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26 //
27 // -------------------------------------------------------------------
28 //
29 // GEANT4 Class file
30 //
31 //
32 // File name: G4RDPhotoElectricAngularGeneratorPolarized
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 (G4RDGenerator2BN, 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 "G4RDPhotoElectricAngularGeneratorPolarized.hh"
65 #include "G4RotationMatrix.hh"
66 #include "Randomize.hh"
67 #include "G4PhysicalConstants.hh"
68
69 //
70
71 G4RDPhotoElectricAngularGeneratorPolarized::G4RDPhotoElectricAngularGeneratorPolarized(const G4String& name):G4RDVPhotoElectricAngularDistribution(name)
72 {
73 const G4int arrayDim = 980;
74
75 //minimum electron beta parameter allowed
76 betaArray[0] = 0.02;
77 //beta step
78 betaArray[1] = 0.001;
79 //maximum index array for a and c tables
80 betaArray[2] = arrayDim - 1;
81
82 // read Majorant Surface Parameters. This are required in order to generate Gavrila angular photoelectron distribution
83 for(G4int level = 0; level < 2; level++){
84
85 char nameChar0[100] = "ftab0.dat"; // K-shell Majorant Surface Parameters
86 char nameChar1[100] = "ftab1.dat"; // L-shell Majorant Surface Parameters
87
88 G4String filename;
89 if(level == 0) filename = nameChar0;
90 if(level == 1) filename = nameChar1;
91
92 const char* path = G4FindDataDir("G4LEDATA");
93 if (!path)
94 {
95 G4String excep = "G4LEDATA environment variable not set!";
96 G4Exception("G4RDPhotoElectricAngularGeneratorPolarized()",
97 "InvalidSetup", FatalException, excep);
98 }
99
100 G4String pathString(path);
101 G4String dirFile = pathString + "/photoelectric_angular/" + filename;
102 FILE *infile;
103 infile = fopen(dirFile,"r");
104 if (infile == 0)
105 {
106 G4String excep = "Data file: " + dirFile + " not found";
107 G4Exception("G4RDPhotoElectricAngularGeneratorPolarized()",
108 "DataNotFound", FatalException, excep);
109 }
110
111 // Read parameters into tables. The parameters are function of incident electron energy and shell level
112 G4float aRead,cRead, beta;
113 for(G4int i=0 ; i<arrayDim ;i++){
114 fscanf(infile,"%f\t %e\t %e",&beta,&aRead,&cRead);
115 aMajorantSurfaceParameterTable[i][level] = aRead;
116 cMajorantSurfaceParameterTable[i][level] = cRead;
117 }
118 fclose(infile);
119
120 }
121 }
122
123 //
124
125 G4RDPhotoElectricAngularGeneratorPolarized::~G4RDPhotoElectricAngularGeneratorPolarized()
126 {;}
127
128 //
129
130 G4ThreeVector G4RDPhotoElectricAngularGeneratorPolarized::GetPhotoElectronDirection(const G4ThreeVector& direction, const G4double eKineticEnergy,
131 const G4ThreeVector& polarization, const G4int shellId) const
132 {
133 // Calculate Lorentz term (gamma) and beta parameters
134 G4double gamma = 1. + eKineticEnergy/electron_mass_c2;
135 G4double beta = std::sqrt(gamma*gamma-1.)/gamma;
136
137 G4double theta, phi = 0;
138 G4double aBeta = 0; // Majorant surface parameter (function of the outgoing electron kinetic energy)
139 G4double cBeta = 0; // Majorant surface parameter (function of the outgoing electron kinetic energy)
140
141 G4int shellLevel = 0;
142 if(shellId < 2) shellLevel = 0; // K-shell // Polarized model for K-shell
143 if(shellId >= 2) shellLevel = 1; // L1-shell // Polarized model for L1 and higher shells
144
145 // For the outgoing kinetic energy find the current majorant surface parameters
146 PhotoElectronGetMajorantSurfaceAandCParameters( shellLevel, beta, &aBeta, &cBeta);
147
148 // Generate pho and theta according to the shell level and beta parameter of the electron
149 PhotoElectronGeneratePhiAndTheta(shellLevel, beta, aBeta, cBeta, &phi, &theta);
150
151 // Determine the rotation matrix
152 G4RotationMatrix rotation = PhotoElectronRotationMatrix(direction, polarization);
153
154 // Compute final direction of the outgoing electron
155 G4ThreeVector final_direction = PhotoElectronComputeFinalDirection(rotation, theta, phi);
156
157 return final_direction;
158 }
159
160 //
161
162 void G4RDPhotoElectricAngularGeneratorPolarized::PhotoElectronGeneratePhiAndTheta(const G4int shellLevel, const G4double beta,
163 const G4double aBeta, const G4double cBeta,
164 G4double *pphi, G4double *ptheta) const
165 {
166 G4double rand1, rand2, rand3 = 0;
167 G4double phi = 0;
168 G4double theta = 0;
169 G4double crossSectionValue = 0;
170 G4double crossSectionMajorantFunctionValue = 0;
171 G4double maxBeta = 0;
172
173 do {
174
175 rand1 = G4UniformRand();
176 rand2 = G4UniformRand();
177 rand3 = G4UniformRand();
178
179 phi=2*pi*rand1;
180
181 if(shellLevel == 0){
182
183 // Polarized Gavrila Cross-Section for K-shell (1959)
184 theta=std::sqrt(((std::exp(rand2*std::log(1+cBeta*pi*pi)))-1)/cBeta);
185 crossSectionMajorantFunctionValue = CrossSectionMajorantFunction(theta, cBeta);
186 crossSectionValue = DSigmaKshellGavrila1959(beta, theta, phi);
187
188 } else {
189
190 // Polarized Gavrila Cross-Section for other shells (L1-shell) (1961)
191 theta = std::sqrt(((std::exp(rand2*std::log(1+cBeta*pi*pi)))-1)/cBeta);
192 crossSectionMajorantFunctionValue = CrossSectionMajorantFunction(theta, cBeta);
193 crossSectionValue = DSigmaL1shellGavrila(beta, theta, phi);
194
195 }
196
197 maxBeta=rand3*aBeta*crossSectionMajorantFunctionValue;
198
199 }while(maxBeta > crossSectionValue);
200
201 *pphi = phi;
202 *ptheta = theta;
203 }
204
205 //
206
207 G4double G4RDPhotoElectricAngularGeneratorPolarized::CrossSectionMajorantFunction(const G4double theta, const G4double cBeta) const
208 {
209 // Compute Majorant Function
210 G4double crossSectionMajorantFunctionValue = 0;
211 crossSectionMajorantFunctionValue = theta/(1+cBeta*theta*theta);
212 return crossSectionMajorantFunctionValue;
213 }
214
215 //
216
217 G4double G4RDPhotoElectricAngularGeneratorPolarized::DSigmaKshellGavrila1959(const G4double beta, const G4double theta, const G4double phi) const
218 {
219
220 //Double differential K shell cross-section (Gavrila 1959)
221
222 G4double beta2 = beta*beta;
223 G4double oneBeta2 = 1 - beta2;
224 G4double sqrtOneBeta2 = std::sqrt(oneBeta2);
225 G4double oneBeta2_to_3_2 = std::pow(oneBeta2,1.5);
226 G4double cosTheta = std::cos(theta);
227 G4double sinTheta2 = std::sin(theta)*std::sin(theta);
228 G4double cosPhi2 = std::cos(phi)*std::cos(phi);
229 G4double oneBetaCosTheta = 1-beta*cosTheta;
230 G4double dsigma = 0;
231 G4double firstTerm = 0;
232 G4double secondTerm = 0;
233
234 firstTerm = sinTheta2*cosPhi2/std::pow(oneBetaCosTheta,4)-(1 - sqrtOneBeta2)/(2*oneBeta2) *
235 (sinTheta2 * cosPhi2)/std::pow(oneBetaCosTheta,3) + (1-sqrtOneBeta2)*
236 (1-sqrtOneBeta2)/(4*oneBeta2_to_3_2) * sinTheta2/std::pow(oneBetaCosTheta,3);
237
238 secondTerm = std::sqrt(1 - sqrtOneBeta2)/(std::pow(2.,3.5)*beta2*std::pow(oneBetaCosTheta,2.5)) *
239 (4*beta2/sqrtOneBeta2 * sinTheta2*cosPhi2/oneBetaCosTheta + 4*beta/oneBeta2 * cosTheta * cosPhi2
240 - 4*(1-sqrtOneBeta2)/oneBeta2 *(1+cosPhi2) - beta2 * (1-sqrtOneBeta2)/oneBeta2 * sinTheta2/oneBetaCosTheta
241 + 4*beta2*(1-sqrtOneBeta2)/oneBeta2_to_3_2 - 4*beta*(1-sqrtOneBeta2)*(1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta)
242 + (1-sqrtOneBeta2)/(4*beta2*oneBetaCosTheta*oneBetaCosTheta) * (beta/oneBeta2 - 2/oneBeta2 * cosTheta * cosPhi2 +
243 (1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta - beta * (1-sqrtOneBeta2)/oneBeta2_to_3_2);
244
245 dsigma = ( firstTerm*(1-pi*fine_structure_const/beta) + secondTerm*(pi*fine_structure_const) );
246
247 return dsigma;
248 }
249
250 //
251
252 G4double G4RDPhotoElectricAngularGeneratorPolarized::DSigmaL1shellGavrila(const G4double beta, const G4double theta, const G4double phi) const
253 {
254
255 //Double differential L1 shell cross-section (Gavrila 1961)
256
257 G4double beta2 = beta*beta;
258 G4double oneBeta2 = 1-beta2;
259 G4double sqrtOneBeta2 = std::sqrt(oneBeta2);
260 G4double oneBeta2_to_3_2=std::pow(oneBeta2,1.5);
261 G4double cosTheta = std::cos(theta);
262 G4double sinTheta2 =std::sin(theta)*std::sin(theta);
263 G4double cosPhi2 = std::cos(phi)*std::cos(phi);
264 G4double oneBetaCosTheta = 1-beta*cosTheta;
265
266 G4double dsigma = 0;
267 G4double firstTerm = 0;
268 G4double secondTerm = 0;
269
270 firstTerm = sinTheta2*cosPhi2/std::pow(oneBetaCosTheta,4)-(1 - sqrtOneBeta2)/(2*oneBeta2)
271 * (sinTheta2 * cosPhi2)/std::pow(oneBetaCosTheta,3) + (1-sqrtOneBeta2)*
272 (1-sqrtOneBeta2)/(4*oneBeta2_to_3_2) * sinTheta2/std::pow(oneBetaCosTheta,3);
273
274 secondTerm = std::sqrt(1 - sqrtOneBeta2)/(std::pow(2.,3.5)*beta2*std::pow(oneBetaCosTheta,2.5)) *
275 (4*beta2/sqrtOneBeta2 * sinTheta2*cosPhi2/oneBetaCosTheta + 4*beta/oneBeta2 * cosTheta * cosPhi2
276 - 4*(1-sqrtOneBeta2)/oneBeta2 *(1+cosPhi2) - beta2 * (1-sqrtOneBeta2)/oneBeta2 * sinTheta2/oneBetaCosTheta
277 + 4*beta2*(1-sqrtOneBeta2)/oneBeta2_to_3_2 - 4*beta*(1-sqrtOneBeta2)*(1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta)
278 + (1-sqrtOneBeta2)/(4*beta2*oneBetaCosTheta*oneBetaCosTheta) * (beta/oneBeta2 - 2/oneBeta2 * cosTheta * cosPhi2 +
279 (1-sqrtOneBeta2)/oneBeta2_to_3_2*cosTheta - beta*(1-sqrtOneBeta2)/oneBeta2_to_3_2);
280
281 dsigma = ( firstTerm*(1-pi*fine_structure_const/beta) + secondTerm*(pi*fine_structure_const) );
282
283 return dsigma;
284 }
285
286 G4double G4RDPhotoElectricAngularGeneratorPolarized::GetMax(const G4double arg1, const G4double arg2) const
287 {
288 if (arg1 > arg2)
289 return arg1;
290 else
291 return arg2;
292 }
293
294 //
295
296 G4RotationMatrix G4RDPhotoElectricAngularGeneratorPolarized::PhotoElectronRotationMatrix(const G4ThreeVector& direction,
297 const G4ThreeVector& polarization) const
298 {
299 G4double mK = direction.mag();
300 G4double mS = polarization.mag();
301 G4ThreeVector polarization2 = polarization;
302 const G4double kTolerance = 1e-6;
303
304 if(!(polarization.isOrthogonal(direction,kTolerance)) || mS == 0){
305 G4ThreeVector d0 = direction.unit();
306 G4ThreeVector a1 = SetPerpendicularVector(d0);
307 G4ThreeVector a0 = a1.unit();
308 G4double rand1 = G4UniformRand();
309 G4double angle = twopi*rand1;
310 G4ThreeVector b0 = d0.cross(a0);
311 G4ThreeVector c;
312 c.setX(std::cos(angle)*(a0.x())+std::sin(angle)*b0.x());
313 c.setY(std::cos(angle)*(a0.y())+std::sin(angle)*b0.y());
314 c.setZ(std::cos(angle)*(a0.z())+std::sin(angle)*b0.z());
315 polarization2 = c.unit();
316 mS = polarization2.mag();
317 }else
318 {
319 if ( polarization.howOrthogonal(direction) != 0)
320 {
321 polarization2 = polarization - polarization.dot(direction)/direction.dot(direction) * direction;
322 }
323 }
324
325 G4ThreeVector direction2 = direction/mK;
326 polarization2 = polarization2/mS;
327
328 G4ThreeVector y = direction2.cross(polarization2);
329
330 G4RotationMatrix R(polarization2,y,direction2);
331 return R;
332 }
333
334 void G4RDPhotoElectricAngularGeneratorPolarized::PhotoElectronGetMajorantSurfaceAandCParameters(const G4int shellLevel, const G4double beta,G4double *majorantSurfaceParameterA, G4double *majorantSurfaceParameterC) const
335 {
336 // This member function finds for a given shell and beta value of the outgoing electron the correct Majorant Surface parameters
337
338 G4double aBeta,cBeta;
339 G4double bMin,bStep;
340 G4int indexMax;
341 G4int level = shellLevel;
342 if(shellLevel > 1) level = 1; // protection since only K and L1 polarized double differential cross-sections were implemented
343
344 bMin = betaArray[0];
345 bStep = betaArray[1];
346 indexMax = (G4int)betaArray[2];
347 const G4double kBias = 1e-9;
348
349 G4int k = (G4int)((beta-bMin+kBias)/bStep);
350
351 if(k < 0)
352 k = 0;
353 if(k > indexMax)
354 k = indexMax;
355
356 if(k == 0)
357 aBeta = GetMax(aMajorantSurfaceParameterTable[k][level],aMajorantSurfaceParameterTable[k+1][level]);
358 else if(k==indexMax)
359 aBeta = GetMax(aMajorantSurfaceParameterTable[k-1][level],aMajorantSurfaceParameterTable[k][level]);
360 else{
361 aBeta = GetMax(aMajorantSurfaceParameterTable[k-1][level],aMajorantSurfaceParameterTable[k][level]);
362 aBeta = GetMax(aBeta,aMajorantSurfaceParameterTable[k+1][level]);
363 }
364
365 if(k == 0)
366 cBeta = GetMax(cMajorantSurfaceParameterTable[k][level],cMajorantSurfaceParameterTable[k+1][level]);
367 else if(k == indexMax)
368 cBeta = GetMax(cMajorantSurfaceParameterTable[k-1][level],cMajorantSurfaceParameterTable[k][level]);
369 else{
370 cBeta = GetMax(cMajorantSurfaceParameterTable[k-1][level],cMajorantSurfaceParameterTable[k][level]);
371 cBeta = GetMax(cBeta,cMajorantSurfaceParameterTable[k+1][level]);
372 }
373
374 *majorantSurfaceParameterA = aBeta;
375 *majorantSurfaceParameterC = cBeta;
376
377 }
378
379
380 //
381 G4ThreeVector G4RDPhotoElectricAngularGeneratorPolarized::PhotoElectronComputeFinalDirection(const G4RotationMatrix& rotation, const G4double theta, const G4double phi) const
382 {
383
384 //computes the photoelectron momentum unitary vector
385 G4double px = std::cos(phi)*std::sin(theta);
386 G4double py = std::sin(phi)*std::sin(theta);
387 G4double pz = std::cos(theta);
388
389 G4ThreeVector samplingDirection(px,py,pz);
390
391 G4ThreeVector outgoingDirection = rotation*samplingDirection;
392 return outgoingDirection;
393 }
394
395 //
396
397 void G4RDPhotoElectricAngularGeneratorPolarized::PrintGeneratorInformation() const
398 {
399 G4cout << "\n" << G4endl;
400 G4cout << "Polarized Photoelectric Angular Generator" << G4endl;
401 G4cout << "PhotoElectric Electron Angular Generator based on the general Gavrila photoelectron angular distribution" << G4endl;
402 G4cout << "Includes polarization effects for K and L1 atomic shells, according to Gavrilla (1959, 1961)." << G4endl;
403 G4cout << "For higher shells the L1 cross-section is used." << G4endl;
404 G4cout << "(see Physics Reference Manual) \n" << G4endl;
405 }
406
407 G4ThreeVector G4RDPhotoElectricAngularGeneratorPolarized::SetPerpendicularVector(const G4ThreeVector& a) const
408 {
409 G4double dx = a.x();
410 G4double dy = a.y();
411 G4double dz = a.z();
412 G4double x = dx < 0.0 ? -dx : dx;
413 G4double y = dy < 0.0 ? -dy : dy;
414 G4double z = dz < 0.0 ? -dz : dz;
415 if (x < y) {
416 return x < z ? G4ThreeVector(-dy,dx,0) : G4ThreeVector(0,-dz,dy);
417 }else{
418 return y < z ? G4ThreeVector(dz,0,-dx) : G4ThreeVector(-dy,dx,0);
419 }
420 }
421