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G4ecpssrBaseLixsModel.cc
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26 
27 #include <cmath>
28 #include <iostream>
29 
30 #include "G4ecpssrBaseLixsModel.hh"
31 
32 #include "globals.hh"
33 #include "G4PhysicalConstants.hh"
34 #include "G4SystemOfUnits.hh"
35 #include "G4AtomicTransitionManager.hh"
36 #include "G4NistManager.hh"
37 #include "G4Proton.hh"
38 #include "G4Alpha.hh"
39 #include "G4LinLogInterpolation.hh"
40 
41 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
42 
43 G4ecpssrBaseLixsModel::G4ecpssrBaseLixsModel()
44 {
45  verboseLevel=0;
46 
47  // Storing FLi data needed for 0.2 to 3.0 velocities region
48 
49  char *path = getenv("G4LEDATA");
50 
51  if (!path) {
52  G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0006", FatalException ,"G4LEDATA environment variable not set");
53  return;
54  }
55  std::ostringstream fileName1;
56  std::ostringstream fileName2;
57 
58  fileName1 << path << "/pixe/uf/FL1.dat";
59  fileName2 << path << "/pixe/uf/FL2.dat";
60 
61  // Reading of FL1.dat
62 
63  std::ifstream FL1(fileName1.str().c_str());
64  if (!FL1) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003",FatalException, "error opening FL1 data file");
65 
66  dummyVec1.push_back(0.);
67 
68  while(!FL1.eof())
69  {
70  double x1;
71  double y1;
72 
73  FL1>>x1>>y1;
74 
75  // Mandatory vector initialization
76  if (x1 != dummyVec1.back())
77  {
78  dummyVec1.push_back(x1);
79  aVecMap1[x1].push_back(-1.);
80  }
81 
82  FL1>>FL1Data[x1][y1];
83 
84  if (y1 != aVecMap1[x1].back()) aVecMap1[x1].push_back(y1);
85  }
86 
87  // Reading of FL2.dat
88 
89  std::ifstream FL2(fileName2.str().c_str());
90  if (!FL2) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003", FatalException," error opening FL2 data file");
91 
92  dummyVec2.push_back(0.);
93 
94  while(!FL2.eof())
95  {
96  double x2;
97  double y2;
98 
99  FL2>>x2>>y2;
100 
101  // Mandatory vector initialization
102  if (x2 != dummyVec2.back())
103  {
104  dummyVec2.push_back(x2);
105  aVecMap2[x2].push_back(-1.);
106  }
107 
108  FL2>>FL2Data[x2][y2];
109 
110  if (y2 != aVecMap2[x2].back()) aVecMap2[x2].push_back(y2);
111  }
112 
113 }
114 
115 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
116 
117 G4ecpssrBaseLixsModel::~G4ecpssrBaseLixsModel()
118 {}
119 
120 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
121 
122 G4double G4ecpssrBaseLixsModel::ExpIntFunction(G4int n,G4double x)
123 
124 {
125 // this function allows fast evaluation of the n order exponential integral function En(x)
126 
127  G4int i;
128  G4int ii;
129  G4int nm1;
130  G4double a;
131  G4double b;
132  G4double c;
133  G4double d;
134  G4double del;
135  G4double fact;
136  G4double h;
137  G4double psi;
138  G4double ans = 0;
139  const G4double euler= 0.5772156649;
140  const G4int maxit= 100;
141  const G4double fpmin = 1.0e-30;
142  const G4double eps = 1.0e-7;
143  nm1=n-1;
144  if (n<0 || x<0.0 || (x==0.0 && (n==0 || n==1)))
145  G4cout << "*** WARNING in G4ecpssrBaseLixsModel::ExpIntFunction: bad arguments in ExpIntFunction"
146  << G4endl;
147  else {
148  if (n==0) ans=std::exp(-x)/x;
149  else {
150  if (x==0.0) ans=1.0/nm1;
151  else {
152  if (x > 1.0) {
153  b=x+n;
154  c=1.0/fpmin;
155  d=1.0/b;
156  h=d;
157  for (i=1;i<=maxit;i++) {
158  a=-i*(nm1+i);
159  b +=2.0;
160  d=1.0/(a*d+b);
161  c=b+a/c;
162  del=c*d;
163  h *=del;
164  if (std::fabs(del-1.0) < eps) {
165  ans=h*std::exp(-x);
166  return ans;
167  }
168  }
169  } else {
170  ans = (nm1!=0 ? 1.0/nm1 : -std::log(x)-euler);
171  fact=1.0;
172  for (i=1;i<=maxit;i++) {
173  fact *=-x/i;
174  if (i !=nm1) del = -fact/(i-nm1);
175  else {
176  psi = -euler;
177  for (ii=1;ii<=nm1;ii++) psi +=1.0/ii;
178  del=fact*(-std::log(x)+psi);
179  }
180  ans += del;
181  if (std::fabs(del) < std::fabs(ans)*eps) return ans;
182  }
183  }
184  }
185  }
186  }
187 return ans;
188 }
189 
190 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
191 
192 G4double G4ecpssrBaseLixsModel::CalculateL1CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
193 {
194 
195  if (zTarget <=4) return 0.;
196 
197  //this L1-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
198  //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
199 
200  G4NistManager* massManager = G4NistManager::Instance();
201 
202  G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
203 
204  G4double zIncident = 0;
205  G4Proton* aProtone = G4Proton::Proton();
206  G4Alpha* aAlpha = G4Alpha::Alpha();
207 
208  if (massIncident == aProtone->GetPDGMass() )
209 
210  zIncident = (aProtone->GetPDGCharge())/eplus;
211 
212  else
213  {
214  if (massIncident == aAlpha->GetPDGMass())
215 
216  zIncident = (aAlpha->GetPDGCharge())/eplus;
217 
218  else
219  {
220  G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL1CrossSection : Proton or Alpha incident particles only. " << G4endl;
221  G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
222  return 0;
223  }
224  }
225 
226  G4double l1BindingEnergy = transitionManager->Shell(zTarget,1)->BindingEnergy(); //Observed binding energy of L1-subshell
227 
228  G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
229 
230  G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
231 
232  const G4double zlshell= 4.15;
233  // *** see Benka, ADANDT 22, p 223
234 
235  G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L1-sub shell
236 
237  const G4double rydbergMeV= 13.6056923e-6;
238 
239  const G4double nl= 2.;
240  // *** see Benka, ADANDT 22, p 220, f3
241 
242  G4double tetal1 = (l1BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
243  // *** see Benka, ADANDT 22, p 220, f3
244 
245  if (verboseLevel>0) G4cout << " tetal1=" << tetal1<< G4endl;
246 
247  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
248  // *** also called etaS
249  // *** see Benka, ADANDT 22, p 220, f3
250 
251  const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
252 
253  G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
254  // *** see Benka, ADANDT 22, p 220, f2, for protons
255  // *** see Basbas, Phys Rev A7, p 1000
256 
257  G4double velocityl1 = CalculateVelocity(1, zTarget, massIncident, energyIncident); // Scaled velocity
258 
259  if (verboseLevel>0) G4cout << " velocityl1=" << velocityl1<< G4endl;
260 
261  const G4double l1AnalyticalApproximation= 1.5;
262  G4double x1 =(nl*l1AnalyticalApproximation)/velocityl1;
263  // *** 1.5 is cK = cL1 (it is 1.25 for L2 & L3)
264  // *** see Brandt, Phys Rev A20, p 469, f16 in expression of h
265 
266  if (verboseLevel>0) G4cout << " x1=" << x1<< G4endl;
267 
268  G4double electrIonizationEnergyl1=0.;
269  // *** see Basbas, Phys Rev A17, p1665, f27
270  // *** see Brandt, Phys Rev A20, p469
271  // *** see Liu, Comp Phys Comm 97, p325, f A5
272 
273  if ( x1<=0.035) electrIonizationEnergyl1= 0.75*pi*(std::log(1./(x1*x1))-1.);
274  else
275  {
276  if ( x1<=3.)
277  electrIonizationEnergyl1 =std::exp(-2.*x1)/(0.031+(0.213*std::pow(x1,0.5))+(0.005*x1)-(0.069*std::pow(x1,3./2.))+(0.324*x1*x1));
278  else
279  {if ( x1<=11.) electrIonizationEnergyl1 =2.*std::exp(-2.*x1)/std::pow(x1,1.6);}
280  }
281 
282  G4double hFunctionl1 =(electrIonizationEnergyl1*2.*nl)/(tetal1*std::pow(velocityl1,3)); //takes into account the polarization effect
283  // *** see Brandt, Phys Rev A20, p 469, f16
284 
285  if (verboseLevel>0) G4cout << " hFunctionl1=" << hFunctionl1<< G4endl;
286 
287  G4double gFunctionl1 = (1.+(9.*velocityl1)+(31.*velocityl1*velocityl1)+(49.*std::pow(velocityl1,3.))+(162.*std::pow(velocityl1,4.))+(63.*std::pow(velocityl1,5.))+(18.*std::pow(velocityl1,6.))+(1.97*std::pow(velocityl1,7.)))/std::pow(1.+velocityl1,9.);//takes into account the reduced binding effect
288  // *** see Brandt, Phys Rev A20, p 469, f19
289 
290  if (verboseLevel>0) G4cout << " gFunctionl1=" << gFunctionl1<< G4endl;
291 
292  G4double sigmaPSS_l1 = 1.+(((2.*zIncident)/(screenedzTarget*tetal1))*(gFunctionl1-hFunctionl1)); //Binding-polarization factor
293  // *** also called dzeta
294  // *** also called epsilon
295  // *** see Basbas, Phys Rev A17, p1667, f45
296 
297  if (verboseLevel>0) G4cout << "sigmaPSS_l1 =" << sigmaPSS_l1<< G4endl;
298 
299  const G4double cNaturalUnit= 137.;
300 
301  G4double yl1Formula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(nl*velocityl1/sigmaPSS_l1);
302  // *** also called yS
303  // *** see Brandt, Phys Rev A20, p467, f6
304  // *** see Brandt, Phys Rev A23, p1728
305 
306  G4double l1relativityCorrection = std::pow((1.+(1.1*yl1Formula*yl1Formula)),0.5)+yl1Formula; // Relativistic correction parameter
307  // *** also called mRS
308  // *** see Brandt, Phys Rev A20, p467, f6
309 
310  //G4double reducedVelocity_l1 = velocityl1*std::pow(l1relativityCorrection,0.5); //Reduced velocity parameter
311 
312  G4double L1etaOverTheta2;
313 
314  G4double universalFunction_l1 = 0.;
315 
316  G4double sigmaPSSR_l1;
317 
318  // low velocity formula
319  // *****************
320  if ( velocityl1 <20. )
321  {
322 
323  L1etaOverTheta2 =(reducedEnergy* l1relativityCorrection)/((tetal1*sigmaPSS_l1)*(tetal1*sigmaPSS_l1));
324  // *** 1) RELATIVISTIC CORRECTION ADDED
325  // *** 2) sigma_PSS_l1 ADDED
326  // *** reducedEnergy is etaS, l1relativityCorrection is mRS
327  // *** see Phys Rev A20, p468, top
328 
329  if ( ((tetal1*sigmaPSS_l1) >=0.2) && ((tetal1*sigmaPSS_l1) <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
330 
331  universalFunction_l1 = FunctionFL1((tetal1*sigmaPSS_l1),L1etaOverTheta2);
332 
333  if (verboseLevel>0) G4cout << "at low velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
334 
335  sigmaPSSR_l1 = (sigma0/(tetal1*sigmaPSS_l1))*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
336  // *** see Benka, ADANDT 22, p220, f1
337 
338  if (verboseLevel>0) G4cout << " at low velocity range, sigma PWBA L1 CS = " << sigmaPSSR_l1<< G4endl;
339 
340  }
341 
342  else
343 
344  {
345 
346  L1etaOverTheta2 = reducedEnergy/(tetal1*tetal1);
347  // Medium & high velocity
348  // *** 1) NO RELATIVISTIC CORRECTION
349  // *** 2) NO sigma_PSS_l1
350  // *** see Benka, ADANDT 22, p223
351 
352  if ( (tetal1 >=0.2) && (tetal1 <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
353 
354  universalFunction_l1 = FunctionFL1(tetal1,L1etaOverTheta2);
355 
356  if (verboseLevel>0) G4cout << "at medium and high velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
357 
358  sigmaPSSR_l1 = (sigma0/tetal1)*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
359  // *** see Benka, ADANDT 22, p220, f1
360 
361  if (verboseLevel>0) G4cout << " sigma PWBA L1 CS at medium and high velocity range = " << sigmaPSSR_l1<< G4endl;
362  }
363 
364  G4double pssDeltal1 = (4./(systemMass *sigmaPSS_l1*tetal1))*(sigmaPSS_l1/velocityl1)*(sigmaPSS_l1/velocityl1);
365  // *** also called dzeta*delta
366  // *** see Brandt, Phys Rev A23, p1727, f B2
367 
368  if (verboseLevel>0) G4cout << " pssDeltal1=" << pssDeltal1<< G4endl;
369 
370  if (pssDeltal1>1) return 0.;
371 
372  G4double energyLossl1 = std::pow(1-pssDeltal1,0.5);
373  // *** also called z
374  // *** see Brandt, Phys Rev A23, p1727, after f B2
375 
376  if (verboseLevel>0) G4cout << " energyLossl1=" << energyLossl1<< G4endl;
377 
378  G4double coulombDeflectionl1 =
379  (8.*pi*zIncident/systemMass)*std::pow(tetal1*sigmaPSS_l1,-2.)*std::pow(velocityl1/sigmaPSS_l1,-3.)*(zTarget/screenedzTarget);
380  // *** see Brandt, Phys Rev A20, v2s and f2 and B2
381  // *** with factor n2 compared to Brandt, Phys Rev A23, p1727, f B3
382 
383  G4double cParameterl1 =2.* coulombDeflectionl1/(energyLossl1*(energyLossl1+1.));
384  // *** see Brandt, Phys Rev A23, p1727, f B4
385 
386  G4double coulombDeflectionFunction_l1 = 9.*ExpIntFunction(10,cParameterl1); //Coulomb-deflection effect correction
387 
388  if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l1 =" << coulombDeflectionFunction_l1 << G4endl;
389 
390  G4double crossSection_L1 = coulombDeflectionFunction_l1 * sigmaPSSR_l1;
391 
392  //ECPSSR L1 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
393  //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
394 
395  if (verboseLevel>0) G4cout << " crossSection_L1 =" << crossSection_L1 << G4endl;
396 
397  if (crossSection_L1 >= 0)
398  {
399  return crossSection_L1 * barn;
400  }
401 
402  else {return 0;}
403 }
404 
405 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
406 
407 G4double G4ecpssrBaseLixsModel::CalculateL2CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
408 
409 {
410  if (zTarget <=13 ) return 0.;
411 
412  // this L2-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
413  // and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
414 
415  G4NistManager* massManager = G4NistManager::Instance();
416 
417  G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
418 
419  G4double zIncident = 0;
420 
421  G4Proton* aProtone = G4Proton::Proton();
422  G4Alpha* aAlpha = G4Alpha::Alpha();
423 
424  if (massIncident == aProtone->GetPDGMass() )
425 
426  zIncident = (aProtone->GetPDGCharge())/eplus;
427 
428  else
429  {
430  if (massIncident == aAlpha->GetPDGMass())
431 
432  zIncident = (aAlpha->GetPDGCharge())/eplus;
433 
434  else
435  {
436  G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL2CrossSection : Proton or Alpha incident particles only. " << G4endl;
437  G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
438  return 0;
439  }
440  }
441 
442  G4double l2BindingEnergy = transitionManager->Shell(zTarget,2)->BindingEnergy(); //Observed binding energy of L2-subshell
443 
444  G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
445 
446  G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
447 
448  const G4double zlshell= 4.15;
449 
450  G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L2-subshell
451 
452  const G4double rydbergMeV= 13.6056923e-6;
453 
454  const G4double nl= 2.;
455 
456  G4double tetal2 = (l2BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
457 
458  if (verboseLevel>0) G4cout << " tetal2=" << tetal2<< G4endl;
459 
460  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
461 
462  const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
463 
464  G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
465 
466  G4double velocityl2 = CalculateVelocity(2, zTarget, massIncident, energyIncident); // Scaled velocity
467 
468  if (verboseLevel>0) G4cout << " velocityl2=" << velocityl2<< G4endl;
469 
470  const G4double l23AnalyticalApproximation= 1.25;
471 
472  G4double x2 = (nl*l23AnalyticalApproximation)/velocityl2;
473 
474  if (verboseLevel>0) G4cout << " x2=" << x2<< G4endl;
475 
476  G4double electrIonizationEnergyl2=0.;
477 
478  if ( x2<=0.035) electrIonizationEnergyl2= 0.75*pi*(std::log(1./(x2*x2))-1.);
479  else
480  {
481  if ( x2<=3.)
482  electrIonizationEnergyl2 =std::exp(-2.*x2)/(0.031+(0.213*std::pow(x2,0.5))+(0.005*x2)-(0.069*std::pow(x2,3./2.))+(0.324*x2*x2));
483  else
484  {if ( x2<=11.) electrIonizationEnergyl2 =2.*std::exp(-2.*x2)/std::pow(x2,1.6); }
485  }
486 
487  G4double hFunctionl2 =(electrIonizationEnergyl2*2.*nl)/(tetal2*std::pow(velocityl2,3)); //takes into account the polarization effect
488 
489  if (verboseLevel>0) G4cout << " hFunctionl2=" << hFunctionl2<< G4endl;
490 
491  G4double gFunctionl2 = (1.+(10.*velocityl2)+(45.*velocityl2*velocityl2)+(102.*std::pow(velocityl2,3.))+(331.*std::pow(velocityl2,4.))+(6.7*std::pow(velocityl2,5.))+(58.*std::pow(velocityl2,6.))+(7.8*std::pow(velocityl2,7.))+ (0.888*std::pow(velocityl2,8.)) )/std::pow(1.+velocityl2,10.);
492  //takes into account the reduced binding effect
493 
494  if (verboseLevel>0) G4cout << " gFunctionl2=" << gFunctionl2<< G4endl;
495 
496  G4double sigmaPSS_l2 = 1.+(((2.*zIncident)/(screenedzTarget*tetal2))*(gFunctionl2-hFunctionl2)); //Binding-polarization factor
497 
498  if (verboseLevel>0) G4cout << " sigmaPSS_l2=" << sigmaPSS_l2<< G4endl;
499 
500  const G4double cNaturalUnit= 137.;
501 
502  G4double yl2Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl2/sigmaPSS_l2);
503 
504  G4double l2relativityCorrection = std::pow((1.+(1.1*yl2Formula*yl2Formula)),0.5)+yl2Formula; // Relativistic correction parameter
505 
506  G4double L2etaOverTheta2;
507 
508  G4double universalFunction_l2 = 0.;
509 
510  G4double sigmaPSSR_l2 ;
511 
512  if ( velocityl2 < 20. )
513  {
514 
515  L2etaOverTheta2 = (reducedEnergy*l2relativityCorrection)/((sigmaPSS_l2*tetal2)*(sigmaPSS_l2*tetal2));
516 
517  if ( (tetal2*sigmaPSS_l2>=0.2) && (tetal2*sigmaPSS_l2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
518 
519  universalFunction_l2 = FunctionFL2((tetal2*sigmaPSS_l2),L2etaOverTheta2);
520 
521  sigmaPSSR_l2 = (sigma0/(tetal2*sigmaPSS_l2))*universalFunction_l2;
522 
523  if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at low velocity range = " << sigmaPSSR_l2<< G4endl;
524  }
525  else
526  {
527 
528  L2etaOverTheta2 = reducedEnergy /(tetal2*tetal2);
529 
530  if ( (tetal2>=0.2) && (tetal2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
531 
532  universalFunction_l2 = FunctionFL2((tetal2),L2etaOverTheta2);
533 
534  sigmaPSSR_l2 = (sigma0/tetal2)*universalFunction_l2;
535 
536  if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at medium and high velocity range = " << sigmaPSSR_l2<< G4endl;
537 
538  }
539 
540  G4double pssDeltal2 = (4./(systemMass*sigmaPSS_l2*tetal2))*(sigmaPSS_l2/velocityl2)*(sigmaPSS_l2/velocityl2);
541 
542  if (pssDeltal2>1) return 0.;
543 
544  G4double energyLossl2 = std::pow(1-pssDeltal2,0.5);
545 
546  if (verboseLevel>0) G4cout << " energyLossl2=" << energyLossl2<< G4endl;
547 
548  G4double coulombDeflectionl2
549  =(8.*pi*zIncident/systemMass)*std::pow(tetal2*sigmaPSS_l2,-2.)*std::pow(velocityl2/sigmaPSS_l2,-3.)*(zTarget/screenedzTarget);
550 
551  G4double cParameterl2 = 2.*coulombDeflectionl2/(energyLossl2*(energyLossl2+1.));
552 
553  G4double coulombDeflectionFunction_l2 = 11.*ExpIntFunction(12,cParameterl2); //Coulomb-deflection effect correction
554  // *** see Brandt, Phys Rev A10, p477, f25
555 
556  if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l2 =" << coulombDeflectionFunction_l2 << G4endl;
557 
558  G4double crossSection_L2 = coulombDeflectionFunction_l2 * sigmaPSSR_l2;
559  //ECPSSR L2 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
560  //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
561 
562  if (verboseLevel>0) G4cout << " crossSection_L2 =" << crossSection_L2 << G4endl;
563 
564  if (crossSection_L2 >= 0)
565  {
566  return crossSection_L2 * barn;
567  }
568  else {return 0;}
569 }
570 
571 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
572 
573 
574 G4double G4ecpssrBaseLixsModel::CalculateL3CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
575 
576 {
577  if (zTarget <=13) return 0.;
578 
579  //this L3-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
580  //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
581 
582  G4NistManager* massManager = G4NistManager::Instance();
583 
584  G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
585 
586  G4double zIncident = 0;
587 
588  G4Proton* aProtone = G4Proton::Proton();
589  G4Alpha* aAlpha = G4Alpha::Alpha();
590 
591  if (massIncident == aProtone->GetPDGMass() )
592 
593  zIncident = (aProtone->GetPDGCharge())/eplus;
594 
595  else
596  {
597  if (massIncident == aAlpha->GetPDGMass())
598 
599  zIncident = (aAlpha->GetPDGCharge())/eplus;
600 
601  else
602  {
603  G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL3CrossSection : Proton or Alpha incident particles only. " << G4endl;
604  G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
605  return 0;
606  }
607  }
608 
609  G4double l3BindingEnergy = transitionManager->Shell(zTarget,3)->BindingEnergy();
610 
611  G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
612 
613  G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2;//Mass of the system (projectile, target)
614 
615  const G4double zlshell= 4.15;
616 
617  G4double screenedzTarget = zTarget-zlshell;//Effective nuclear charge as seen by electrons in L3-subshell
618 
619  const G4double rydbergMeV= 13.6056923e-6;
620 
621  const G4double nl= 2.;
622 
623  G4double tetal3 = (l3BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV);//Screening parameter
624 
625  if (verboseLevel>0) G4cout << " tetal3=" << tetal3<< G4endl;
626 
627  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
628 
629  const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ;//Bohr radius of hydrogen
630 
631  G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
632 
633  G4double velocityl3 = CalculateVelocity(3, zTarget, massIncident, energyIncident);// Scaled velocity
634 
635  if (verboseLevel>0) G4cout << " velocityl3=" << velocityl3<< G4endl;
636 
637  const G4double l23AnalyticalApproximation= 1.25;
638 
639  G4double x3 = (nl*l23AnalyticalApproximation)/velocityl3;
640 
641  if (verboseLevel>0) G4cout << " x3=" << x3<< G4endl;
642 
643  G4double electrIonizationEnergyl3=0.;
644 
645  if ( x3<=0.035) electrIonizationEnergyl3= 0.75*pi*(std::log(1./(x3*x3))-1.);
646  else
647  {
648  if ( x3<=3.) electrIonizationEnergyl3 =std::exp(-2.*x3)/(0.031+(0.213*std::pow(x3,0.5))+(0.005*x3)-(0.069*std::pow(x3,3./2.))+(0.324*x3*x3));
649  else
650  {
651  if ( x3<=11.) electrIonizationEnergyl3 =2.*std::exp(-2.*x3)/std::pow(x3,1.6);}
652  }
653 
654  G4double hFunctionl3 =(electrIonizationEnergyl3*2.*nl)/(tetal3*std::pow(velocityl3,3));//takes into account the polarization effect
655 
656  if (verboseLevel>0) G4cout << " hFunctionl3=" << hFunctionl3<< G4endl;
657 
658  G4double gFunctionl3 = (1.+(10.*velocityl3)+(45.*velocityl3*velocityl3)+(102.*std::pow(velocityl3,3.))+(331.*std::pow(velocityl3,4.))+(6.7*std::pow(velocityl3,5.))+(58.*std::pow(velocityl3,6.))+(7.8*std::pow(velocityl3,7.))+ (0.888*std::pow(velocityl3,8.)) )/std::pow(1.+velocityl3,10.);
659  //takes into account the reduced binding effect
660 
661  if (verboseLevel>0) G4cout << " gFunctionl3=" << gFunctionl3<< G4endl;
662 
663  G4double sigmaPSS_l3 = 1.+(((2.*zIncident)/(screenedzTarget*tetal3))*(gFunctionl3-hFunctionl3));//Binding-polarization factor
664 
665  if (verboseLevel>0) G4cout << "sigmaPSS_l3 =" << sigmaPSS_l3<< G4endl;
666 
667  const G4double cNaturalUnit= 137.;
668 
669  G4double yl3Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl3/sigmaPSS_l3);
670 
671  G4double l3relativityCorrection = std::pow((1.+(1.1*yl3Formula*yl3Formula)),0.5)+yl3Formula; // Relativistic correction parameter
672 
673  G4double L3etaOverTheta2;
674 
675  G4double universalFunction_l3 = 0.;
676 
677  G4double sigmaPSSR_l3;
678 
679  if ( velocityl3 < 20. )
680  {
681 
682  L3etaOverTheta2 = (reducedEnergy* l3relativityCorrection)/((sigmaPSS_l3*tetal3)*(sigmaPSS_l3*tetal3));
683 
684  if ( (tetal3*sigmaPSS_l3>=0.2) && (tetal3*sigmaPSS_l3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
685 
686  universalFunction_l3 = 2.*FunctionFL2((tetal3*sigmaPSS_l3), L3etaOverTheta2 );
687 
688  sigmaPSSR_l3 = (sigma0/(tetal3*sigmaPSS_l3))*universalFunction_l3;
689 
690  if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at low velocity range = " << sigmaPSSR_l3<< G4endl;
691 
692  }
693 
694  else
695 
696  {
697 
698  L3etaOverTheta2 = reducedEnergy/(tetal3*tetal3);
699 
700  if ( (tetal3>=0.2) && (tetal3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
701 
702  universalFunction_l3 = 2.*FunctionFL2(tetal3, L3etaOverTheta2 );
703 
704  sigmaPSSR_l3 = (sigma0/tetal3)*universalFunction_l3;
705 
706  if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at medium and high velocity range = " << sigmaPSSR_l3<< G4endl;
707  }
708 
709  G4double pssDeltal3 = (4./(systemMass*sigmaPSS_l3*tetal3))*(sigmaPSS_l3/velocityl3)*(sigmaPSS_l3/velocityl3);
710 
711  if (verboseLevel>0) G4cout << " pssDeltal3=" << pssDeltal3<< G4endl;
712 
713  if (pssDeltal3>1) return 0.;
714 
715  G4double energyLossl3 = std::pow(1-pssDeltal3,0.5);
716 
717  if (verboseLevel>0) G4cout << " energyLossl3=" << energyLossl3<< G4endl;
718 
719  G4double coulombDeflectionl3 =
720  (8.*pi*zIncident/systemMass)*std::pow(tetal3*sigmaPSS_l3,-2.)*std::pow(velocityl3/sigmaPSS_l3,-3.)*(zTarget/screenedzTarget);
721 
722  G4double cParameterl3 = 2.*coulombDeflectionl3/(energyLossl3*(energyLossl3+1.));
723 
724  G4double coulombDeflectionFunction_l3 = 11.*ExpIntFunction(12,cParameterl3);//Coulomb-deflection effect correction
725  // *** see Brandt, Phys Rev A10, p477, f25
726 
727  if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l3 =" << coulombDeflectionFunction_l3 << G4endl;
728 
729  G4double crossSection_L3 = coulombDeflectionFunction_l3 * sigmaPSSR_l3;
730  //ECPSSR L3 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
731  //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
732 
733  if (verboseLevel>0) G4cout << " crossSection_L3 =" << crossSection_L3 << G4endl;
734 
735  if (crossSection_L3 >= 0)
736  {
737  return crossSection_L3 * barn;
738  }
739  else {return 0;}
740 }
741 
742 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
743 
744 G4double G4ecpssrBaseLixsModel::CalculateVelocity(G4int subShell, G4int zTarget, G4double massIncident, G4double energyIncident)
745 
746 {
747 
748  G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
749 
750  G4double liBindingEnergy = transitionManager->Shell(zTarget,subShell)->BindingEnergy();
751 
752  G4Proton* aProtone = G4Proton::Proton();
753  G4Alpha* aAlpha = G4Alpha::Alpha();
754 
755  if (!((massIncident == aProtone->GetPDGMass()) || (massIncident == aAlpha->GetPDGMass())))
756  {
757  G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateVelocity : Proton or Alpha incident particles only. " << G4endl;
758  G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
759  return 0;
760  }
761 
762  const G4double zlshell= 4.15;
763 
764  G4double screenedzTarget = zTarget- zlshell;
765 
766  const G4double rydbergMeV= 13.6056923e-6;
767 
768  const G4double nl= 2.;
769 
770  G4double tetali = (liBindingEnergy*nl*nl)/(screenedzTarget*screenedzTarget*rydbergMeV);
771 
772  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
773 
774  G4double velocity = 2.*nl*std::pow(reducedEnergy,0.5)/tetali;
775  // *** see Brandt, Phys Rev A10, p10, f4
776 
777  return velocity;
778 }
779 
780 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
781 
782 G4double G4ecpssrBaseLixsModel::FunctionFL1(G4double k, G4double theta)
783 {
784 
785  G4double sigma = 0.;
786  G4double valueT1 = 0;
787  G4double valueT2 = 0;
788  G4double valueE21 = 0;
789  G4double valueE22 = 0;
790  G4double valueE12 = 0;
791  G4double valueE11 = 0;
792  G4double xs11 = 0;
793  G4double xs12 = 0;
794  G4double xs21 = 0;
795  G4double xs22 = 0;
796 
797  // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
798 
799  if (
800  theta==8.66e-4 ||
801  theta==8.66e-3 ||
802  theta==8.66e-2 ||
803  theta==8.66e-1 ||
804  theta==8.66e+00 ||
805  theta==8.66e+01
806  ) theta=theta-1e-12;
807 
808  if (
809  theta==1.e-4 ||
810  theta==1.e-3 ||
811  theta==1.e-2 ||
812  theta==1.e-1 ||
813  theta==1.e+00 ||
814  theta==1.e+01
815  ) theta=theta+1e-12;
816 
817  // END PROTECTION
818 
819  std::vector<double>::iterator t2 = std::upper_bound(dummyVec1.begin(),dummyVec1.end(), k);
820  std::vector<double>::iterator t1 = t2-1;
821 
822  std::vector<double>::iterator e12 = std::upper_bound(aVecMap1[(*t1)].begin(),aVecMap1[(*t1)].end(), theta);
823  std::vector<double>::iterator e11 = e12-1;
824 
825  std::vector<double>::iterator e22 = std::upper_bound(aVecMap1[(*t2)].begin(),aVecMap1[(*t2)].end(), theta);
826  std::vector<double>::iterator e21 = e22-1;
827 
828  valueT1 =*t1;
829  valueT2 =*t2;
830  valueE21 =*e21;
831  valueE22 =*e22;
832  valueE12 =*e12;
833  valueE11 =*e11;
834 
835  xs11 = FL1Data[valueT1][valueE11];
836  xs12 = FL1Data[valueT1][valueE12];
837  xs21 = FL1Data[valueT2][valueE21];
838  xs22 = FL1Data[valueT2][valueE22];
839 
840  if (verboseLevel>0)
841  G4cout
842  << valueT1 << " "
843  << valueT2 << " "
844  << valueE11 << " "
845  << valueE12 << " "
846  << valueE21 << " "
847  << valueE22 << " "
848  << xs11 << " "
849  << xs12 << " "
850  << xs21 << " "
851  << xs22 << " "
852  << G4endl;
853 
854  G4double xsProduct = xs11 * xs12 * xs21 * xs22;
855 
856  if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
857 
858  if (xsProduct != 0.)
859  {
860  sigma = QuadInterpolator( valueE11, valueE12,
861  valueE21, valueE22,
862  xs11, xs12,
863  xs21, xs22,
864  valueT1, valueT2,
865  k, theta );
866  }
867 
868  return sigma;
869 }
870 
871 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
872 
873 G4double G4ecpssrBaseLixsModel::FunctionFL2(G4double k, G4double theta)
874 {
875 
876  G4double sigma = 0.;
877  G4double valueT1 = 0;
878  G4double valueT2 = 0;
879  G4double valueE21 = 0;
880  G4double valueE22 = 0;
881  G4double valueE12 = 0;
882  G4double valueE11 = 0;
883  G4double xs11 = 0;
884  G4double xs12 = 0;
885  G4double xs21 = 0;
886  G4double xs22 = 0;
887 
888  // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
889 
890  if (
891  theta==8.66e-4 ||
892  theta==8.66e-3 ||
893  theta==8.66e-2 ||
894  theta==8.66e-1 ||
895  theta==8.66e+00 ||
896  theta==8.66e+01
897  ) theta=theta-1e-12;
898 
899  if (
900  theta==1.e-4 ||
901  theta==1.e-3 ||
902  theta==1.e-2 ||
903  theta==1.e-1 ||
904  theta==1.e+00 ||
905  theta==1.e+01
906  ) theta=theta+1e-12;
907 
908  // END PROTECTION
909 
910  std::vector<double>::iterator t2 = std::upper_bound(dummyVec2.begin(),dummyVec2.end(), k);
911  std::vector<double>::iterator t1 = t2-1;
912 
913  std::vector<double>::iterator e12 = std::upper_bound(aVecMap2[(*t1)].begin(),aVecMap2[(*t1)].end(), theta);
914  std::vector<double>::iterator e11 = e12-1;
915 
916  std::vector<double>::iterator e22 = std::upper_bound(aVecMap2[(*t2)].begin(),aVecMap2[(*t2)].end(), theta);
917  std::vector<double>::iterator e21 = e22-1;
918 
919  valueT1 =*t1;
920  valueT2 =*t2;
921  valueE21 =*e21;
922  valueE22 =*e22;
923  valueE12 =*e12;
924  valueE11 =*e11;
925 
926  xs11 = FL2Data[valueT1][valueE11];
927  xs12 = FL2Data[valueT1][valueE12];
928  xs21 = FL2Data[valueT2][valueE21];
929  xs22 = FL2Data[valueT2][valueE22];
930 
931  if (verboseLevel>0)
932  G4cout
933  << valueT1 << " "
934  << valueT2 << " "
935  << valueE11 << " "
936  << valueE12 << " "
937  << valueE21 << " "
938  << valueE22 << " "
939  << xs11 << " "
940  << xs12 << " "
941  << xs21 << " "
942  << xs22 << " "
943  << G4endl;
944 
945  G4double xsProduct = xs11 * xs12 * xs21 * xs22;
946 
947  if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
948 
949  if (xsProduct != 0.)
950  {
951  sigma = QuadInterpolator( valueE11, valueE12,
952  valueE21, valueE22,
953  xs11, xs12,
954  xs21, xs22,
955  valueT1, valueT2,
956  k, theta );
957  }
958 
959  return sigma;
960 }
961 
962 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
963 
964 G4double G4ecpssrBaseLixsModel::LinLinInterpolate(G4double e1,
965  G4double e2,
966  G4double e,
967  G4double xs1,
968  G4double xs2)
969 {
970  G4double value = xs1 + (xs2 - xs1)*(e - e1)/ (e2 - e1);
971  return value;
972 }
973 
974 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
975 
976 G4double G4ecpssrBaseLixsModel::LinLogInterpolate(G4double e1,
977  G4double e2,
978  G4double e,
979  G4double xs1,
980  G4double xs2)
981 {
982  G4double d1 = std::log(xs1);
983  G4double d2 = std::log(xs2);
984  G4double value = std::exp(d1 + (d2 - d1)*(e - e1)/ (e2 - e1));
985  return value;
986 }
987 
988 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
989 
990 G4double G4ecpssrBaseLixsModel::LogLogInterpolate(G4double e1,
991  G4double e2,
992  G4double e,
993  G4double xs1,
994  G4double xs2)
995 {
996  G4double a = (std::log10(xs2)-std::log10(xs1)) / (std::log10(e2)-std::log10(e1));
997  G4double b = std::log10(xs2) - a*std::log10(e2);
998  G4double sigma = a*std::log10(e) + b;
999  G4double value = (std::pow(10.,sigma));
1000  return value;
1001 }
1002 
1003 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
1004 
1005 G4double G4ecpssrBaseLixsModel::QuadInterpolator(G4double e11, G4double e12,
1006  G4double e21, G4double e22,
1007  G4double xs11, G4double xs12,
1008  G4double xs21, G4double xs22,
1009  G4double t1, G4double t2,
1010  G4double t, G4double e)
1011 {
1012 // Log-Log
1013  G4double interpolatedvalue1 = LogLogInterpolate(e11, e12, e, xs11, xs12);
1014  G4double interpolatedvalue2 = LogLogInterpolate(e21, e22, e, xs21, xs22);
1015  G4double value = LogLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1016 
1017 /*
1018 // Lin-Log
1019  G4double interpolatedvalue1 = LinLogInterpolate(e11, e12, e, xs11, xs12);
1020  G4double interpolatedvalue2 = LinLogInterpolate(e21, e22, e, xs21, xs22);
1021  G4double value = LinLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1022 */
1023 
1024 /*
1025 // Lin-Lin
1026  G4double interpolatedvalue1 = LinLinInterpolate(e11, e12, e, xs11, xs12);
1027  G4double interpolatedvalue2 = LinLinInterpolate(e21, e22, e, xs21, xs22);
1028  G4double value = LinLinInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1029 */
1030  return value;
1031 
1032 }
1033 
G4LinLogInterpolation.hh
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Definition: G4Proton.cc:93
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Definition: G4Exception.cc:41
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Definition: G4ParticleDefinition.hh:161
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Definition: plottest35.py:33
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Definition: G4NistManager.hh:344
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Definition: include/expat.h:331
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Definition: G4ios.hh:61
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Definition: G4Alpha.cc:89
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Definition: G4Types.hh:76
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Definition: G4ParticleDefinition.hh:163
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Definition: G4AtomicTransitionManager.cc:162
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Definition: G4AtomicTransitionManager.cc:173
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