#include <stdlib.h>
#include <cmath>
#include "nf_specialFunctions.h"

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Functions
static int	parity (int x)

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)

static double	w6j0 (int, int *)

static double	w6j1 (int *)

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)

double	nf_amc_log_factorial (int n)

double	nf_amc_factorial (int n)

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_racah (int j1, int j2, int l2, int l1, int j3, int l3)

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

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)

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

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

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

static

Definition at line 337 of file nf_angularMomentumCoupling.cc.

                                             {
 
     int p1, p2, p3, p4, q1, q2, q3, q4;
     double a;
 
     p1 = x1 + x2 + x3 - 1; if ( ( p1 % 2 ) != 0 ) return( 0.0 );
     p2 = x1 + x2 - x3;
     p3 =-x1 + x2 + x3;
     p4 = x1 - x2 + x3;
     if ( p2 <= 0 || p3 <= 0 || p4 <= 0 ) return( 0.0 );
     if ( p1 >= MAX_FACTORIAL ) return( INFINITY );
 
     q1 = ( p1 + 1 ) / 2 - 1; p1--;
     q2 = ( p2 + 1 ) / 2 - 1; p2--;
     q3 = ( p3 + 1 ) / 2 - 1; p3--;
     q4 = ( p4 + 1 ) / 2 - 1; p4--;
 
     a = nf_amc_log_fact[q1]-( nf_amc_log_fact[q2] + nf_amc_log_fact[q3] + nf_amc_log_fact[q4] )
         + 0.5 * ( nf_amc_log_fact[ 2 * x3 - 1 ] - nf_amc_log_fact[ 2 * x3 - 2 ]
         + nf_amc_log_fact[p2] + nf_amc_log_fact[p3] + nf_amc_log_fact[p4] - nf_amc_log_fact[p1] );
 
     return( ( ( ( q1 + x1 - x2 ) % 2 == 0 ) ? 1.0 : -1.0 ) * G4Exp( a ) );
 }

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

static

Definition at line 363 of file nf_angularMomentumCoupling.cc.

                                                                                    {
 
     int q1, q2, q3, q4, p1, p2, p3, p4;
     double a;
 
     p1 =  z1 + q0 + 2;
     p2 =  z1 - q0 + 1;
     p3 =  z2 + q0 + 1;
     p4 = -z2 + q0 + 1;
     if ( p2 <= 0 || p3 <= 0 || p4 <= 0) return( 0.0 );
     if ( p1 >= MAX_FACTORIAL ) return( INFINITY );
 
     q1 = ( p1 + 1 ) / 2 - 1; p1--;
     q2 = ( p2 + 1 ) / 2 - 1; p2--;
     q3 = ( p3 + 1 ) / 2 - 1; p3--;
     q4 = ( p4 + 1 ) / 2 - 1; p4--;
 
     a = nf_amc_log_fact[q1] - ( nf_amc_log_fact[ q2 ] + nf_amc_log_fact[ q3 ] + nf_amc_log_fact[ q4 ] )
         + 0.5 * ( nf_amc_log_fact[ w3 + 1 ] - nf_amc_log_fact[ w3  ]
                 + nf_amc_log_fact[ w1  ]    - nf_amc_log_fact[ w1 + 1 ]
                 + nf_amc_log_fact[ w2  ]    - nf_amc_log_fact[ w2 + 1 ]
                 + nf_amc_log_fact[ p2 ]     + nf_amc_log_fact[ p3 ] + nf_amc_log_fact[ p4 ] - nf_amc_log_fact[ p1 ] );
 
     return( ( ( ( q4 + k + ( mm > 0 ) * ( p1 + 2 ) ) % 2 == 0 ) ? -1.0 : 1.0 ) * 2.0 * G4Exp( a ) );
 }

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

static

Definition at line 391 of file nf_angularMomentumCoupling.cc.

                                                                     {
 
     int nx, i, k1, k2, q1, q2, q3, q4, p1, p2, p3, z1, z2, z3;
     double a, cg;
 
     nx = x1 + x2 + x3 - 1;
     if ( ( z1 = nx - x1 - y1 ) < 0 ) return( 0.0 );
     if ( ( z2 = nx - x2 - y2 ) < 0 ) return( 0.0 );
     if ( ( z3 = nx - x3 - y3 ) < 0 ) return( 0.0 );
 
     k1 = x2 - y3;
     k2 = y1 - x3;
 
     q1 = max3( k1, k2, 0 );
     q2 = min3( y1, x2, z3 + 1 ) - 1;
     q3 = q1 - k1;
     q4 = q1 - k2;
 
     p1 = y1 - q1 - 1;
     p2 = x2 - q1 - 1;
     p3 = z3 - q1;
 
     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 ]
                  + nf_amc_log_fact[ z1  ]    + nf_amc_log_fact[ z2  ]    + nf_amc_log_fact[ z3  ]
                  + nf_amc_log_fact[ x1 - 1 ] + nf_amc_log_fact[ x2 - 1 ] + nf_amc_log_fact[ x3 - 1 ]
                  + nf_amc_log_fact[ y1 - 1 ] + nf_amc_log_fact[ y2 - 1 ] + nf_amc_log_fact[ y3 - 1 ] )
                  - nf_amc_log_fact[ p1  ]    - nf_amc_log_fact[ p2  ]    - nf_amc_log_fact[ p3  ]
                  - nf_amc_log_fact[ q1  ]    - nf_amc_log_fact[ q3  ]    - nf_amc_log_fact[ q4  ] ) * ( ( ( q1 % 2 ) == 0 ) ? 1 : -1 );
     if( cg == INFINITY ) return( INFINITY );
 
     if ( q1 != q2 ){
         q3 = q2 - k1;
         q4 = q2 - k2;
         p1 = y1 - q2;
         p2 = x2 - q2;
         p3 = z3 - q2 + 1;
         for( i = 0; i < ( q2 - q1 ); i++ )
             cg = a - cg * ( ( p1 + i ) * ( p2 + i ) * ( p3 + i ) ) / ( ( q2 - i ) * ( q3 - i ) * ( q4 - i ) );
     }
     return( cg );
 }

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

static

Definition at line 528 of file nf_angularMomentumCoupling.cc.

                                        {
 
     if( a < b ) a = b;
     if( a < c ) a = c;
     return( a );
 }

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

static

Definition at line 537 of file nf_angularMomentumCoupling.cc.

                                               {
 
     if( a < b ) a = b;
     if( a < c ) a = c;
     if( a < d ) a = d;
     return( a );
 }

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

static

Definition at line 547 of file nf_angularMomentumCoupling.cc.

                                        {
 
     if( a > b ) a = b;
     if( a > c ) a = c;
     return( a );
 }

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

Definition at line 286 of file nf_angularMomentumCoupling.cc.

                                                                       {
 /*
 *       Clebsh-Gordan coefficient 
 *           = <j1,j2,m1,m2|j3,m1+m2>
 *           = (-)^(j1-j2+m1+m2) * std::sqrt(2*j3+1) * / j1 j2   j3   \
 *                                                \ m1 m2 -m1-m2 /
 *
 *   Note: Last value m3 is preset to m1+m2.  Any other value will evaluate to 0.0.
 */
 
     int m3, x1, x2, x3, y1, y2, y3;
     double cg = 0.0;
 
     if ( j1 < 0 || j2 < 0 || j3 < 0) return( 0.0 );
     if ( j1 + j2 + j3 > 2 * MAX_FACTORIAL ) return( INFINITY );
 
     m3 = m1 + m2;
 
     if ( ( x1 = ( j1 + m1 ) / 2 + 1 ) <= 0 ) return( 0.0 );
     if ( ( x2 = ( j2 + m2 ) / 2 + 1 ) <= 0 ) return( 0.0 );
     if ( ( x3 = ( j3 - m3 ) / 2 + 1 ) <= 0 ) return( 0.0 );
 
     if ( ( y1 = x1 - m1 ) <= 0 ) return( 0.0 );
     if ( ( y2 = x2 - m2 ) <= 0 ) return( 0.0 );
     if ( ( y3 = x3 + m3 ) <= 0 ) return( 0.0 );
 
     if ( j3 == 0 ){
         if ( j1 == j2 ) cg = ( 1.0 / std::sqrt( (double)j1 + 1.0 ) * ( ( y1 % 2 == 0 ) ? -1:1 ) );
     }
     else if ( (j1 == 0 || j2 == 0 ) ){
         if ( ( j1 + j2 ) == j3 ) cg = 1.0;
     }
     else {
         if( m3 == 0 && std::abs( m1 ) <= 1 ){
             if( m1 == 0 ) cg = cg1( x1, x2, x3 );
             else          cg = cg2( x1 + y1 - y2, x3 - 1, x1 + x2 - 2, x1 - y2, j1, j2, j3, m2 );
         }
         else if ( m2 == 0 && std::abs( m1 ) <=1 ){
                           cg = cg2( x1 - y2 + y3, x2 - 1, x1 + x3 - 2, x3 - y1, j1, j3, j3, m1 );
         }
         else if ( m1 == 0 && std::abs( m3 ) <= 1 ){
                           cg = cg2( x1, x1 - 1, x2 + x3 - 2, x2 - y3, j2, j3, j3, -m3 );
         }
         else              cg = cg3( x1, x2, x3, y1, y2, y3 );
     }
 
     return( cg );
 }

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double nf_amc_factorial ( int n )

Definition at line 96 of file nf_angularMomentumCoupling.cc.

                                   {
 /*
 *       returns n! for pre-computed table. INFINITY is return if n is negative or too large.
 */
     return G4Exp( nf_amc_log_factorial( n ) );
 }

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double nf_amc_log_factorial ( int n )

Definition at line 85 of file nf_angularMomentumCoupling.cc.

                                       {
 /*
 *       returns ln( n! ).
 */
     if( n > MAX_FACTORIAL ) return( INFINITY );
     if( n < 0 ) return( INFINITY );
     return nf_amc_log_fact[n];
 }

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

Definition at line 251 of file nf_angularMomentumCoupling.cc.

                                                                       {
 /*
 *       Racah coefficient definition in Edmonds (AR Edmonds, "Angular Momentum in Quantum Mechanics", Princeton (1980) is
 *       W(j1, j2, l2, l1 ; j3, l3) = (-1)^(j1+j2+l1+l2) * { j1 j2 j3 }
 *                                                         { l1 l2 l3 }
 *       The call signature of W(...) appears jumbled, but hey, that's the convention.
 *
 *       This convention is exactly that used by Blatt-Biedenharn (Rev. Mod. Phys. 24, 258 (1952)) too
 */
 
     double sig;
 
     sig = ( ( ( j1 + j2 + l1 + l2 ) % 4 == 0 ) ?  1.0 : -1.0 );
     return sig * nf_amc_wigner_6j( j1, j2, j3, l1, l2, l3 );
 }

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

Definition at line 471 of file nf_angularMomentumCoupling.cc.

                                                                                                {
 /*
 *       Reduced Matrix Element for Tensor Operator
 *           = < l1j1 || T(YL,sigma_S)J || l0j0 >
 *
 *   M.B.Johnson, L.W.Owen, G.R.Satchler
 *   Phys. Rev. 142, 748 (1966)
 *   Note: definition differs from JOS by the factor sqrt(2j1+1)
 */
     int    llt;
     double x1, x2, x3, reduced_mat, clebsh_gordan;
 
     if ( parity( lt ) != parity( l0 ) * parity( l1 ) ) return( 0.0 );
     if ( std::abs( l0 - l1 ) > lt || ( l0 + l1 ) < lt ) return( 0.0 );
     if ( std::abs( ( j0 - j1 ) / 2 ) > jt || ( ( j0 + j1 ) / 2 ) < jt ) return( 0.0 );
 
     llt = 2 * lt;
     jt *= 2;
     st *= 2;
 
     if( ( clebsh_gordan = nf_amc_clebsh_gordan( j1, j0, 1, -1, jt ) ) == INFINITY ) return( INFINITY );
 
     reduced_mat = 1.0 / std::sqrt( 4 * M_PI ) * clebsh_gordan / std::sqrt( jt + 1.0 )         /* BRB jt + 1 <= 0? */
                 * std::sqrt( ( j0 + 1.0 ) * ( j1 + 1.0 ) * ( llt + 1.0 ) )
                 * parity( ( j1 - j0 ) / 2 ) * parity( ( -l0 + l1 + lt ) / 2 ) * parity( ( j0 - 1 ) / 2 );
 
     if( st == 2 ){
         x1 = ( l0 - j0 / 2.0 ) * ( j0 + 1.0 );
         x2 = ( l1 - j1 / 2.0 ) * ( j1 + 1.0 );
         if ( jt == llt ){
             x3 = ( lt == 0 ) ? 0 :  ( x1 - x2 ) / std::sqrt( lt * ( lt + 1.0 ) );
         }
         else if ( jt == ( llt - st ) ){
             x3 = ( lt == 0 ) ? 0 : -( lt + x1 + x2 ) / std::sqrt( lt * ( 2.0 * lt + 1.0 ) );
         }
         else if ( jt == ( llt + st ) ){
             x3 = ( lt + 1 - x1 - x2 ) / std::sqrt( ( 2.0 * lt + 1.0 ) * ( lt + 1.0 ) );
         }
         else{
             x3 = 1.0;
         }
     }
     else x3 = 1.0;
     reduced_mat *= x3;
 
     return( reduced_mat );
 }

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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.

                                                                           {
 /*
 *       Wigner's 3J symbol (similar to Clebsh-Gordan)
 *           = / j1 j2 j3 \
 *             \ j4 j5 j6 /
 */
     double cg;
 
     if( ( j4 + j5 + j6 ) != 0 ) return( 0.0 );
     if( ( cg = nf_amc_clebsh_gordan( j1, j2, j4, j5, j3 ) ) == 0.0 ) return ( 0.0 );
     if( cg == INFINITY ) return( cg );
     return( ( ( ( j1 - j2 - j6 ) % 4 == 0 ) ?  1.0 : -1.0 ) * cg / std::sqrt( j3 + 1.0 ) );          /* BRB j3 + 1 <= 0? */
 }

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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.

                                                                           {
 /*
 *       Wigner's 6J symbol (similar to Racah)
 *               = { j1 j2 j3 }
 *                 { j4 j5 j6 }
 */
     int i, x[6];
 
     x[0] = j1; x[1] = j2; x[2] = j3; x[3] = j4; x[4] = j5; x[5] = j6;
     for( i = 0; i < 6; i++ ) if ( x[i] == 0 ) return( w6j0( i, x ) );
 
     return( w6j1( x ) );
 }

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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 224 of file nf_angularMomentumCoupling.cc.

                                                                                                   {
 /*
 *       Wigner's 9J symbol
 *             / j1 j2 j3 \
 *           = | j4 j5 j6 |
 *             \ j7 j8 j9 /
 *
 */
     int i, i0, i1;
     double rac;
 
     i0 = max3( std::abs( j1 - j9 ), std::abs( j2 - j6 ), std::abs( j4 - j8 ) );
     i1 = min3(     ( j1 + j9 ),     ( j2 + j6 ),     ( j4 + j8 ) );
 
     rac = 0.0;
     for ( i = i0; i <= i1; i += 2 ){ 
         rac += nf_amc_racah( j1, j4, j9, j8, j7,  i )
             *  nf_amc_racah( j2, j5,  i, j4, j8, j6 )
             *  nf_amc_racah( j9,  i, j3, j2, j1, j6 ) * ( i + 1 );
         if( rac == INFINITY ) return( INFINITY );
     }
 
     return( ( ( (int)( ( j1 + j3 + j5 + j8 ) / 2 + j2 + j4 + j9 ) % 4 == 0 ) ?  1.0 : -1.0 ) * rac );
 }

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

Definition at line 435 of file nf_angularMomentumCoupling.cc.

                                                                              {
 /*
 *       Biedenharn's Z-coefficient coefficient
 *           =  Z(l1  j1  l2  j2 | S L )
 */
     double z, clebsh_gordan = nf_amc_clebsh_gordan( l1, l2, 0, 0, ll ), racah = nf_amc_racah( l1, j1, l2, j2, s, ll );
 
     if( ( clebsh_gordan == INFINITY ) || ( racah == INFINITY ) ) return( INFINITY );
     z = ( ( ( -l1 + l2 + ll ) % 8 == 0 ) ? 1.0 : -1.0 )
         * std::sqrt( l1 + 1.0 ) * std::sqrt( l2 + 1.0 ) * std::sqrt( j1 + 1.0 ) * std::sqrt( j2 + 1.0 ) * clebsh_gordan * racah;
 
    return( z );
 }

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

Definition at line 451 of file nf_angularMomentumCoupling.cc.

                                                                                 {
 /*
 *       Lane & Thomas's Zbar-coefficient coefficient
 *           = Zbar(l1  j1  l2  j2 | S L )
 *           = (-i)^( -l1 + l2 + ll ) * Z(l1  j1  l2  j2 | S L )
 *
 *       Lane & Thomas Rev. Mod. Phys. 30, 257-353 (1958).
 *       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.
 *       Froehner uses Lane & Thomas convention as does T. Kawano.
 */
     double zbar, clebsh_gordan = nf_amc_clebsh_gordan( l1, l2, 0, 0, ll ), racah = nf_amc_racah( l1, j1, l2, j2, s, ll );
 
     if( ( clebsh_gordan == INFINITY ) || ( racah == INFINITY ) ) return( INFINITY );
     zbar = std::sqrt( l1 + 1.0 ) * std::sqrt( l2 + 1.0 ) * std::sqrt( j1 + 1.0 ) * std::sqrt( j2 + 1.0 ) * clebsh_gordan * racah;
 
    return( zbar );
 }

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static int parity ( int x )

static

Definition at line 521 of file nf_angularMomentumCoupling.cc.

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

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static double w6j0	(	int	i,
		int *	x
	)

static

Definition at line 137 of file nf_angularMomentumCoupling.cc.

                                     {
 
     switch( i ){
        case 0: if ( ( x[1] != x[2] ) || ( x[4] != x[5] ) ) return( 0.0 );
                x[5] = x[3]; x[0] = x[1]; x[3] = x[4];      break;
        case 1: if ( ( x[0] != x[2] ) || ( x[3] != x[5] ) ) return( 0.0 );
                x[5] = x[4];                                break;
        case 2: if ( ( x[0] != x[1] ) || ( x[3] != x[4] ) ) return( 0.0 );
                if ( x[3] != x[4] )                         break;
        case 3: if ( ( x[1] != x[5] ) || ( x[2] != x[4] ) ) return( 0.0 );
                x[5] = x[0]; x[0] = x[4]; x[3] = x[1];      break;
        case 4: if ( ( x[0] != x[5] ) || ( x[2] != x[3] ) ) return( 0.0 );
                x[5] = x[1];                                break;
        case 5: if ( ( x[0] != x[4] ) || ( x[1] != x[3] ) ) return( 0.0 );
                x[5] = x[2];                                break;
     }
 
     if( ( x[5] > ( x[0] + x[3] ) ) || ( x[5] < std::abs( x[0] - x[3] ) ) ) return( 0.0 );
     if( x[0] > MAX_FACTORIAL || x[3] > MAX_FACTORIAL ) {        /* BRB Why this test? Why not x[5]? */
         return( INFINITY );
     }
 
     return( 1.0 / std::sqrt( (double) ( ( x[0] + 1 ) * ( x[3] + 1 ) ) ) * ( ( ( x[0] + x[3] + x[5] ) / 2 ) % 2 != 0 ? -1 : 1 ) );
 }

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static double w6j1 ( int * x )

static

Definition at line 164 of file nf_angularMomentumCoupling.cc.

                              {
 
     double w6j, w;
     int i, k, k1, k2, n, l1, l2, l3, l4, n1, n2, n3, m1, m2, m3, x1, x2, x3, y[4];
     static int a[3][4] = { { 0, 0, 3, 3},
                            { 1, 4, 1, 4},
                            { 2, 5, 5, 2} };
 
     w6j = 0.0;
 
     for ( k = 0; k < 4; k++ ){
         x1 = x[ ( a[0][k] ) ];
         x2 = x[ ( a[1][k] ) ];
         x3 = x[ ( a[2][k] ) ];
 
         n = ( x1 + x2 + x3 ) / 2;
         if( n > MAX_FACTORIAL ) {
             return( INFINITY ); }
         else if( n < 0 ) {
             return( 0.0 );
         }
 
         if ( ( n1 = n - x3 ) < 0 ) return( 0.0 );
         if ( ( n2 = n - x2 ) < 0 ) return( 0.0 );
         if ( ( n3 = n - x1 ) < 0 ) return( 0.0 );
 
         y[k] = n + 2;
         w6j += nf_amc_log_fact[n1] + nf_amc_log_fact[n2] + nf_amc_log_fact[n3] - nf_amc_log_fact[n+1];
     }
 
     n1 = ( x[0] + x[1] + x[3] + x[4] ) / 2;
     n2 = ( x[0] + x[2] + x[3] + x[5] ) / 2;
     n3 = ( x[1] + x[2] + x[4] + x[5] ) / 2;
 
     k1 = max4( y[0], y[1], y[2], y[3] ) - 1;
     k2 = min3( n1, n2, n3 ) + 1;
 
     l1 = k1 - y[0] + 1;  m1 = n1 - k1 + 1;
     l2 = k1 - y[1] + 1;  m2 = n2 - k1 + 1;
     l3 = k1 - y[2] + 1;  m3 = n3 - k1 + 1;
     l4 = k1 - y[3] + 1;
 
     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]
                              - nf_amc_log_fact[m1] - nf_amc_log_fact[m2] - nf_amc_log_fact[m3] ) * ( ( k1 % 2 ) == 0 ? -1: 1 );
     if( w6j == INFINITY ) return( INFINITY );
 
     if( k1 != k2 ){
         k = k2 - k1;
         m1 -= k-1; m2 -= k-1; m3 -= k-1;
         l1 += k  ; l2 += k  ; l3 += k  ; l4 += k;
 
         for ( i = 0; i < k; i++ )
             w6j = w - w6j * ( ( k2 - i ) * ( m1 + i ) * ( m2 + i ) * ( m3 + i ) )
                     / ( ( l1 - i ) * ( l2 - i ) * ( l3 - i ) * ( l4 - i ) );
     }
     return( w6j );
 }

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Variable Documentation

const int MAX_FACTORIAL = 200

static

Definition at line 68 of file nf_angularMomentumCoupling.cc.

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.

Functions

Variables

Function Documentation

Variable Documentation