linux and DEC
37 // Introduced sizes of L0, L1, L2 arrays
38 // 23/05/2000 MGP Made compliant to design
39 // 02/08/2000 V.Ivanchenko Clean up according new design
40 // 16/09/2000 S. Chauvie Oscillator for all materials
41 // 03/10/2000 V.Ivanchenko CodeWizard clean up
42 // 05/11/2000 V.Ivanchenko "Aluminum" - correct name, end of cycle
43 // over shells, and two bugs from previous edition
44 // 10/05/2001 V.Ivanchenko Clean up againist Linux compilation with -Wall
45 // 13/05/2001 S. Chauvie corrected bugs
46 // 01/06/2001 V.Ivanchenko replace names by Z, change the validity range
47 // from 50 keV to 5 KeV and change sign of the
48 // Barkas term
49 // 4/06/2001 S. Chauvie Corrected small bugs
50 //
51 // ************************************************************
52 // It is the Quantal Harmonic Oscillator Model for energy loss
53 // of slow antiproton
54 // ************************************************************
55 // --------------------------------------------------------------
56 
57 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
58 
59 #include "G4QAOLowEnergyLoss.hh"
60 #include "G4PhysicalConstants.hh"
61 #include "G4SystemOfUnits.hh"
62 #include "G4DynamicParticle.hh"
63 #include "G4Material.hh"
64 #include "G4ParticleDefinition.hh"
65 #include "G4AntiProton.hh"
66 
67 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
68 
69 G4QAOLowEnergyLoss::G4QAOLowEnergyLoss(const G4String& name)
70  : G4VLowEnergyModel(name)
71 {
72  numberOfMaterials = 6;
73  sizeL0 = 67;
74  sizeL1 = 22;
75  sizeL2 = 14;
76 }
77 
78 
79 G4QAOLowEnergyLoss::~G4QAOLowEnergyLoss()
80 {;}
81 
82 
83 G4double G4QAOLowEnergyLoss::HighEnergyLimit(const G4ParticleDefinition* ,
84  const G4Material* ) const
85 {
86  return 2.0*MeV ;
87 }
88 
89 
90 G4double G4QAOLowEnergyLoss::LowEnergyLimit(const G4ParticleDefinition* ,
91  const G4Material* ) const
92 {
93  // return 50.0*keV ;
94  return 5.0*keV ;
95 }
96 
97 
98 G4double G4QAOLowEnergyLoss::HighEnergyLimit(const G4ParticleDefinition* ) const
99 {
100  return 2.0*MeV ;
101 }
102 
103 G4double G4QAOLowEnergyLoss::LowEnergyLimit(const G4ParticleDefinition* ) const
104 {
105  // return 50.0*keV ;
106  return 5.0*keV ;
107 }
108 
109 
110 G4bool G4QAOLowEnergyLoss::IsInCharge(const G4DynamicParticle* particle,
111  const G4Material* material) const
112 {
113  G4bool isInCharge = false;
114 
115  G4bool hasMaterial = false;
116 
117  if (material->GetNumberOfElements() == 1) hasMaterial = true;
118 
119  if ((particle->GetDefinition()) == (G4AntiProton::AntiProtonDefinition())
120  && hasMaterial) isInCharge = true;
121 
122  return isInCharge;
123 
124 }
125 
126 G4bool G4QAOLowEnergyLoss::IsInCharge(const G4ParticleDefinition* aParticle,
127  const G4Material* material) const
128 {
129 
130  G4bool isInCharge = false;
131 
132  G4bool hasMaterial = false;
133 
134  if (material->GetNumberOfElements() == 1) hasMaterial = true;
135 
136 
137  if (aParticle == (G4AntiProton::AntiProtonDefinition())
138  && hasMaterial) isInCharge = true;
139 
140  return isInCharge;
141 
142 }
143 
144 
145 G4double G4QAOLowEnergyLoss::TheValue(const G4DynamicParticle* particle,
146  const G4Material* material)
147 {
148  G4double zParticle = (G4int)(particle->GetCharge())/eplus;
149 
150  G4double energy = particle->GetKineticEnergy() ;
151  G4double eloss = EnergyLoss(material,energy,zParticle) ;
152 
153  return eloss ;
154 }
155 
156 
157 G4double G4QAOLowEnergyLoss::TheValue(const G4ParticleDefinition* aParticle,
158  const G4Material* material,
159  G4double kineticEnergy)
160 {
161  G4double zParticle = (aParticle->GetPDGCharge())/eplus;
162 
163  G4double eloss = EnergyLoss(material,kineticEnergy,zParticle) ;
164 
165  return eloss ;
166 }
167 
168 
169 
170 G4double G4QAOLowEnergyLoss::EnergyLoss(const G4Material* material,
171  G4double kineticEnergy,
172  G4double zParticle) const
173 {
174  G4int nbOfShell = GetNumberOfShell(material);
175  if(nbOfShell < 1) nbOfShell = 1;
176 
177  //G4int iz = (G4int)(material->GetZ());
178  //if(iz < 1) iz = 1;
179  //else if(iz > 100) iz = 100;
180  //G4int nbOfShell = fNumberOfShells[iz];
181 
182  /*
183  if(material->GetName()=="Graphite"){
184  G4cout << " E(MeV)= " << kineticEnergy/MeV << " n= "
185  << nbOfShell
186  << " for " << material->GetZ() << G4endl;
187  }
188  */
189  G4double dedx=0;
190 
191  G4double v = c_light * std::sqrt( 2.0 * kineticEnergy / proton_mass_c2 );
192  G4double coeff = twopi * proton_mass_c2 *
193  (material-> GetTotNbOfElectPerVolume()) /
194  electron_mass_c2 ;
195  G4double fBetheVelocity = fine_structure_const * c_light / v;
196  coeff *= fine_structure_const * fine_structure_const * hbarc_squared /
197  kineticEnergy ;
198 
199  //G4double beta = std::sqrt( 2.0 * kineticEnergy / proton_mass_c2 );
200  //G4double fBetheVelocity = std::sqrt( 2.0 * 25.0 * keV / proton_mass_c2 )/beta;
201  //G4double coeff= twopi_mc2_rcl2*(material->GetElectronDensity())/(beta*beta);
202 
203 
204  G4double l0Term = 0, l1Term = 0, l2Term = 0;
205 
206  for (G4int nos = 0 ; nos < nbOfShell ; nos++){
207 
208  G4double l0 = 0, l1 = 0, l2 = 0;
209  G4double NormalizedEnergy = ( 2.0 * electron_mass_c2 * v * v ) /
210  ( c_squared * GetShellEnergy(material,nos) );
211  //G4double NormalizedEnergy = ( 2.0 * electron_mass_c2 * beta * beta ) /
212  // GetShellEnergy(material,nos);
213  G4double shStrength = GetShellStrength(material,nos);
214 
215  l0 = GetL0(NormalizedEnergy);
216  l0Term += shStrength * l0;
217 
218  l1 = GetL1(NormalizedEnergy);
219  l1Term += shStrength * l1;
220 
221  l2 = GetL2(NormalizedEnergy);
222  l2Term += shStrength * l2;
223 
224  /*
225  if(material->GetName()=="Graphite"){
226  G4cout << nos << ". "
227  << " E(MeV)= " << kineticEnergy/MeV
228  << " normE= " << NormalizedEnergy
229  << " sh en= " << GetShellEnergy(material,nos)
230  << " str= " << shStrength
231  << " v0/v= " << fBetheVelocity
232  << " l0= " << l0Term
233  << " l1= " << l1Term
234  << " l2= " << l2Term
235  << G4endl;
236  }
237  */
238  }
239 
240  dedx = coeff * zParticle * zParticle * (l0Term
241  + zParticle * fBetheVelocity * l1Term
242  + zParticle * zParticle * fBetheVelocity * fBetheVelocity * l2Term);
243 
244  // G4cout << " E(MeV)= " << kineticEnergy/MeV
245  // << " dedx(Mev/mm)= " << dedx*mm/MeV << G4endl;
246 
247  return dedx ;
248 
249 }
250 
251 
252 G4int G4QAOLowEnergyLoss::GetNumberOfShell(const G4Material* material) const
253 {
254  // Set return value from table
255  G4int Z = (G4int)(material->GetZ());
256  G4int nShell = 0;
257 
258  // Set return value if in material available from Aahrus
259  for(G4int i=0; i<numberOfMaterials; i++) {
260 
261  if(materialAvailable[i] == Z){
262  nShell = nbofShellForMaterial[i];
263  break;
264  }
265  else nShell = fNumberOfShells[Z];
266  }
267 
268  return nShell;
269 }
270 
271 
272 
273 G4double G4QAOLowEnergyLoss::GetShellEnergy(const G4Material* material,
274  G4int nbOfTheShell) const
275 {
276  //
277  G4double shellEnergy = alShellEnergy[0];
278 
279  if(material->GetZ() == 13) shellEnergy = alShellEnergy[nbOfTheShell];
280  else if(material->GetZ() == 14)shellEnergy = siShellEnergy[nbOfTheShell];
281  else if(material->GetZ() == 29)shellEnergy = cuShellEnergy[nbOfTheShell];
282  else if(material->GetZ() == 73)shellEnergy = taShellEnergy[nbOfTheShell];
283  else if(material->GetZ() == 79)shellEnergy = auShellEnergy[nbOfTheShell];
284  else if(material->GetZ() == 78)shellEnergy = ptShellEnergy[nbOfTheShell];
285  else if (material->GetNumberOfElements() == 1)
286  shellEnergy = GetOscillatorEnergy(material, nbOfTheShell);
287  else G4cout << "WARNING - G4QAOLowEnergyLoss::GetShellEnergy - "
288  << "The model is not available for "
289  << material->GetName()
290  << G4endl;
291 
292  return shellEnergy;
293 }
294 
295 
296 G4double G4QAOLowEnergyLoss::GetOscillatorEnergy(const G4Material* material,
297  G4int nbOfTheShell) const
298 {
299 
300  const G4Element* element = material->GetElement(0);
301 
302  G4int Z = (G4int)(element->GetZ());
303 
304 G4double squaredPlasmonEnergy = 28.816 * 28.816 * 1e-6
305  * material->GetDensity()/g/cm3
306  * (Z/element->GetN()) ;
307 //G4double squaredPlasmonEnergy = 28.16 * 28.16 * 1e-6
308 // * (material->GetDensity()) * (cm3/g)
309 // * Z / (element->GetN()) ;
310 
311  G4double plasmonTerm = 0.66667 * GetOccupationNumber(Z,nbOfTheShell)
312  * squaredPlasmonEnergy / (Z*Z) ;
313 
314  G4double ionTerm = std::exp(0.5) * (element->GetAtomicShell(nbOfTheShell)) ;
315 
316  ionTerm = ionTerm*ionTerm ;
317 
318  G4double oscShellEnergy = std::sqrt( ionTerm + plasmonTerm );
319 
320 /* if(material->GetName()=="Graphite"){
321  G4cout << "\t" << Z
322  << "\t" << nbOfTheShell
323  << "\t" << squaredPlasmonEnergy
324  << "\t" << plasmonTerm
325  << "\t" << ionTerm
326  << "\t" << GetOccupationNumber(Z,nbOfTheShell)
327  << "\t" << element->GetAtomicShell(nbOfTheShell)
328  << "\t" << oscShellEnergy << G4endl;}
329 */
330  return oscShellEnergy;
331 }
332 
333 G4double G4QAOLowEnergyLoss::GetShellStrength(const G4Material* material,
334  G4int nbOfTheShell) const
335 {
336  G4double shellStrength = alShellStrength[0];
337 
338  if(material->GetZ() == 13) shellStrength = alShellStrength[nbOfTheShell];
339  else if(material->GetZ() == 14)shellStrength =siShellStrength[nbOfTheShell];
340  else if(material->GetZ() == 29)shellStrength =cuShellStrength[nbOfTheShell];
341  else if(material->GetZ() == 73)shellStrength =taShellStrength[nbOfTheShell];
342  else if(material->GetZ() == 79)shellStrength =auShellStrength[nbOfTheShell];
343  else if(material->GetZ() == 78)shellStrength =ptShellStrength[nbOfTheShell];
344  else if (material->GetNumberOfElements() == 1){
345  G4int Z = (G4int)(material->GetZ());
346  shellStrength = GetOccupationNumber(Z,nbOfTheShell) / Z ;}
347  else G4cout << "WARNING - G4QAOLowEnergyLoss::GetShellEnergy - "
348  << "The model is not available for "
349  << material->GetName()
350  << G4endl;
351 
352  return shellStrength;
353 }
354 
355 G4double G4QAOLowEnergyLoss::GetOccupationNumber(G4int Z, G4int ShellNb) const
356 {
357 
358  G4int indice = ShellNb ;
359  for (G4int z = 1 ; z < Z ; z++) {indice += fNumberOfShells[z];}
360 
361  return nbOfElectronPerSubShell[indice+1];
362 }
363 
364 
365 G4double G4QAOLowEnergyLoss::GetL0(G4double normEnergy) const
366 {
367  G4int n;
368 
369  for(n = 0; n < sizeL0; n++) {
370  if( normEnergy < L0[n][0] ) break;
371  }
372  if(0 == n) n = 1 ;
373  if(n >= sizeL0) n = sizeL0 - 1 ;
374 
375  G4double l0 = L0[n][1];
376  G4double l0p = L0[n-1][1];
377  G4double bethe = l0p + (l0 - l0p) * ( normEnergy - L0[n-1][0]) /
378  (L0[n][0] - L0[n-1][0]);
379  return bethe ;
380 
381 }
382 
383 G4double G4QAOLowEnergyLoss::GetL1(G4double normEnergy) const
384 {
385  G4int n;
386 
387  for(n = 0; n < sizeL1; n++) {
388  if( normEnergy < L1[n][0] ) break;
389  }
390  if(0 == n) n = 1 ;
391  if(n >= sizeL1) n = sizeL1 - 1 ;
392 
393  G4double l1 = L1[n][1];
394  G4double l1p = L1[n-1][1];
395  G4double barkas= l1p + (l1 - l1p) * ( normEnergy - L1[n-1][0]) /
396  (L1[n][0] - L1[n-1][0]);
397 
398  return barkas;
399 
400 }
401 
402 
403 G4double G4QAOLowEnergyLoss::GetL2(G4double normEnergy) const
404 {
405  G4int n;
406  for(n = 0; n < sizeL2; n++) {
407  if( normEnergy < L2[n][0] ) break;
408  }
409  if(0 == n) n = 1 ;
410  if(n >= sizeL2) n = sizeL2 - 1 ;
411 
412  G4double l2 = L2[n][1];
413  G4double l2p = L2[n-1][1];
414  G4double bloch = l2p + (l2 - l2p) * ( normEnergy - L2[n-1][0]) /
415  (L2[n][0] - L2[n-1][0]);
416 
417  return bloch;
418 }
419 
420 
421 const G4int G4QAOLowEnergyLoss::materialAvailable[6] = {13,14,29,73,79,78};
422  /*
423  "Aluminum",
424  "Silicon",
425  "Copper",
426  "Tantalum",
427  "Gold",
428  "Platinum"};
429  */
430 const G4int G4QAOLowEnergyLoss::nbofShellForMaterial[6] = {3,3,4,6,6,6 };
431 
432 const G4double G4QAOLowEnergyLoss::alShellEnergy[3] ={ 2795e-6, 202e-6, 16.9e-6};
433 const G4double G4QAOLowEnergyLoss::alShellStrength[3]={ 0.1349, 0.6387, 0.2264};
434 const G4double G4QAOLowEnergyLoss::siShellEnergy[3] ={ 3179e-6, 249e-6, 20.3e-6 };
435 const G4double G4QAOLowEnergyLoss::siShellStrength[3]={ 0.1222, 0.5972, 0.2806};
436 const G4double G4QAOLowEnergyLoss::cuShellEnergy[4] ={ 16931e-6, 1930e-6, 199e-6, 39.6e-6};
437 const G4double G4QAOLowEnergyLoss::cuShellStrength[4]={ 0.0505, 0.2561, 0.4913, 0.2021};
438 const G4double G4QAOLowEnergyLoss::taShellEnergy[6] ={ 88926e-6, 18012e-6, 3210e-6, 575e-6, 108.7e-6, 30.8e-6};
439 const G4double G4QAOLowEnergyLoss::taShellStrength[6]={ 0.0126, 0.0896, 0.2599, 0.3413, 0.2057, 0.0908};
440 const G4double G4QAOLowEnergyLoss::auShellEnergy[6]={ 96235e-6, 25918e-6, 4116e-6, 599e-6, 87.3e-6, 36.9e-6};
441 const G4double G4QAOLowEnergyLoss::auShellStrength[6]={ 0.0139, 0.0803, 0.2473, 0.423, 0.1124, 0.1231};
442 const G4double G4QAOLowEnergyLoss::ptShellEnergy[6]={ 95017e-6, 25590e-6, 4063e-6, 576e-6, 81.9e-6, 31.4e-6};
443 const G4double G4QAOLowEnergyLoss::ptShellStrength[6]={ 0.0129, 0.0745, 0.2295, 0.4627, 0.1324, 0.0879};
444 
445 
446 const G4double G4QAOLowEnergyLoss::L0[67][2] =
447 {
448  {0.00, 0.000001},
449  {0.10, 0.000001},
450  {0.12, 0.00001},
451  {0.14, 0.00005},
452  {0.16, 0.00014},
453  {0.18, 0.00030},
454  {0.20, 0.00057},
455  {0.25, 0.00189},
456  {0.30, 0.00429},
457  {0.35, 0.00784},
458  {0.40, 0.01248},
459  {0.45, 0.01811},
460  {0.50, 0.02462},
461  {0.60, 0.03980},
462  {0.70, 0.05731},
463  {0.80, 0.07662},
464  {0.90, 0.09733},
465  {1.00, 0.11916},
466  {1.20, 0.16532},
467  {1.40, 0.21376},
468  {1.60, 0.26362},
469  {1.80, 0.31428},
470  {2.00, 0.36532},
471  {2.50, 0.49272},
472  {3.00, 0.61765},
473  {3.50, 0.73863},
474  {4.00, 0.85496},
475  {4.50, 0.96634},
476  {5.00, 1.07272},
477  {6.00, 1.27086},
478  {7.00, 1.45075},
479  {8.00, 1.61412},
480  {9.00, 1.76277},
481  {10.00, 1.89836},
482  {12.00, 2.13625},
483  {14.00, 2.33787},
484  {16.00, 2.51093},
485  {18.00, 2.66134},
486  {20.00, 2.79358},
487  {25.00, 3.06539},
488  {30.00, 3.27902},
489  {35.00, 3.45430},
490  {40.00, 3.60281},
491  {45.00, 3.73167},
492  {50.00, 3.84555},
493  {60.00, 4.04011},
494  {70.00, 4.20264},
495  {80.00, 4.34229},
496  {90.00, 4.46474},
497  {100.00, 4.57378},
498  {120.00, 4.76155},
499  {140.00, 4.91953},
500  {160.00, 5.05590},
501  {180.00, 5.17588},
502  {200.00, 5.28299},
503  {250.00, 5.50925},
504  {300.00, 5.69364},
505  {350.00, 5.84926},
506  {400.00, 5.98388},
507  {450.00, 6.10252},
508  {500.00, 6.20856},
509  {600.00, 6.39189},
510  {700.00, 6.54677},
511  {800.00, 6.68084},
512  {900.00, 6.79905},
513  {1000.00, 6.90474}
514 };
515 
516 const G4double G4QAOLowEnergyLoss::L1[22][2] =
517 {
518  {0.00, -0.000001},
519  {0.10, -0.00001},
520  {0.20, -0.00049},
521  {0.30, -0.00084},
522  {0.40, 0.00085},
523  {0.50, 0.00519},
524  {0.60, 0.01198},
525  {0.70, 0.02074},
526  {0.80, 0.03133},
527  {0.90, 0.04369},
528  {1.00, 0.06035},
529  {2.00, 0.24023},
530  {3.00, 0.44284},
531  {4.00, 0.62012},
532  {5.00, 0.77031},
533  {6.00, 0.90390},
534  {7.00, 1.02705},
535  {8.00, 1.10867},
536  {9.00, 1.17546},
537  {10.00, 1.21599},
538  {15.00, 1.24349},
539  {20.00, 1.16752}
540 };
541 
542 const G4double G4QAOLowEnergyLoss::L2[14][2] =
543 {
544  {0.00, 0.000001},
545  {0.10, 0.00001},
546  {0.20, 0.00000},
547  {0.40, -0.00120},
548  {0.60, -0.00036},
549  {0.80, 0.00372},
550  {1.00, 0.01298},
551  {2.00, 0.08296},
552  {4.00, 0.21953},
553  {6.00, 0.23903},
554  {8.00, 0.20893},
555  {10.00, 0.10879},
556  {20.00, -0.88409},
557  {40.00, -1.13902}
558 };
559 
560 const G4int G4QAOLowEnergyLoss::nbOfElectronPerSubShell[1540] =
561 {
562  0, // consistency with G4AtomicShells
563  1,//------ H
564  2,//------ He
565  2, 1,//------ Li
566  2, 2,//------ Be
567  2, 2, 1,//------ B
568  2, 2, 2,//------ C
569  2, 2, 2, 1,//------ N
570  2, 2, 2, 2,//------ O
571  2, 2, 5,//------ F
572  2, 2, 2, 4,//------ Ne
573  2, 2, 2, 4, 1,//------ Na
574  2, 2, 2, 4, 2,//------ Mg
575  2, 2, 2, 4, 2, 1,//------ Al
576  2, 2, 2, 4, 2, 2,//------ Si
577  2, 2, 2, 4, 2, 3,//------ P
578  2, 2, 2, 4, 2, 4,//------
579  2, 2, 2, 4, 2, 5,//------
580  2, 2, 2, 4, 2, 2, 4,//------
581  2, 2, 2, 4, 2, 2, 4, 1,//------
582  2, 2, 2, 4, 2, 2, 4, 2,//------
583  2, 2, 2, 4, 2, 2, 4, 1, 2,//------
584  2, 2, 2, 4, 2, 2, 4, 2, 2,//------
585  2, 2, 2, 4, 2, 2, 4, 3, 2,//------
586  2, 2, 2, 4, 2, 2, 4, 4, 2,//------
587  2, 2, 2, 4, 2, 2, 4, 5, 2,//------
588  2, 2, 2, 4, 2, 2, 4, 6, 2,//------
589  2, 2, 2, 4, 2, 2, 4, 7, 2,//------
590  2, 2, 2, 4, 2, 2, 4, 4, 4, 2,//------
591  2, 2, 2, 4, 2, 2, 4, 4, 5, 2,//------
592  2, 2, 2, 4, 2, 2, 4, 4, 6, 2,//------
593  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 1,//------
594  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2,//------
595  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 3,//------
596  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 4,//------
597  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 5,//------
598  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4,//------
599  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
600  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
601  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
602  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 2, 2,//------
603  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 3, 2,//------
604  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 2,//------
605  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 5, 2,//------
606  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 6, 2,//------
607  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 7, 2,//------
608  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 4, 2,//------
609  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 5, 2,//------
610  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2,//------
611  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 1,//------
612  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2,//------
613  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 3,//------
614  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 4,//------
615  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 5,//------
616  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4,//------
617  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
618  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
619  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
620  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 2, 4, 2,//------
621  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 3, 2, 2, 4, 2,//------
622  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 4, 2, 2, 4, 2,//------
623  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 5, 2, 2, 4, 2,//------
624  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 2, 2, 4, 2,//------
625  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 7, 2, 2, 4, 2,//------
626  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 7, 2, 2, 4, 1, 2,//------
627  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 9, 2, 2, 4, 2,//------
628  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 10, 2, 2, 4, 2,//------
629  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 11, 2, 2, 4, 2,//------
630  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 12, 2, 2, 4, 2,//------
631  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 13, 2, 2, 4, 2,//------
632  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 2,//------
633  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 1, 2,//------
634  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 2, 2,//------
635  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 3, 2,//------
636  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 2,//------
637  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 5, 2,//------
638  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 6, 2,//------
639  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 7, 2,//------
640  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 9, 1,//------
641  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 1,//------
642  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2,//------
643  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 1,//------
644  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2,//------
645  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 3,//------
646  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 4,//------
647  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 3,//------
648  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4,//------
649  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
650  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
651  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
652  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4, 2, 2,//------
653  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 2, 4, 1, 2,//------
654  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 3, 2, 2, 4, 1, 2,//------
655  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 4, 2, 2, 4, 1, 2,//------
656  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 6, 2, 2, 4, 2,//------
657  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 7, 2, 2, 4, 2,//------
658  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 7, 2, 2, 4, 1, 2,//------
659  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 8, 2, 2, 4, 1, 2,//------
660  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 10, 2, 2, 4, 2,//------
661  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 11, 2, 2, 4, 2,//------
662  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 12, 2, 2, 4, 2 //-----
663 };
664 
665 const G4int G4QAOLowEnergyLoss::fNumberOfShells[101] =
666 {
667  0 , // nonexisting zero element
668 
669  1 , 1 , 2 , 2 , 3 , 3 , 4 , 4 , 3 , 4 , // 1 - 10
670 
671  5 , 5 , 6 , 6 , 6 , 6 , 6 , 7 , 8 , 8 , // 11 - 20
672 
673  9 , 9 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 10 , // 21 - 30
674 
675 11 , 11 , 11 , 11 , 11 , 12 , 13 , 13 , 14 , 14 , // 31 - 40
676 
677 14 , 14 , 14 , 14 , 14 , 15 , 15 , 15 , 16 , 16 , // 41 - 50
678 
679 // ----------------------------------------------------------
680 
681 16 , 16 , 16 , 17 , 18 , 18 , 19 , 19 , 19 , 19 , // 51 - 60
682 
683 19 , 19 , 19 , 20 , 19 , 19 , 19 , 19 , 19 , 20 , // 61 - 70
684 
685 21 , 21 , 21 , 21 , 21 , 21 , 21 , 21 , 22 , 22 , // 71 - 80
686 
687 23 , 23 , 23 , 23 , 24 , 24 , 25 , 25 , 26 , 26 , // 81 - 90
688 
689 27 , 27 , 27 , 26 , 26 , 27 , 27 , 26 , 26 , 26 // 91 - 100
690 
691 };
692 
693 
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