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G4hQAOModel.cc
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28 //
29 // GEANT4 Class file
30 //
31 //
32 // File name: G4hQAOModel
33 //
34 // Author: V.Ivanchenko (Vladimir.Ivanchenko@cern.ch)
35 //
36 // Creation date: 27 April 2004
37 //
38 // Modifications:
39 //
40 // Class Description:
41 //
42 // Electronic stopping power for negative heavy partiles
43 //
44 // Class Description: End
45 //
46 // -------------------------------------------------------------------
47 //
48 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
49 
50 #include "G4hQAOModel.hh"
51 #include "G4PhysicalConstants.hh"
52 #include "G4SystemOfUnits.hh"
53 #include "G4UnitsTable.hh"
54 #include "G4Element.hh"
55 #include "G4Material.hh"
56 
57 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
58 
59 G4hQAOModel::G4hQAOModel():G4VhElectronicStoppingPower(),
60  numberOfMaterials(6),
61  sizeL0(67),
62  sizeL1(22),
63  sizeL2(14),
64  currentMaterial(0),
65  currentElement(0)
66 {
67  theZieglerFactor = eV*cm2*1.0e-15;
68  thePlasmonFactor = 28.816 * 28.816 * 1e-6;
69 }
70 
71 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
72 
73 G4hQAOModel::~G4hQAOModel()
74 {}
75 
76 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
77 
78 G4double G4hQAOModel::StoppingPower(const G4Material* material,
79  G4double kineticEnergy)
80 {
81  G4double eloss = 0.0 ;
82  G4int numberOfElements = material->GetNumberOfElements() ;
83  const G4ElementVector* theElementVector = material->GetElementVector();
84  const G4double* theAtomicNumDensityVector = material->GetAtomicNumDensityVector() ;
85  currentMaterial = material;
86 
87  // loop for the elements in the material
88  for (G4int i=0; i<numberOfElements; i++)
89  {
90  currentElement = (*theElementVector)[i] ;
91  G4double z = currentElement->GetZ() ;
92  eloss += ElectronicStoppingPower(z,kineticEnergy)*theAtomicNumDensityVector[i];
93  }
94 
95  return eloss;
96 }
97 
98 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
99 
100 G4double G4hQAOModel::ElectronicStoppingPower(G4double z,
101  G4double kineticEnergy) const
102 {
103  G4int Z = (G4int)z;
104  G4int nbOfShell = GetNumberOfShell(Z);
105  if(nbOfShell < 1) nbOfShell = 1;
106 
107  G4double dedx=0.0;
108 
109  G4double v = c_light * std::sqrt( 2.0 * kineticEnergy / proton_mass_c2 );
110  G4double coeff = twopi*proton_mass_c2*z / (electron_mass_c2*theZieglerFactor) ;
111  G4double fBetheVelocity = fine_structure_const * c_light / v;
112  coeff *= fine_structure_const * fine_structure_const * hbarc_squared /
113  kineticEnergy ;
114 
115  G4double l0Term = 0, l1Term = 0, l2Term = 0;
116 
117  for (G4int nos = 0 ; nos < nbOfShell ; nos++){
118 
119  G4double l0 = 0, l1 = 0, l2 = 0;
120  G4double NormalizedEnergy = ( 2.0 * electron_mass_c2 * v * v ) /
121  ( c_squared * GetShellEnergy(Z, nos) );
122  G4double shStrength = GetShellStrength(Z, nos);
123 
124  l0 = GetL0(NormalizedEnergy);
125  l0Term += shStrength * l0;
126 
127  l1 = GetL1(NormalizedEnergy);
128  l1Term += shStrength * l1;
129 
130  l2 = GetL2(NormalizedEnergy);
131  l2Term += shStrength * l2;
132 
133 /*
134  //if(Z == 6){
135  G4cout << nos << ". "
136  << " E(MeV)= " << kineticEnergy/MeV
137  << " normE= " << NormalizedEnergy
138  << " sh en= " << GetShellEnergy(Z,nos)
139  << " str= " << shStrength
140  << " v0/v= " << fBetheVelocity
141  << " l0= " << l0Term
142  << " l1= " << l1Term
143  << " l2= " << l2Term
144  << G4endl;
145  // }
146 */
147  }
148 
149  dedx = coeff * (l0Term - fBetheVelocity*l1Term + fBetheVelocity*fBetheVelocity*l2Term);
150 
151  //G4cout << " E(MeV)= " << kineticEnergy/MeV
152  // << " dedx(Mev/mm)= " << dedx*mm/MeV << G4endl;
153 
154  if(dedx < 0.0) dedx = 0.0;
155  return dedx;
156 }
157 
158 
159 G4int G4hQAOModel::GetNumberOfShell(G4int Z) const
160 {
161  // Set return value from table
162  G4int nShell = 0;
163 
164  // Set return value if in material available from Aahrus
165  for(G4int i=0; i<numberOfMaterials; i++) {
166 
167  if(materialAvailable[i] == Z){
168  nShell = nbofShellForMaterial[i];
169  break;
170  }
171  else nShell = fNumberOfShells[Z];
172  }
173 
174  return nShell;
175 }
176 
177 
178 
179 G4double G4hQAOModel::GetShellEnergy(G4int Z, G4int nbOfTheShell) const
180 {
181  G4double shellEnergy = alShellEnergy[0];
182  if (Z == 13) shellEnergy = alShellEnergy[nbOfTheShell];
183  else if(Z == 14) shellEnergy = siShellEnergy[nbOfTheShell];
184  else if(Z == 29) shellEnergy = cuShellEnergy[nbOfTheShell];
185  else if(Z == 73) shellEnergy = taShellEnergy[nbOfTheShell];
186  else if(Z == 79) shellEnergy = auShellEnergy[nbOfTheShell];
187  else if(Z == 78) shellEnergy = ptShellEnergy[nbOfTheShell];
188  else shellEnergy = GetOscillatorEnergy(Z, nbOfTheShell);
189 
190  return shellEnergy;
191 }
192 
193 
194 G4double G4hQAOModel::GetOscillatorEnergy(G4int Z, G4int nbOfTheShell) const
195 {
196  G4double squaredPlasmonEnergy = thePlasmonFactor;
197  G4double zeff = (G4double)Z;
198  if(currentMaterial)
199  squaredPlasmonEnergy *= (currentMaterial->GetDensity()*zeff*cm3)
200  / (g * currentElement->GetN());
201 
202  G4double occn = GetOccupationNumber(Z,nbOfTheShell);
203  G4double plasmonTerm = 0.66667 * occn * squaredPlasmonEnergy/(zeff*zeff);
204 
205  G4double ionTerm = std::exp(0.5) * currentElement->GetAtomicShell(nbOfTheShell);
206 
207  ionTerm = ionTerm*ionTerm ;
208 
209  G4double oscShellEnergy = std::sqrt( ionTerm + plasmonTerm );
210 
211 /* if(material->GetName()=="Graphite"){
212  G4cout << "\t" << Z
213  << "\t" << nbOfTheShell
214  << "\t" << squaredPlasmonEnergy
215  << "\t" << plasmonTerm
216  << "\t" << ionTerm
217  << "\t" << GetOccupationNumber(Z,nbOfTheShell)
218  << "\t" << element->GetAtomicShell(nbOfTheShell)
219  << "\t" << oscShellEnergy << G4endl;}
220 */
221  return oscShellEnergy;
222 }
223 
224 
225 G4double G4hQAOModel::GetShellStrength(G4int Z, G4int nbOfTheShell) const
226 {
227  G4double shellStrength = alShellStrength[0];
228 
229  if(Z == 13) shellStrength = alShellStrength[nbOfTheShell];
230  else if(Z == 14) shellStrength = siShellStrength[nbOfTheShell];
231  else if(Z == 29) shellStrength = cuShellStrength[nbOfTheShell];
232  else if(Z == 73) shellStrength = taShellStrength[nbOfTheShell];
233  else if(Z == 79) shellStrength = auShellStrength[nbOfTheShell];
234  else if(Z == 78) shellStrength = ptShellStrength[nbOfTheShell];
235  else shellStrength = GetOccupationNumber(Z,nbOfTheShell) / (G4double)Z;
236 
237  return shellStrength;
238 }
239 
240 G4double G4hQAOModel::GetOccupationNumber(G4int Z, G4int ShellNb) const
241 {
242 
243  G4int indice = ShellNb ;
244  for (G4int z = 1 ; z < Z ; z++) {indice += fNumberOfShells[z];}
245  G4double x = (G4double)(nbOfElectronPerSubShell[indice+1]);
246  return x;
247 }
248 
249 
250 G4double G4hQAOModel::GetL0(G4double normEnergy) const
251 {
252  G4int n;
253 
254  for(n = 0; n < sizeL0; n++) {
255  if( normEnergy < L0[n][0] ) break;
256  }
257  if(0 == n) n = 1 ;
258  if(n >= sizeL0) n = sizeL0 - 1 ;
259 
260  G4double l0 = L0[n][1];
261  G4double l0p = L0[n-1][1];
262  G4double bethe = l0p + (l0 - l0p) * ( normEnergy - L0[n-1][0]) /
263  (L0[n][0] - L0[n-1][0]);
264  return bethe ;
265 
266 }
267 
268 G4double G4hQAOModel::GetL1(G4double normEnergy) const
269 {
270  G4int n;
271 
272  for(n = 0; n < sizeL1; n++) {
273  if( normEnergy < L1[n][0] ) break;
274  }
275  if(0 == n) n = 1 ;
276  if(n >= sizeL1) n = sizeL1 - 1 ;
277 
278  G4double l1 = L1[n][1];
279  G4double l1p = L1[n-1][1];
280  G4double barkas= l1p + (l1 - l1p) * ( normEnergy - L1[n-1][0]) /
281  (L1[n][0] - L1[n-1][0]);
282 
283  return barkas;
284 
285 }
286 
287 
288 G4double G4hQAOModel::GetL2(G4double normEnergy) const
289 {
290  G4int n;
291  for(n = 0; n < sizeL2; n++) {
292  if( normEnergy < L2[n][0] ) break;
293  }
294  if(0 == n) n = 1 ;
295  if(n >= sizeL2) n = sizeL2 - 1 ;
296 
297  G4double l2 = L2[n][1];
298  G4double l2p = L2[n-1][1];
299  G4double bloch = l2p + (l2 - l2p) * ( normEnergy - L2[n-1][0]) /
300  (L2[n][0] - L2[n-1][0]);
301 
302  return bloch;
303 }
304 
305 
306 const G4int G4hQAOModel::materialAvailable[6] = {13,14,29,73,79,78};
307  /*
308  "Aluminum",
309  "Silicon",
310  "Copper",
311  "Tantalum",
312  "Gold",
313  "Platinum"};
314  */
315 const G4int G4hQAOModel::nbofShellForMaterial[6] = {3,3,4,6,6,6};
316 
317 const G4double G4hQAOModel::alShellEnergy[3] ={ 2795e-6, 202e-6, 16.9e-6};
318 const G4double G4hQAOModel::alShellStrength[3]={ 0.1349, 0.6387, 0.2264};
319 const G4double G4hQAOModel::siShellEnergy[3] ={ 3179e-6, 249e-6, 20.3e-6 };
320 const G4double G4hQAOModel::siShellStrength[3]={ 0.1222, 0.5972, 0.2806};
321 const G4double G4hQAOModel::cuShellEnergy[4] ={ 16931e-6, 1930e-6, 199e-6, 39.6e-6};
322 const G4double G4hQAOModel::cuShellStrength[4]={ 0.0505, 0.2561, 0.4913, 0.2021};
323 const G4double G4hQAOModel::taShellEnergy[6] ={ 88926e-6, 18012e-6, 3210e-6, 575e-6, 108.7e-6, 30.8e-6};
324 const G4double G4hQAOModel::taShellStrength[6]={ 0.0126, 0.0896, 0.2599, 0.3413, 0.2057, 0.0908};
325 const G4double G4hQAOModel::auShellEnergy[6]={ 96235e-6, 25918e-6, 4116e-6, 599e-6, 87.3e-6, 36.9e-6};
326 const G4double G4hQAOModel::auShellStrength[6]={ 0.0139, 0.0803, 0.2473, 0.423, 0.1124, 0.1231};
327 const G4double G4hQAOModel::ptShellEnergy[6]={ 95017e-6, 25590e-6, 4063e-6, 576e-6, 81.9e-6, 31.4e-6};
328 const G4double G4hQAOModel::ptShellStrength[6]={ 0.0129, 0.0745, 0.2295, 0.4627, 0.1324, 0.0879};
329 
330 
331 const G4double G4hQAOModel::L0[67][2] =
332 {
333  {0.00, 0.000001},
334  {0.10, 0.000001},
335  {0.12, 0.00001},
336  {0.14, 0.00005},
337  {0.16, 0.00014},
338  {0.18, 0.00030},
339  {0.20, 0.00057},
340  {0.25, 0.00189},
341  {0.30, 0.00429},
342  {0.35, 0.00784},
343  {0.40, 0.01248},
344  {0.45, 0.01811},
345  {0.50, 0.02462},
346  {0.60, 0.03980},
347  {0.70, 0.05731},
348  {0.80, 0.07662},
349  {0.90, 0.09733},
350  {1.00, 0.11916},
351  {1.20, 0.16532},
352  {1.40, 0.21376},
353  {1.60, 0.26362},
354  {1.80, 0.31428},
355  {2.00, 0.36532},
356  {2.50, 0.49272},
357  {3.00, 0.61765},
358  {3.50, 0.73863},
359  {4.00, 0.85496},
360  {4.50, 0.96634},
361  {5.00, 1.07272},
362  {6.00, 1.27086},
363  {7.00, 1.45075},
364  {8.00, 1.61412},
365  {9.00, 1.76277},
366  {10.00, 1.89836},
367  {12.00, 2.13625},
368  {14.00, 2.33787},
369  {16.00, 2.51093},
370  {18.00, 2.66134},
371  {20.00, 2.79358},
372  {25.00, 3.06539},
373  {30.00, 3.27902},
374  {35.00, 3.45430},
375  {40.00, 3.60281},
376  {45.00, 3.73167},
377  {50.00, 3.84555},
378  {60.00, 4.04011},
379  {70.00, 4.20264},
380  {80.00, 4.34229},
381  {90.00, 4.46474},
382  {100.00, 4.57378},
383  {120.00, 4.76155},
384  {140.00, 4.91953},
385  {160.00, 5.05590},
386  {180.00, 5.17588},
387  {200.00, 5.28299},
388  {250.00, 5.50925},
389  {300.00, 5.69364},
390  {350.00, 5.84926},
391  {400.00, 5.98388},
392  {450.00, 6.10252},
393  {500.00, 6.20856},
394  {600.00, 6.39189},
395  {700.00, 6.54677},
396  {800.00, 6.68084},
397  {900.00, 6.79905},
398  {1000.00, 6.90474}
399 };
400 
401 
402 const G4double G4hQAOModel::L1[22][2] =
403 {
404  {0.00, -0.000001},
405  {0.10, -0.00001},
406  {0.20, -0.00049},
407  {0.30, -0.00084},
408  {0.40, 0.00085},
409  {0.50, 0.00519},
410  {0.60, 0.01198},
411  {0.70, 0.02074},
412  {0.80, 0.03133},
413  {0.90, 0.04369},
414  {1.00, 0.06035},
415  {2.00, 0.24023},
416  {3.00, 0.44284},
417  {4.00, 0.62012},
418  {5.00, 0.77031},
419  {6.00, 0.90390},
420  {7.00, 1.02705},
421  {8.00, 1.10867},
422  {9.00, 1.17546},
423  {10.00, 1.21599},
424  {15.00, 1.24349},
425  {20.00, 1.16752}
426 };
427 
428 
429 const G4double G4hQAOModel::L2[14][2] =
430 {
431  {0.00, 0.000001},
432  {0.10, 0.00001},
433  {0.20, 0.00000},
434  {0.40, -0.00120},
435  {0.60, -0.00036},
436  {0.80, 0.00372},
437  {1.00, 0.01298},
438  {2.00, 0.08296},
439  {4.00, 0.21953},
440  {6.00, 0.23903},
441  {8.00, 0.20893},
442  {10.00, 0.10879},
443  {20.00, -0.88409},
444  {40.00, -1.13902}
445 };
446 
447 
448 const G4int G4hQAOModel::nbOfElectronPerSubShell[1540] =
449 {
450  0, // consistency with G4AtomicShells
451  1,//------ H
452  2,//------ He
453  2, 1,//------ Li
454  2, 2,//------ Be
455  2, 2, 1,//------ B
456  2, 2, 2,//------ C
457  2, 2, 2, 1,//------ N
458  2, 2, 2, 2,//------ O
459  2, 2, 5,//------ F
460  2, 2, 2, 4,//------ Ne
461  2, 2, 2, 4, 1,//------ Na
462  2, 2, 2, 4, 2,//------ Mg
463  2, 2, 2, 4, 2, 1,//------ Al
464  2, 2, 2, 4, 2, 2,//------ Si
465  2, 2, 2, 4, 2, 3,//------ P
466  2, 2, 2, 4, 2, 4,//------
467  2, 2, 2, 4, 2, 5,//------
468  2, 2, 2, 4, 2, 2, 4,//------
469  2, 2, 2, 4, 2, 2, 4, 1,//------
470  2, 2, 2, 4, 2, 2, 4, 2,//------
471  2, 2, 2, 4, 2, 2, 4, 1, 2,//------
472  2, 2, 2, 4, 2, 2, 4, 2, 2,//------
473  2, 2, 2, 4, 2, 2, 4, 3, 2,//------
474  2, 2, 2, 4, 2, 2, 4, 4, 2,//------
475  2, 2, 2, 4, 2, 2, 4, 5, 2,//------
476  2, 2, 2, 4, 2, 2, 4, 6, 2,//------
477  2, 2, 2, 4, 2, 2, 4, 7, 2,//------
478  2, 2, 2, 4, 2, 2, 4, 4, 4, 2,//------
479  2, 2, 2, 4, 2, 2, 4, 4, 5, 2,//------
480  2, 2, 2, 4, 2, 2, 4, 4, 6, 2,//------
481  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 1,//------
482  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2,//------
483  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 3,//------
484  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 4,//------
485  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 5,//------
486  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4,//------
487  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
488  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
489  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
490  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 2, 2,//------
491  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 3, 2,//------
492  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 2,//------
493  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 5, 2,//------
494  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 6, 2,//------
495  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 7, 2,//------
496  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 4, 2,//------
497  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 5, 2,//------
498  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2,//------
499  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 1,//------
500  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2,//------
501  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 3,//------
502  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 4,//------
503  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 5,//------
504  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4,//------
505  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 1,//------
506  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 2,//------
507  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 4, 1, 2,//------
508  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 2, 2, 2, 4, 2,//------
509  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 3, 2, 2, 4, 2,//------
510  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 4, 2, 2, 4, 2,//------
511  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 5, 2, 2, 4, 2,//------
512  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 2, 2, 4, 2,//------
513  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 7, 2, 2, 4, 2,//------
514  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 7, 2, 2, 4, 1, 2,//------
515  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 9, 2, 2, 4, 2,//------
516  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 10, 2, 2, 4, 2,//------
517  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 11, 2, 2, 4, 2,//------
518  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 12, 2, 2, 4, 2,//------
519  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 13, 2, 2, 4, 2,//------
520  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 2,//------
521  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 1, 2,//------
522  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 2, 2,//------
523  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 3, 2,//------
524  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 2,//------
525  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 5, 2,//------
526  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 6, 2,//------
527  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 7, 2,//------
528  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 9, 1,//------
529  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 1,//------
530  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2,//------
531  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 1,//------
532  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2,//------
533  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 3,//------
534  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 4,//------
535  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 3,//------
536  2, 2, 2, 4, 2, 2, 4, 4, 6, 2, 2, 4, 4, 6, 6, 8, 2, 2, 4, 4, 6, 2, 2, 4,//------
537  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,//------
538  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,//------
539  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,//------
540  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,//------
541  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,//------
542  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,//------
543  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,//------
544  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,//------
545  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,//------
546  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,//------
547  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,//------
548  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,//------
549  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,//------
550  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 //-----
551 };
552 
553 const G4int G4hQAOModel::fNumberOfShells[101] =
554 {
555  0 , // nonexisting zero element
556 
557  1 , 1 , 2 , 2 , 3 , 3 , 4 , 4 , 3 , 4 , // 1 - 10
558 
559  5 , 5 , 6 , 6 , 6 , 6 , 6 , 7 , 8 , 8 , // 11 - 20
560 
561  9 , 9 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 10 , // 21 - 30
562 
563 11 , 11 , 11 , 11 , 11 , 12 , 13 , 13 , 14 , 14 , // 31 - 40
564 
565 14 , 14 , 14 , 14 , 14 , 15 , 15 , 15 , 16 , 16 , // 41 - 50
566 
567 // ----------------------------------------------------------
568 
569 16 , 16 , 16 , 17 , 18 , 18 , 19 , 19 , 19 , 19 , // 51 - 60
570 
571 19 , 19 , 19 , 20 , 19 , 19 , 19 , 19 , 19 , 20 , // 61 - 70
572 
573 21 , 21 , 21 , 21 , 21 , 21 , 21 , 21 , 22 , 22 , // 71 - 80
574 
575 23 , 23 , 23 , 23 , 24 , 24 , 25 , 25 , 26 , 26 , // 81 - 90
576 
577 27 , 27 , 27 , 26 , 26 , 27 , 27 , 26 , 26 , 26 // 91 - 100
578 
579 };
580 
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