source: trunk/source/processes/electromagnetic/lowenergy/src/G4PhotoElectricAngularGeneratorPolarized.cc

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27// -------------------------------------------------------------------
28//
29// GEANT4 Class file
30//
31//
32// File name:     G4PhotoElectricAngularGeneratorPolarized
33//
34// Author: A. C. Farinha, L. Peralta, P. Rodrigues and A. Trindade
35//
36// Creation date:
37//
38// Modifications:
39// 10 January 2006       
40//
41// Class Description:
42//
43// Concrete class for PhotoElectric Electron Angular Polarized Distribution Generation
44//
45// Class Description:
46// PhotoElectric Electron Angular Generator based on the general Gavrila photoelectron angular distribution.
47// Includes polarization effects for K and L1 atomic shells, according to Gavrila (1959, 1961).
48// For higher shells the L1 cross-section is used.
49//
50// The Gavrila photoelectron angular distribution is a complex function which can not be sampled using
51// the inverse-transform method (James 1980). Instead a more general approach based on the one already
52// used to sample bremsstrahlung 2BN cross section (G4Generator2BN, Peralta, 2005) was used.
53//
54// M. Gavrila, "Relativistic K-Shell Photoeffect", Phys. Rev. 113, 514-526   (1959)
55// M. Gavrila, "Relativistic L-Shell Photoeffect", Phys. Rev. 124, 1132-1141 (1961)
56// F. James, Rept. on Prog. in Phys. 43, 1145 (1980)
57// L. Peralta et al., "A new low-energy bremsstrahlung generator for GEANT4", Radiat. Prot. Dosimetry. 116, 59-64 (2005)
58//
59//
60// -------------------------------------------------------------------
61//
62//   
63
64#include "G4PhotoElectricAngularGeneratorPolarized.hh"
65#include "G4RotationMatrix.hh"
66#include "Randomize.hh"
67
68//   
69
70G4PhotoElectricAngularGeneratorPolarized::G4PhotoElectricAngularGeneratorPolarized(const G4String& name):G4VPhotoElectricAngularDistribution(name)
71{
72  const G4int arrayDim = 980;
73
74  //minimum electron beta parameter allowed
75  betaArray[0] = 0.02;
76  //beta step
77  betaArray[1] = 0.001;
78  //maximum index array for a and c tables
79  betaArray[2] = arrayDim - 1;
80
81  // read Majorant Surface Parameters. This are required in order to generate Gavrila angular photoelectron distribution
82  for(G4int level = 0; level < 2; level++){
83
84    char nameChar0[100] = "ftab0.dat"; // K-shell Majorant Surface Parameters
85    char nameChar1[100] = "ftab1.dat"; // L-shell Majorant Surface Parameters
86
87    G4String filename;
88    if(level == 0) filename = nameChar0;
89    if(level == 1) filename = nameChar1;
90
91    char* path = getenv("G4LEDATA");
92    if (!path)
93      {
94        G4String excep = "G4EMDataSet - G4LEDATA environment variable not set";
95        G4Exception(excep);
96      }
97
98    G4String pathString(path);
99    G4String dirFile = pathString + "/photoelectric_angular/" + filename;
100    FILE *infile;
101    infile = fopen(dirFile,"r"); 
102    if (infile == 0)
103      {
104        G4String excep = "G4PhotoElectricAngularGeneratorPolarized - data file: " + dirFile + " not found";
105        G4Exception(excep);
106      }
107
108    // Read parameters into tables. The parameters are function of incident electron energy and shell level
109    G4float aRead,cRead, beta;
110    for(G4int i=0 ; i<arrayDim ;i++){
111      fscanf(infile,"%f\t %e\t %e",&beta,&aRead,&cRead);
112      aMajorantSurfaceParameterTable[i][level] = aRead;   
113      cMajorantSurfaceParameterTable[i][level] = cRead;
114    }
115    fclose(infile);
116
117  }
118}
119
120//   
121
122G4PhotoElectricAngularGeneratorPolarized::~G4PhotoElectricAngularGeneratorPolarized() 
123{;}
124
125//
126
127G4ThreeVector G4PhotoElectricAngularGeneratorPolarized::GetPhotoElectronDirection(const G4ThreeVector& direction, const G4double eKineticEnergy,
128                                                                                  const G4ThreeVector& polarization, const G4int shellId) const
129{
130  // Calculate Lorentz term (gamma) and beta parameters
131  G4double gamma   = 1. + eKineticEnergy/electron_mass_c2;
132  G4double beta  = std::sqrt(gamma*gamma-1.)/gamma;
133
134  G4double theta, phi = 0;
135  G4double aBeta = 0; // Majorant surface parameter (function of the outgoing electron kinetic energy)
136  G4double cBeta = 0; // Majorant surface parameter (function of the outgoing electron kinetic energy)
137
138  G4int shellLevel = 0;
139  if(shellId <  2) shellLevel = 0; // K-shell  // Polarized model for K-shell
140  if(shellId >= 2) shellLevel = 1; // L1-shell // Polarized model for L1 and higher shells
141
142  // For the outgoing kinetic energy find the current majorant surface parameters
143  PhotoElectronGetMajorantSurfaceAandCParameters( shellLevel, beta, &aBeta, &cBeta);
144
145  // Generate pho and theta according to the shell level and beta parameter of the electron
146  PhotoElectronGeneratePhiAndTheta(shellLevel, beta, aBeta, cBeta, &phi, &theta);
147
148  // Determine the rotation matrix
149  G4RotationMatrix rotation = PhotoElectronRotationMatrix(direction, polarization);
150
151  // Compute final direction of the outgoing electron
152  G4ThreeVector final_direction = PhotoElectronComputeFinalDirection(rotation, theta, phi);
153
154  return final_direction;
155}
156
157//
158
159void G4PhotoElectricAngularGeneratorPolarized::PhotoElectronGeneratePhiAndTheta(const G4int shellLevel, const G4double beta, 
160                                                                                const G4double aBeta, const G4double cBeta, 
161                                                                                G4double *pphi, G4double *ptheta) const
162{
163  G4double rand1, rand2, rand3 = 0;
164  G4double phi = 0;
165  G4double theta = 0;
166  G4double crossSectionValue = 0;
167  G4double crossSectionMajorantFunctionValue = 0;
168  G4double maxBeta = 0;
169
170  do {
171
172    rand1 = G4UniformRand();
173    rand2 = G4UniformRand();
174    rand3 = G4UniformRand();
175       
176    phi=2*pi*rand1;
177
178    if(shellLevel == 0){
179
180      // Polarized Gavrila Cross-Section for K-shell (1959)
181      theta=std::sqrt(((std::exp(rand2*std::log(1+cBeta*pi*pi)))-1)/cBeta);
182      crossSectionMajorantFunctionValue = CrossSectionMajorantFunction(theta, cBeta);
183      crossSectionValue = DSigmaKshellGavrila1959(beta, theta, phi);
184
185    } else {
186
187      //  Polarized Gavrila Cross-Section for other shells (L1-shell) (1961)
188      theta = std::sqrt(((std::exp(rand2*std::log(1+cBeta*pi*pi)))-1)/cBeta);
189      crossSectionMajorantFunctionValue = CrossSectionMajorantFunction(theta, cBeta);
190      crossSectionValue = DSigmaL1shellGavrila(beta, theta, phi);
191
192    }
193
194    maxBeta=rand3*aBeta*crossSectionMajorantFunctionValue;
195
196  }while(maxBeta > crossSectionValue);
197
198  *pphi = phi;
199  *ptheta = theta;
200}
201
202//
203
204G4double G4PhotoElectricAngularGeneratorPolarized::CrossSectionMajorantFunction(const G4double theta, const G4double cBeta) const
205{
206  // Compute Majorant Function
207  G4double crossSectionMajorantFunctionValue = 0; 
208  crossSectionMajorantFunctionValue = theta/(1+cBeta*theta*theta);
209  return crossSectionMajorantFunctionValue;
210}
211
212//
213
214G4double G4PhotoElectricAngularGeneratorPolarized::DSigmaKshellGavrila1959(const G4double beta, const G4double theta, const G4double phi) const
215{
216
217  //Double differential K shell cross-section (Gavrila 1959)
218
219  G4double beta2 = beta*beta;
220  G4double oneBeta2 = 1 - beta2;
221  G4double sqrtOneBeta2 = std::sqrt(oneBeta2);
222  G4double oneBeta2_to_3_2 = std::pow(oneBeta2,1.5);
223  G4double cosTheta = std::cos(theta);
224  G4double sinTheta2 = std::sin(theta)*std::sin(theta);
225  G4double cosPhi2 = std::cos(phi)*std::cos(phi);
226  G4double oneBetaCosTheta = 1-beta*cosTheta;
227  G4double dsigma = 0;
228  G4double firstTerm = 0;
229  G4double secondTerm = 0;
230
231  firstTerm = sinTheta2*cosPhi2/std::pow(oneBetaCosTheta,4)-(1 - sqrtOneBeta2)/(2*oneBeta2) * 
232              (sinTheta2 * cosPhi2)/std::pow(oneBetaCosTheta,3) + (1-sqrtOneBeta2)*
233              (1-sqrtOneBeta2)/(4*oneBeta2_to_3_2) * sinTheta2/std::pow(oneBetaCosTheta,3);
234
235  secondTerm = std::sqrt(1 - sqrtOneBeta2)/(std::pow(2.,3.5)*beta2*std::pow(oneBetaCosTheta,2.5)) *
236               (4*beta2/sqrtOneBeta2 * sinTheta2*cosPhi2/oneBetaCosTheta + 4*beta/oneBeta2 * cosTheta * cosPhi2
237               - 4*(1-sqrtOneBeta2)/oneBeta2 *(1+cosPhi2) - beta2 * (1-sqrtOneBeta2)/oneBeta2 * sinTheta2/oneBetaCosTheta
238               + 4*beta2*(1-sqrtOneBeta2)/oneBeta2_to_3_2 - 4*beta*(1-sqrtOneBeta2)*(1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta)
239               + (1-sqrtOneBeta2)/(4*beta2*oneBetaCosTheta*oneBetaCosTheta) * (beta/oneBeta2 - 2/oneBeta2 * cosTheta * cosPhi2 + 
240               (1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta - beta * (1-sqrtOneBeta2)/oneBeta2_to_3_2);
241
242  dsigma = ( firstTerm*(1-pi*fine_structure_const/beta) + secondTerm*(pi*fine_structure_const) );
243
244  return dsigma;
245}
246
247//
248
249G4double G4PhotoElectricAngularGeneratorPolarized::DSigmaL1shellGavrila(const G4double beta, const G4double theta, const G4double phi) const
250{
251
252  //Double differential L1 shell cross-section (Gavrila 1961)
253
254  G4double beta2 = beta*beta;
255  G4double oneBeta2 = 1-beta2;
256  G4double sqrtOneBeta2 = std::sqrt(oneBeta2);
257  G4double oneBeta2_to_3_2=std::pow(oneBeta2,1.5);
258  G4double cosTheta = std::cos(theta);
259  G4double sinTheta2 =std::sin(theta)*std::sin(theta);
260  G4double cosPhi2 = std::cos(phi)*std::cos(phi);
261  G4double oneBetaCosTheta = 1-beta*cosTheta;
262       
263  G4double dsigma = 0;
264  G4double firstTerm = 0;
265  G4double secondTerm = 0;
266
267  firstTerm = sinTheta2*cosPhi2/std::pow(oneBetaCosTheta,4)-(1 - sqrtOneBeta2)/(2*oneBeta2)
268              *  (sinTheta2 * cosPhi2)/std::pow(oneBetaCosTheta,3) + (1-sqrtOneBeta2)*
269              (1-sqrtOneBeta2)/(4*oneBeta2_to_3_2) * sinTheta2/std::pow(oneBetaCosTheta,3);
270
271  secondTerm = std::sqrt(1 - sqrtOneBeta2)/(std::pow(2.,3.5)*beta2*std::pow(oneBetaCosTheta,2.5)) *
272               (4*beta2/sqrtOneBeta2 * sinTheta2*cosPhi2/oneBetaCosTheta + 4*beta/oneBeta2 * cosTheta * cosPhi2
273               - 4*(1-sqrtOneBeta2)/oneBeta2 *(1+cosPhi2) - beta2 * (1-sqrtOneBeta2)/oneBeta2 * sinTheta2/oneBetaCosTheta
274               + 4*beta2*(1-sqrtOneBeta2)/oneBeta2_to_3_2 - 4*beta*(1-sqrtOneBeta2)*(1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta)
275               + (1-sqrtOneBeta2)/(4*beta2*oneBetaCosTheta*oneBetaCosTheta) * (beta/oneBeta2 - 2/oneBeta2 * cosTheta * cosPhi2 + 
276               (1-sqrtOneBeta2)/oneBeta2_to_3_2*cosTheta - beta*(1-sqrtOneBeta2)/oneBeta2_to_3_2);
277
278  dsigma = ( firstTerm*(1-pi*fine_structure_const/beta) + secondTerm*(pi*fine_structure_const) );
279
280  return dsigma;
281}
282
283G4double G4PhotoElectricAngularGeneratorPolarized::GetMax(const G4double arg1, const G4double arg2) const
284{
285  if (arg1 > arg2)
286    return arg1;
287  else
288    return arg2;
289}
290
291//
292
293G4RotationMatrix G4PhotoElectricAngularGeneratorPolarized::PhotoElectronRotationMatrix(const G4ThreeVector& direction, 
294                                                                                       const G4ThreeVector& polarization) const
295{
296  G4double mK = direction.mag();
297  G4double mS = polarization.mag();
298  G4ThreeVector polarization2 = polarization;
299  const G4double kTolerance = 1e-6;
300
301  if(!(polarization.isOrthogonal(direction,kTolerance)) || mS == 0){
302    G4ThreeVector d0 = direction.unit();
303    G4ThreeVector a1 = SetPerpendicularVector(d0); 
304    G4ThreeVector a0 = a1.unit(); 
305    G4double rand1 = G4UniformRand();
306    G4double angle = twopi*rand1; 
307    G4ThreeVector b0 = d0.cross(a0); 
308    G4ThreeVector c;
309    c.setX(std::cos(angle)*(a0.x())+std::sin(angle)*b0.x());
310    c.setY(std::cos(angle)*(a0.y())+std::sin(angle)*b0.y());
311    c.setZ(std::cos(angle)*(a0.z())+std::sin(angle)*b0.z());
312    polarization2 = c.unit();
313    mS = polarization2.mag();
314  }else
315    {
316      if ( polarization.howOrthogonal(direction) != 0)
317        {
318          polarization2 = polarization - polarization.dot(direction)/direction.dot(direction) * direction;
319        }
320    }
321
322  G4ThreeVector direction2 = direction/mK;
323  polarization2 = polarization2/mS;
324
325  G4ThreeVector y = direction2.cross(polarization2);
326   
327  G4RotationMatrix R(polarization2,y,direction2);
328  return R;
329}
330
331void G4PhotoElectricAngularGeneratorPolarized::PhotoElectronGetMajorantSurfaceAandCParameters(const G4int shellLevel, const G4double beta,G4double *majorantSurfaceParameterA, G4double *majorantSurfaceParameterC) const
332{
333  // This member function finds for a given shell and beta value of the outgoing electron the correct Majorant Surface parameters
334
335  G4double aBeta,cBeta;
336  G4double bMin,bStep;
337  G4int indexMax;
338  G4int level = shellLevel;   
339  if(shellLevel > 1) level = 1; // protection since only K and L1 polarized double differential cross-sections were implemented
340   
341  bMin = betaArray[0];
342  bStep = betaArray[1];
343  indexMax = (G4int)betaArray[2];
344  const G4double kBias = 1e-9;
345
346  G4int k = (G4int)((beta-bMin+kBias)/bStep);   
347   
348  if(k < 0)
349    k = 0;
350  if(k > indexMax)
351    k = indexMax; 
352   
353  if(k == 0) 
354    aBeta = GetMax(aMajorantSurfaceParameterTable[k][level],aMajorantSurfaceParameterTable[k+1][level]);
355  else if(k==indexMax)
356    aBeta = GetMax(aMajorantSurfaceParameterTable[k-1][level],aMajorantSurfaceParameterTable[k][level]);
357  else{
358    aBeta = GetMax(aMajorantSurfaceParameterTable[k-1][level],aMajorantSurfaceParameterTable[k][level]);
359    aBeta = GetMax(aBeta,aMajorantSurfaceParameterTable[k+1][level]);
360  }   
361   
362  if(k == 0)
363    cBeta = GetMax(cMajorantSurfaceParameterTable[k][level],cMajorantSurfaceParameterTable[k+1][level]);
364  else if(k == indexMax)
365    cBeta = GetMax(cMajorantSurfaceParameterTable[k-1][level],cMajorantSurfaceParameterTable[k][level]);
366  else{
367    cBeta = GetMax(cMajorantSurfaceParameterTable[k-1][level],cMajorantSurfaceParameterTable[k][level]);
368    cBeta = GetMax(cBeta,cMajorantSurfaceParameterTable[k+1][level]);
369  }
370
371  *majorantSurfaceParameterA = aBeta;
372  *majorantSurfaceParameterC = cBeta;
373
374}
375
376
377//
378G4ThreeVector G4PhotoElectricAngularGeneratorPolarized::PhotoElectronComputeFinalDirection(const G4RotationMatrix& rotation, const G4double theta, const G4double phi) const
379{
380
381  //computes the photoelectron momentum unitary vector
382  G4double px = std::cos(phi)*std::sin(theta);
383  G4double py = std::sin(phi)*std::sin(theta);
384  G4double pz = std::cos(theta);
385
386  G4ThreeVector samplingDirection(px,py,pz);
387
388  G4ThreeVector outgoingDirection = rotation*samplingDirection;
389  return outgoingDirection;
390}
391
392//
393
394void G4PhotoElectricAngularGeneratorPolarized::PrintGeneratorInformation() const
395{
396  G4cout << "\n" << G4endl;
397  G4cout << "Polarized Photoelectric Angular Generator" << G4endl;
398  G4cout << "PhotoElectric Electron Angular Generator based on the general Gavrila photoelectron angular distribution" << G4endl;
399  G4cout << "Includes polarization effects for K and L1 atomic shells, according to Gavrilla (1959, 1961)." << G4endl;
400  G4cout << "For higher shells the L1 cross-section is used." << G4endl;
401  G4cout << "(see Physics Reference Manual) \n" << G4endl;
402} 
403
404G4ThreeVector G4PhotoElectricAngularGeneratorPolarized::SetPerpendicularVector(const G4ThreeVector& a) const
405{
406  G4double dx = a.x();
407  G4double dy = a.y();
408  G4double dz = a.z();
409  G4double x = dx < 0.0 ? -dx : dx;
410  G4double y = dy < 0.0 ? -dy : dy;
411  G4double z = dz < 0.0 ? -dz : dz;
412  if (x < y) {
413    return x < z ? G4ThreeVector(-dy,dx,0) : G4ThreeVector(0,-dz,dy);
414  }else{
415    return y < z ? G4ThreeVector(dz,0,-dx) : G4ThreeVector(-dy,dx,0);
416  }
417}
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