Geant4-11
Functions | Variables
nf_angularMomentumCoupling.cc File Reference
#include <stdlib.h>
#include <cmath>
#include "nf_specialFunctions.h"

Go to the source code of this file.

Functions

static double cg1 (int, int, int)
 
static double cg2 (int, int, int, int, int, int, int, int)
 
static double cg3 (int, int, int, int, int, int)
 
static int max3 (int a, int b, int c)
 
static int max4 (int a, int b, int c, int d)
 
static int min3 (int a, int b, int c)
 
double nf_amc_clebsh_gordan (int j1, int j2, int m1, int m2, int j3)
 
double nf_amc_factorial (int n)
 
double nf_amc_log_factorial (int n)
 
double nf_amc_racah (int j1, int j2, int l2, int l1, int j3, int l3)
 
double nf_amc_reduced_matrix_element (int lt, int st, int jt, int l0, int j0, int l1, int j1)
 
double nf_amc_wigner_3j (int j1, int j2, int j3, int j4, int j5, int j6)
 
double nf_amc_wigner_6j (int j1, int j2, int j3, int j4, int j5, int j6)
 
double nf_amc_wigner_9j (int j1, int j2, int j3, int j4, int j5, int j6, int j7, int j8, int j9)
 
double nf_amc_z_coefficient (int l1, int j1, int l2, int j2, int s, int ll)
 
double nf_amc_zbar_coefficient (int l1, int j1, int l2, int j2, int s, int ll)
 
static int parity (int x)
 
static double w6j0 (int, int *)
 
static double w6j1 (int *)
 

Variables

static const int MAX_FACTORIAL = 200
 
static const double nf_amc_log_fact [] = {0.0, 0.0, 0.69314718056, 1.79175946923, 3.17805383035, 4.78749174278, 6.57925121201, 8.52516136107, 10.6046029027, 12.8018274801, 15.1044125731, 17.5023078459, 19.9872144957, 22.5521638531, 25.1912211827, 27.8992713838, 30.6718601061, 33.5050734501, 36.395445208, 39.3398841872, 42.3356164608, 45.3801388985, 48.4711813518, 51.6066755678, 54.7847293981, 58.003605223, 61.261701761, 64.557538627, 67.8897431372, 71.2570389672, 74.6582363488, 78.0922235533, 81.5579594561, 85.0544670176, 88.5808275422, 92.1361756037, 95.7196945421, 99.3306124548, 102.968198615, 106.631760261, 110.320639715, 114.034211781, 117.7718814, 121.533081515, 125.317271149, 129.123933639, 132.952575036, 136.802722637, 140.673923648, 144.565743946, 148.477766952, 152.409592584, 156.360836303, 160.331128217, 164.320112263, 168.327445448, 172.352797139, 176.395848407, 180.456291418, 184.533828861, 188.628173424, 192.739047288, 196.866181673, 201.009316399, 205.168199483, 209.342586753, 213.532241495, 217.736934114, 221.956441819, 226.190548324, 230.439043566, 234.701723443, 238.978389562, 243.268849003, 247.572914096, 251.89040221, 256.22113555, 260.564940972, 264.921649799, 269.291097651, 273.673124286, 278.06757344, 282.474292688, 286.893133295, 291.323950094, 295.766601351, 300.220948647, 304.686856766, 309.16419358, 313.65282995, 318.15263962, 322.663499127, 327.185287704, 331.717887197, 336.261181979, 340.815058871, 345.379407062, 349.954118041, 354.539085519, 359.13420537, 363.739375556, 368.354496072, 372.979468886, 377.614197874, 382.258588773, 386.912549123, 391.575988217, 396.248817052, 400.930948279, 405.622296161, 410.322776527, 415.032306728, 419.7508056, 424.478193418, 429.214391867, 433.959323995, 438.712914186, 443.475088121, 448.245772745, 453.024896238, 457.812387981, 462.608178527, 467.412199572, 472.224383927, 477.044665493, 481.87297923, 486.709261137, 491.553448223, 496.405478487, 501.265290892, 506.132825342, 511.008022665, 515.890824588, 520.781173716, 525.679013516, 530.584288294, 535.49694318, 540.416924106, 545.344177791, 550.278651724, 555.220294147, 560.169054037, 565.124881095, 570.087725725, 575.057539025, 580.034272767, 585.017879389, 590.008311976, 595.005524249, 600.009470555, 605.020105849, 610.037385686, 615.061266207, 620.091704128, 625.128656731, 630.172081848, 635.221937855, 640.27818366, 645.340778693, 650.409682896, 655.484856711, 660.566261076, 665.653857411, 670.747607612, 675.84747404, 680.953419514, 686.065407302, 691.183401114, 696.307365094, 701.437263809, 706.573062246, 711.714725802, 716.862220279, 722.015511874, 727.174567173, 732.339353147, 737.509837142, 742.685986874, 747.867770425, 753.05515623, 758.248113081, 763.446610113, 768.6506168, 773.860102953, 779.07503871, 784.295394535, 789.521141209, 794.752249826, 799.988691789, 805.230438804, 810.477462876, 815.729736304, 820.987231676, 826.249921865, 831.517780024, 836.790779582, 842.068894242, 847.35209797, 852.640365001, 857.933669826, 863.231987192}
 

Function Documentation

◆ cg1()

static double cg1 ( int  x1,
int  x2,
int  x3 
)
static

Definition at line 339 of file nf_angularMomentumCoupling.cc.

339 {
340
341 int p1, p2, p3, p4, q1, q2, q3, q4;
342 double a;
343
344 p1 = x1 + x2 + x3 - 1; if ( ( p1 % 2 ) != 0 ) return( 0.0 );
345 p2 = x1 + x2 - x3;
346 p3 =-x1 + x2 + x3;
347 p4 = x1 - x2 + x3;
348 if ( p2 <= 0 || p3 <= 0 || p4 <= 0 ) return( 0.0 );
349 if ( p1 >= MAX_FACTORIAL ) return( INFINITY );
350
351 q1 = ( p1 + 1 ) / 2 - 1; p1--;
352 q2 = ( p2 + 1 ) / 2 - 1; p2--;
353 q3 = ( p3 + 1 ) / 2 - 1; p3--;
354 q4 = ( p4 + 1 ) / 2 - 1; p4--;
355
356 a = nf_amc_log_fact[q1]-( nf_amc_log_fact[q2] + nf_amc_log_fact[q3] + nf_amc_log_fact[q4] )
357 + 0.5 * ( nf_amc_log_fact[ 2 * x3 - 1 ] - nf_amc_log_fact[ 2 * x3 - 2 ]
358 + nf_amc_log_fact[p2] + nf_amc_log_fact[p3] + nf_amc_log_fact[p4] - nf_amc_log_fact[p1] );
359
360 return( ( ( ( q1 + x1 - x2 ) % 2 == 0 ) ? 1.0 : -1.0 ) * G4Exp( a ) );
361}
G4Exp
G4double G4Exp(G4double initial_x)
Exponential Function double precision.
Definition: G4Exp.hh:179
nf_amc_log_fact
static const double nf_amc_log_fact[]
Definition: nf_angularMomentumCoupling.cc:70
MAX_FACTORIAL
static const int MAX_FACTORIAL
Definition: nf_angularMomentumCoupling.cc:68

References G4Exp(), MAX_FACTORIAL, and nf_amc_log_fact.

Referenced by nf_amc_clebsh_gordan().

◆ cg2()

static double cg2 ( int  k,
int  q0,
int  z1,
int  z2,
int  w1,
int  w2,
int  w3,
int  mm 
)
static

Definition at line 365 of file nf_angularMomentumCoupling.cc.

365 {
366
367 int q1, q2, q3, q4, p1, p2, p3, p4;
368 double a;
369
370 p1 = z1 + q0 + 2;
371 p2 = z1 - q0 + 1;
372 p3 = z2 + q0 + 1;
373 p4 = -z2 + q0 + 1;
374 if ( p2 <= 0 || p3 <= 0 || p4 <= 0) return( 0.0 );
375 if ( p1 >= MAX_FACTORIAL ) return( INFINITY );
376
377 q1 = ( p1 + 1 ) / 2 - 1; p1--;
378 q2 = ( p2 + 1 ) / 2 - 1; p2--;
379 q3 = ( p3 + 1 ) / 2 - 1; p3--;
380 q4 = ( p4 + 1 ) / 2 - 1; p4--;
381
382 a = nf_amc_log_fact[q1] - ( nf_amc_log_fact[ q2 ] + nf_amc_log_fact[ q3 ] + nf_amc_log_fact[ q4 ] )
383 + 0.5 * ( nf_amc_log_fact[ w3 + 1 ] - nf_amc_log_fact[ w3 ]
384 + nf_amc_log_fact[ w1 ] - nf_amc_log_fact[ w1 + 1 ]
385 + nf_amc_log_fact[ w2 ] - nf_amc_log_fact[ w2 + 1 ]
386 + nf_amc_log_fact[ p2 ] + nf_amc_log_fact[ p3 ] + nf_amc_log_fact[ p4 ] - nf_amc_log_fact[ p1 ] );
387
388 return( ( ( ( q4 + k + ( mm > 0 ) * ( p1 + 2 ) ) % 2 == 0 ) ? -1.0 : 1.0 ) * 2.0 * G4Exp( a ) );
389}
mm
static constexpr double mm
Definition: G4SIunits.hh:95

References G4Exp(), MAX_FACTORIAL, mm, and nf_amc_log_fact.

Referenced by nf_amc_clebsh_gordan().

◆ cg3()

static double cg3 ( int  x1,
int  x2,
int  x3,
int  y1,
int  y2,
int  y3 
)
static

Definition at line 393 of file nf_angularMomentumCoupling.cc.

393 {
394
395 int nx, i, k1, k2, q1, q2, q3, q4, p1, p2, p3, z1, z2, z3;
396 double a, cg;
397
398 nx = x1 + x2 + x3 - 1;
399 if ( ( z1 = nx - x1 - y1 ) < 0 ) return( 0.0 );
400 if ( ( z2 = nx - x2 - y2 ) < 0 ) return( 0.0 );
401 if ( ( z3 = nx - x3 - y3 ) < 0 ) return( 0.0 );
402
403 k1 = x2 - y3;
404 k2 = y1 - x3;
405
406 q1 = max3( k1, k2, 0 );
407 q2 = min3( y1, x2, z3 + 1 ) - 1;
408 q3 = q1 - k1;
409 q4 = q1 - k2;
410
411 p1 = y1 - q1 - 1;
412 p2 = x2 - q1 - 1;
413 p3 = z3 - q1;
414
415 a = cg = G4Exp( 0.5 * ( nf_amc_log_fact[ x3 + y3 - 1 ] - nf_amc_log_fact[ x3 + y3 - 2 ] - nf_amc_log_fact[ nx - 1 ]
416 + nf_amc_log_fact[ z1 ] + nf_amc_log_fact[ z2 ] + nf_amc_log_fact[ z3 ]
417 + nf_amc_log_fact[ x1 - 1 ] + nf_amc_log_fact[ x2 - 1 ] + nf_amc_log_fact[ x3 - 1 ]
418 + nf_amc_log_fact[ y1 - 1 ] + nf_amc_log_fact[ y2 - 1 ] + nf_amc_log_fact[ y3 - 1 ] )
419 - nf_amc_log_fact[ p1 ] - nf_amc_log_fact[ p2 ] - nf_amc_log_fact[ p3 ]
420 - nf_amc_log_fact[ q1 ] - nf_amc_log_fact[ q3 ] - nf_amc_log_fact[ q4 ] ) * ( ( ( q1 % 2 ) == 0 ) ? 1 : -1 );
421 if( cg == INFINITY ) return( INFINITY );
422
423 if ( q1 != q2 ){
424 q3 = q2 - k1;
425 q4 = q2 - k2;
426 p1 = y1 - q2;
427 p2 = x2 - q2;
428 p3 = z3 - q2 + 1;
429 for( i = 0; i < ( q2 - q1 ); i++ )
430 cg = a - cg * ( ( p1 + i ) * ( p2 + i ) * ( p3 + i ) ) / ( ( q2 - i ) * ( q3 - i ) * ( q4 - i ) );
431 }
432 return( cg );
433}
min3
static int min3(int a, int b, int c)
Definition: nf_angularMomentumCoupling.cc:549
max3
static int max3(int a, int b, int c)
Definition: nf_angularMomentumCoupling.cc:530

References G4Exp(), max3(), min3(), and nf_amc_log_fact.

Referenced by nf_amc_clebsh_gordan().

◆ max3()

static int max3 ( int  a,
int  b,
int  c 
)
static

Definition at line 530 of file nf_angularMomentumCoupling.cc.

530 {
531
532 if( a < b ) a = b;
533 if( a < c ) a = c;
534 return( a );
535}

Referenced by cg3(), and nf_amc_wigner_9j().

◆ max4()

static int max4 ( int  a,
int  b,
int  c,
int  d 
)
static

Definition at line 539 of file nf_angularMomentumCoupling.cc.

539 {
540
541 if( a < b ) a = b;
542 if( a < c ) a = c;
543 if( a < d ) a = d;
544 return( a );
545}

Referenced by w6j1().

◆ min3()

static int min3 ( int  a,
int  b,
int  c 
)
static

Definition at line 549 of file nf_angularMomentumCoupling.cc.

549 {
550
551 if( a > b ) a = b;
552 if( a > c ) a = c;
553 return( a );
554}

Referenced by cg3(), nf_amc_wigner_9j(), w6j1(), and XmlUtf8Encode().

◆ nf_amc_clebsh_gordan()

double nf_amc_clebsh_gordan ( int  j1,
int  j2,
int  m1,
int  m2,
int  j3 
)

Definition at line 288 of file nf_angularMomentumCoupling.cc.

288 {
289/*
290* Clebsh-Gordan coefficient
291* = <j1,j2,m1,m2|j3,m1+m2>
292* = (-)^(j1-j2+m1+m2) * std::sqrt(2*j3+1) * / j1 j2 j3 \
293* \ m1 m2 -m1-m2 /
294*
295* Note: Last value m3 is preset to m1+m2. Any other value will evaluate to 0.0.
296*/
297
298 int m3, x1, x2, x3, y1, y2, y3;
299 double cg = 0.0;
300
301 if ( j1 < 0 || j2 < 0 || j3 < 0) return( 0.0 );
302 if ( j1 + j2 + j3 > 2 * MAX_FACTORIAL ) return( INFINITY );
303
304 m3 = m1 + m2;
305
306 if ( ( x1 = ( j1 + m1 ) / 2 + 1 ) <= 0 ) return( 0.0 );
307 if ( ( x2 = ( j2 + m2 ) / 2 + 1 ) <= 0 ) return( 0.0 );
308 if ( ( x3 = ( j3 - m3 ) / 2 + 1 ) <= 0 ) return( 0.0 );
309
310 if ( ( y1 = x1 - m1 ) <= 0 ) return( 0.0 );
311 if ( ( y2 = x2 - m2 ) <= 0 ) return( 0.0 );
312 if ( ( y3 = x3 + m3 ) <= 0 ) return( 0.0 );
313
314 if ( j3 == 0 ){
315 if ( j1 == j2 ) cg = ( 1.0 / std::sqrt( (double)j1 + 1.0 ) * ( ( y1 % 2 == 0 ) ? -1:1 ) );
316 }
317 else if ( (j1 == 0 || j2 == 0 ) ){
318 if ( ( j1 + j2 ) == j3 ) cg = 1.0;
319 }
320 else {
321 if( m3 == 0 && std::abs( m1 ) <= 1 ){
322 if( m1 == 0 ) cg = cg1( x1, x2, x3 );
323 else cg = cg2( x1 + y1 - y2, x3 - 1, x1 + x2 - 2, x1 - y2, j1, j2, j3, m2 );
324 }
325 else if ( m2 == 0 && std::abs( m1 ) <=1 ){
326 cg = cg2( x1 - y2 + y3, x2 - 1, x1 + x3 - 2, x3 - y1, j1, j3, j3, m1 );
327 }
328 else if ( m1 == 0 && std::abs( m3 ) <= 1 ){
329 cg = cg2( x1, x1 - 1, x2 + x3 - 2, x2 - y3, j2, j3, j3, -m3 );
330 }
331 else cg = cg3( x1, x2, x3, y1, y2, y3 );
332 }
333
334 return( cg );
335}
m3
static constexpr double m3
Definition: G4SIunits.hh:111
m2
static constexpr double m2
Definition: G4SIunits.hh:110
cg2
static double cg2(int, int, int, int, int, int, int, int)
Definition: nf_angularMomentumCoupling.cc:365
cg1
static double cg1(int, int, int)
Definition: nf_angularMomentumCoupling.cc:339
cg3
static double cg3(int, int, int, int, int, int)
Definition: nf_angularMomentumCoupling.cc:393

References cg1(), cg2(), cg3(), m2, m3, and MAX_FACTORIAL.

Referenced by nf_amc_reduced_matrix_element(), nf_amc_wigner_3j(), nf_amc_z_coefficient(), and nf_amc_zbar_coefficient().

◆ nf_amc_factorial()

double nf_amc_factorial ( int  n)

Definition at line 96 of file nf_angularMomentumCoupling.cc.

96 {
97/*
98* returns n! for pre-computed table. INFINITY is return if n is negative or too large.
99*/
100 return G4Exp( nf_amc_log_factorial( n ) );
101}
nf_amc_log_factorial
double nf_amc_log_factorial(int n)
Definition: nf_angularMomentumCoupling.cc:85

References G4Exp(), CLHEP::detail::n, and nf_amc_log_factorial().

◆ nf_amc_log_factorial()

double nf_amc_log_factorial ( int  n)

Definition at line 85 of file nf_angularMomentumCoupling.cc.

85 {
86/*
87* returns ln( n! ).
88*/
89 if( n > MAX_FACTORIAL ) return( INFINITY );
90 if( n < 0 ) return( INFINITY );
91 return nf_amc_log_fact[n];
92}

References MAX_FACTORIAL, CLHEP::detail::n, and nf_amc_log_fact.

Referenced by nf_amc_factorial().

◆ nf_amc_racah()

double nf_amc_racah ( int  j1,
int  j2,
int  l2,
int  l1,
int  j3,
int  l3 
)

Definition at line 253 of file nf_angularMomentumCoupling.cc.

253 {
254/*
255* Racah coefficient definition in Edmonds (AR Edmonds, "Angular Momentum in Quantum Mechanics", Princeton (1980) is
256* W(j1, j2, l2, l1 ; j3, l3) = (-1)^(j1+j2+l1+l2) * { j1 j2 j3 }
257* { l1 l2 l3 }
258* The call signature of W(...) appears jumbled, but hey, that's the convention.
259*
260* This convention is exactly that used by Blatt-Biedenharn (Rev. Mod. Phys. 24, 258 (1952)) too
261*/
262
263 double sig;
264
265 sig = ( ( ( j1 + j2 + l1 + l2 ) % 4 == 0 ) ? 1.0 : -1.0 );
266 return sig * nf_amc_wigner_6j( j1, j2, j3, l1, l2, l3 );
267}
nf_amc_wigner_6j
double nf_amc_wigner_6j(int j1, int j2, int j3, int j4, int j5, int j6)
Definition: nf_angularMomentumCoupling.cc:121

References nf_amc_wigner_6j().

Referenced by nf_amc_wigner_9j(), nf_amc_z_coefficient(), and nf_amc_zbar_coefficient().

◆ nf_amc_reduced_matrix_element()

double nf_amc_reduced_matrix_element ( int  lt,
int  st,
int  jt,
int  l0,
int  j0,
int  l1,
int  j1 
)

Definition at line 473 of file nf_angularMomentumCoupling.cc.

473 {
474/*
475* Reduced Matrix Element for Tensor Operator
476* = < l1j1 || T(YL,sigma_S)J || l0j0 >
477*
478* M.B.Johnson, L.W.Owen, G.R.Satchler
479* Phys. Rev. 142, 748 (1966)
480* Note: definition differs from JOS by the factor sqrt(2j1+1)
481*/
482 int llt;
483 double x1, x2, x3, reduced_mat, clebsh_gordan;
484
485 if ( parity( lt ) != parity( l0 ) * parity( l1 ) ) return( 0.0 );
486 if ( std::abs( l0 - l1 ) > lt || ( l0 + l1 ) < lt ) return( 0.0 );
487 if ( std::abs( ( j0 - j1 ) / 2 ) > jt || ( ( j0 + j1 ) / 2 ) < jt ) return( 0.0 );
488
489 llt = 2 * lt;
490 jt *= 2;
491 st *= 2;
492
493 if( ( clebsh_gordan = nf_amc_clebsh_gordan( j1, j0, 1, -1, jt ) ) == INFINITY ) return( INFINITY );
494
495 reduced_mat = 1.0 / std::sqrt( 4 * M_PI ) * clebsh_gordan / std::sqrt( jt + 1.0 ) /* BRB jt + 1 <= 0? */
496 * std::sqrt( ( j0 + 1.0 ) * ( j1 + 1.0 ) * ( llt + 1.0 ) )
497 * parity( ( j1 - j0 ) / 2 ) * parity( ( -l0 + l1 + lt ) / 2 ) * parity( ( j0 - 1 ) / 2 );
498
499 if( st == 2 ){
500 x1 = ( l0 - j0 / 2.0 ) * ( j0 + 1.0 );
501 x2 = ( l1 - j1 / 2.0 ) * ( j1 + 1.0 );
502 if ( jt == llt ){
503 x3 = ( lt == 0 ) ? 0 : ( x1 - x2 ) / std::sqrt( lt * ( lt + 1.0 ) );
504 }
505 else if ( jt == ( llt - st ) ){
506 x3 = ( lt == 0 ) ? 0 : -( lt + x1 + x2 ) / std::sqrt( lt * ( 2.0 * lt + 1.0 ) );
507 }
508 else if ( jt == ( llt + st ) ){
509 x3 = ( lt + 1 - x1 - x2 ) / std::sqrt( ( 2.0 * lt + 1.0 ) * ( lt + 1.0 ) );
510 }
511 else{
512 x3 = 1.0;
513 }
514 }
515 else x3 = 1.0;
516 reduced_mat *= x3;
517
518 return( reduced_mat );
519}
M_PI
#define M_PI
Definition: SbMath.h:33
parity
static int parity(int x)
Definition: nf_angularMomentumCoupling.cc:523
nf_amc_clebsh_gordan
double nf_amc_clebsh_gordan(int j1, int j2, int m1, int m2, int j3)
Definition: nf_angularMomentumCoupling.cc:288

References M_PI, nf_amc_clebsh_gordan(), and parity().

◆ nf_amc_wigner_3j()

double nf_amc_wigner_3j ( int  j1,
int  j2,
int  j3,
int  j4,
int  j5,
int  j6 
)

Definition at line 105 of file nf_angularMomentumCoupling.cc.

105 {
106/*
107* Wigner's 3J symbol (similar to Clebsh-Gordan)
108* = / j1 j2 j3 \
109* \ j4 j5 j6 /
110*/
111 double cg;
112
113 if( ( j4 + j5 + j6 ) != 0 ) return( 0.0 );
114 if( ( cg = nf_amc_clebsh_gordan( j1, j2, j4, j5, j3 ) ) == 0.0 ) return ( 0.0 );
115 if( cg == INFINITY ) return( cg );
116 return( ( ( ( j1 - j2 - j6 ) % 4 == 0 ) ? 1.0 : -1.0 ) * cg / std::sqrt( j3 + 1.0 ) ); /* BRB j3 + 1 <= 0? */
117}

References nf_amc_clebsh_gordan().

◆ nf_amc_wigner_6j()

double nf_amc_wigner_6j ( int  j1,
int  j2,
int  j3,
int  j4,
int  j5,
int  j6 
)

Definition at line 121 of file nf_angularMomentumCoupling.cc.

121 {
122/*
123* Wigner's 6J symbol (similar to Racah)
124* = { j1 j2 j3 }
125* { j4 j5 j6 }
126*/
127 int i, x[6];
128
129 x[0] = j1; x[1] = j2; x[2] = j3; x[3] = j4; x[4] = j5; x[5] = j6;
130 for( i = 0; i < 6; i++ ) if ( x[i] == 0 ) return( w6j0( i, x ) );
131
132 return( w6j1( x ) );
133}
w6j1
static double w6j1(int *)
Definition: nf_angularMomentumCoupling.cc:166
w6j0
static double w6j0(int, int *)
Definition: nf_angularMomentumCoupling.cc:137

References w6j0(), and w6j1().

Referenced by nf_amc_racah().

◆ nf_amc_wigner_9j()

double nf_amc_wigner_9j ( int  j1,
int  j2,
int  j3,
int  j4,
int  j5,
int  j6,
int  j7,
int  j8,
int  j9 
)

Definition at line 226 of file nf_angularMomentumCoupling.cc.

226 {
227/*
228* Wigner's 9J symbol
229* / j1 j2 j3 \
230* = | j4 j5 j6 |
231* \ j7 j8 j9 /
232*
233*/
234 int i, i0, i1;
235 double rac;
236
237 i0 = max3( std::abs( j1 - j9 ), std::abs( j2 - j6 ), std::abs( j4 - j8 ) );
238 i1 = min3( ( j1 + j9 ), ( j2 + j6 ), ( j4 + j8 ) );
239
240 rac = 0.0;
241 for ( i = i0; i <= i1; i += 2 ){
242 rac += nf_amc_racah( j1, j4, j9, j8, j7, i )
243 * nf_amc_racah( j2, j5, i, j4, j8, j6 )
244 * nf_amc_racah( j9, i, j3, j2, j1, j6 ) * ( i + 1 );
245 if( rac == INFINITY ) return( INFINITY );
246 }
247
248 return( ( ( (int)( ( j1 + j3 + j5 + j8 ) / 2 + j2 + j4 + j9 ) % 4 == 0 ) ? 1.0 : -1.0 ) * rac );
249}
nf_amc_racah
double nf_amc_racah(int j1, int j2, int l2, int l1, int j3, int l3)
Definition: nf_angularMomentumCoupling.cc:253

References max3(), min3(), and nf_amc_racah().

◆ nf_amc_z_coefficient()

double nf_amc_z_coefficient ( int  l1,
int  j1,
int  l2,
int  j2,
int  s,
int  ll 
)

Definition at line 437 of file nf_angularMomentumCoupling.cc.

437 {
438/*
439* Biedenharn's Z-coefficient coefficient
440* = Z(l1 j1 l2 j2 | S L )
441*/
442 double z, clebsh_gordan = nf_amc_clebsh_gordan( l1, l2, 0, 0, ll ), racah = nf_amc_racah( l1, j1, l2, j2, s, ll );
443
444 if( ( clebsh_gordan == INFINITY ) || ( racah == INFINITY ) ) return( INFINITY );
445 z = ( ( ( -l1 + l2 + ll ) % 8 == 0 ) ? 1.0 : -1.0 )
446 * std::sqrt( l1 + 1.0 ) * std::sqrt( l2 + 1.0 ) * std::sqrt( j1 + 1.0 ) * std::sqrt( j2 + 1.0 ) * clebsh_gordan * racah;
447
448 return( z );
449}
s
static constexpr double s
Definition: G4SIunits.hh:154

References nf_amc_clebsh_gordan(), nf_amc_racah(), and s.

◆ nf_amc_zbar_coefficient()

double nf_amc_zbar_coefficient ( int  l1,
int  j1,
int  l2,
int  j2,
int  s,
int  ll 
)

Definition at line 453 of file nf_angularMomentumCoupling.cc.

453 {
454/*
455* Lane & Thomas's Zbar-coefficient coefficient
456* = Zbar(l1 j1 l2 j2 | S L )
457* = (-i)^( -l1 + l2 + ll ) * Z(l1 j1 l2 j2 | S L )
458*
459* Lane & Thomas Rev. Mod. Phys. 30, 257-353 (1958).
460* Note, Lane & Thomas define this because they did not like the different phase convention in Blatt & Biedenharn's Z coefficient. They changed it to get better time-reversal behavior.
461* Froehner uses Lane & Thomas convention as does T. Kawano.
462*/
463 double zbar, clebsh_gordan = nf_amc_clebsh_gordan( l1, l2, 0, 0, ll ), racah = nf_amc_racah( l1, j1, l2, j2, s, ll );
464
465 if( ( clebsh_gordan == INFINITY ) || ( racah == INFINITY ) ) return( INFINITY );
466 zbar = std::sqrt( l1 + 1.0 ) * std::sqrt( l2 + 1.0 ) * std::sqrt( j1 + 1.0 ) * std::sqrt( j2 + 1.0 ) * clebsh_gordan * racah;
467
468 return( zbar );
469}

References nf_amc_clebsh_gordan(), nf_amc_racah(), and s.

◆ parity()

static int parity ( int  x)
static

Definition at line 523 of file nf_angularMomentumCoupling.cc.

523 {
524
525 return( ( ( x / 2 ) % 2 == 0 ) ? 1 : -1 );
526}

Referenced by G4TwistTubsSide::DistanceToPlane(), G4TwistTubsSide::DistanceToSurface(), nf_amc_reduced_matrix_element(), and G4TwistedTubs::SetFields().

◆ w6j0()

static double w6j0 ( int  i,
int *  x 
)
static

Definition at line 137 of file nf_angularMomentumCoupling.cc.

137 {
138
139 switch( i ){
140 case 0: if ( ( x[1] != x[2] ) || ( x[4] != x[5] ) ) return( 0.0 );
141 x[5] = x[3]; x[0] = x[1]; x[3] = x[4]; break;
142 case 1: if ( ( x[0] != x[2] ) || ( x[3] != x[5] ) ) return( 0.0 );
143 x[5] = x[4]; break;
144 case 2: if ( ( x[0] != x[1] ) || ( x[3] != x[4] ) ) return( 0.0 );
145 break;
146 //TK fix bug and add comment on 17-05-23
147 //This is the case of 6.3.2 of A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press 1974.
148 case 3: if ( ( x[1] != x[5] ) || ( x[2] != x[4] ) ) return( 0.0 );
149 x[5] = x[0]; x[0] = x[4]; x[3] = x[1]; break;
150 case 4: if ( ( x[0] != x[5] ) || ( x[2] != x[3] ) ) return( 0.0 );
151 x[5] = x[1]; break;
152 case 5: if ( ( x[0] != x[4] ) || ( x[1] != x[3] ) ) return( 0.0 );
153 x[5] = x[2]; break;
154 }
155
156 if( ( x[5] > ( x[0] + x[3] ) ) || ( x[5] < std::abs( x[0] - x[3] ) ) ) return( 0.0 );
157 if( x[0] > MAX_FACTORIAL || x[3] > MAX_FACTORIAL ) { /* BRB Why this test? Why not x[5]? */
158 return( INFINITY );
159 }
160
161 return( 1.0 / std::sqrt( (double) ( ( x[0] + 1 ) * ( x[3] + 1 ) ) ) * ( ( ( x[0] + x[3] + x[5] ) / 2 ) % 2 != 0 ? -1 : 1 ) );
162}

References MAX_FACTORIAL.

Referenced by nf_amc_wigner_6j().

◆ w6j1()

static double w6j1 ( int *  x)
static

Definition at line 166 of file nf_angularMomentumCoupling.cc.

166 {
167
168 double w6j, w;
169 int i, k, k1, k2, n, l1, l2, l3, l4, n1, n2, n3, m1, m2, m3, x1, x2, x3, y[4];
170 static int a[3][4] = { { 0, 0, 3, 3},
171 { 1, 4, 1, 4},
172 { 2, 5, 5, 2} };
173
174 w6j = 0.0;
175
176 for ( k = 0; k < 4; k++ ){
177 x1 = x[ ( a[0][k] ) ];
178 x2 = x[ ( a[1][k] ) ];
179 x3 = x[ ( a[2][k] ) ];
180
181 n = ( x1 + x2 + x3 ) / 2;
182 if( n > MAX_FACTORIAL ) {
183 return( INFINITY ); }
184 else if( n < 0 ) {
185 return( 0.0 );
186 }
187
188 if ( ( n1 = n - x3 ) < 0 ) return( 0.0 );
189 if ( ( n2 = n - x2 ) < 0 ) return( 0.0 );
190 if ( ( n3 = n - x1 ) < 0 ) return( 0.0 );
191
192 y[k] = n + 2;
193 w6j += nf_amc_log_fact[n1] + nf_amc_log_fact[n2] + nf_amc_log_fact[n3] - nf_amc_log_fact[n+1];
194 }
195
196 n1 = ( x[0] + x[1] + x[3] + x[4] ) / 2;
197 n2 = ( x[0] + x[2] + x[3] + x[5] ) / 2;
198 n3 = ( x[1] + x[2] + x[4] + x[5] ) / 2;
199
200 k1 = max4( y[0], y[1], y[2], y[3] ) - 1;
201 k2 = min3( n1, n2, n3 ) + 1;
202
203 l1 = k1 - y[0] + 1; m1 = n1 - k1 + 1;
204 l2 = k1 - y[1] + 1; m2 = n2 - k1 + 1;
205 l3 = k1 - y[2] + 1; m3 = n3 - k1 + 1;
206 l4 = k1 - y[3] + 1;
207
208 w6j = w = G4Exp( 0.5 * w6j + nf_amc_log_fact[k1] - nf_amc_log_fact[l1] - nf_amc_log_fact[l2] - nf_amc_log_fact[l3] - nf_amc_log_fact[l4]
209 - nf_amc_log_fact[m1] - nf_amc_log_fact[m2] - nf_amc_log_fact[m3] ) * ( ( k1 % 2 ) == 0 ? -1: 1 );
210 if( w6j == INFINITY ) return( INFINITY );
211
212 if( k1 != k2 ){
213 k = k2 - k1;
214 m1 -= k-1; m2 -= k-1; m3 -= k-1;
215 l1 += k ; l2 += k ; l3 += k ; l4 += k;
216
217 for ( i = 0; i < k; i++ )
218 w6j = w - w6j * ( ( k2 - i ) * ( m1 + i ) * ( m2 + i ) * ( m3 + i ) )
219 / ( ( l1 - i ) * ( l2 - i ) * ( l3 - i ) * ( l4 - i ) );
220 }
221 return( w6j );
222}
max4
static int max4(int a, int b, int c, int d)
Definition: nf_angularMomentumCoupling.cc:539

References G4Exp(), m2, m3, max4(), MAX_FACTORIAL, min3(), CLHEP::detail::n, and nf_amc_log_fact.

Referenced by nf_amc_wigner_6j().

Variable Documentation

◆ MAX_FACTORIAL

const int MAX_FACTORIAL = 200
static

Definition at line 68 of file nf_angularMomentumCoupling.cc.

Referenced by cg1(), cg2(), nf_amc_clebsh_gordan(), nf_amc_log_factorial(), w6j0(), and w6j1().

◆ nf_amc_log_fact

const double nf_amc_log_fact[] = {0.0, 0.0, 0.69314718056, 1.79175946923, 3.17805383035, 4.78749174278, 6.57925121201, 8.52516136107, 10.6046029027, 12.8018274801, 15.1044125731, 17.5023078459, 19.9872144957, 22.5521638531, 25.1912211827, 27.8992713838, 30.6718601061, 33.5050734501, 36.395445208, 39.3398841872, 42.3356164608, 45.3801388985, 48.4711813518, 51.6066755678, 54.7847293981, 58.003605223, 61.261701761, 64.557538627, 67.8897431372, 71.2570389672, 74.6582363488, 78.0922235533, 81.5579594561, 85.0544670176, 88.5808275422, 92.1361756037, 95.7196945421, 99.3306124548, 102.968198615, 106.631760261, 110.320639715, 114.034211781, 117.7718814, 121.533081515, 125.317271149, 129.123933639, 132.952575036, 136.802722637, 140.673923648, 144.565743946, 148.477766952, 152.409592584, 156.360836303, 160.331128217, 164.320112263, 168.327445448, 172.352797139, 176.395848407, 180.456291418, 184.533828861, 188.628173424, 192.739047288, 196.866181673, 201.009316399, 205.168199483, 209.342586753, 213.532241495, 217.736934114, 221.956441819, 226.190548324, 230.439043566, 234.701723443, 238.978389562, 243.268849003, 247.572914096, 251.89040221, 256.22113555, 260.564940972, 264.921649799, 269.291097651, 273.673124286, 278.06757344, 282.474292688, 286.893133295, 291.323950094, 295.766601351, 300.220948647, 304.686856766, 309.16419358, 313.65282995, 318.15263962, 322.663499127, 327.185287704, 331.717887197, 336.261181979, 340.815058871, 345.379407062, 349.954118041, 354.539085519, 359.13420537, 363.739375556, 368.354496072, 372.979468886, 377.614197874, 382.258588773, 386.912549123, 391.575988217, 396.248817052, 400.930948279, 405.622296161, 410.322776527, 415.032306728, 419.7508056, 424.478193418, 429.214391867, 433.959323995, 438.712914186, 443.475088121, 448.245772745, 453.024896238, 457.812387981, 462.608178527, 467.412199572, 472.224383927, 477.044665493, 481.87297923, 486.709261137, 491.553448223, 496.405478487, 501.265290892, 506.132825342, 511.008022665, 515.890824588, 520.781173716, 525.679013516, 530.584288294, 535.49694318, 540.416924106, 545.344177791, 550.278651724, 555.220294147, 560.169054037, 565.124881095, 570.087725725, 575.057539025, 580.034272767, 585.017879389, 590.008311976, 595.005524249, 600.009470555, 605.020105849, 610.037385686, 615.061266207, 620.091704128, 625.128656731, 630.172081848, 635.221937855, 640.27818366, 645.340778693, 650.409682896, 655.484856711, 660.566261076, 665.653857411, 670.747607612, 675.84747404, 680.953419514, 686.065407302, 691.183401114, 696.307365094, 701.437263809, 706.573062246, 711.714725802, 716.862220279, 722.015511874, 727.174567173, 732.339353147, 737.509837142, 742.685986874, 747.867770425, 753.05515623, 758.248113081, 763.446610113, 768.6506168, 773.860102953, 779.07503871, 784.295394535, 789.521141209, 794.752249826, 799.988691789, 805.230438804, 810.477462876, 815.729736304, 820.987231676, 826.249921865, 831.517780024, 836.790779582, 842.068894242, 847.35209797, 852.640365001, 857.933669826, 863.231987192}
static

Definition at line 70 of file nf_angularMomentumCoupling.cc.

Referenced by cg1(), cg2(), cg3(), nf_amc_log_factorial(), and w6j1().

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