130 lines
3.9 KiB
C++
130 lines
3.9 KiB
C++
#include <stdlib.h>
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#include <cmath>
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#include <algorithm>
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using namespace std;
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double factorial(double n){
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if( n < 0 ) return -100.;
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return (n == 1. || n == 0.) ? 1. : factorial(n-1) * n ;
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}
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double CGcoeff(double J, double m, double J1, double m1, double J2, double m2){
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// (J1,m1) + (J2, m2) = (J, m)
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if( m != m1 + m2 ) return 0;
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double Jmin = abs(J1 - J2);
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double Jmax = J1+J2;
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if( J < Jmin || Jmax < J ) return 0;
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double s0 = (2*J+1.) * factorial(J+J1-J2) * factorial(J-J1+J2) * factorial(J1+J2-J) / factorial(J+J1+J2 + 1.);
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s0 = sqrt(s0);
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double s = factorial(J +m ) * factorial(J -m);
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double s1 = factorial(J1+m1) * factorial(J1-m1);
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double s2 = factorial(J2+m2) * factorial(J2-m2);
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s = sqrt(s * s1 * s2);
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//printf(" s0, s = %f , %f \n", s0, s);
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int kMax = min( min( J1+J2-J, J1 - m1), J2 + m2);
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double CG = 0.;
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for( int k = 0; k <= kMax; k++){
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double k1 = factorial(J1+J2-J-k);
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double k2 = factorial(J1-m1-k);
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double k3 = factorial(J2+m2-k);
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double k4 = factorial(J - J2 + m1 +k);
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double k5 = factorial(J - J1 - m2 +k);
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double temp = pow(-1, k) / (factorial(k) * k1 * k2 * k3 * k4 * k5);
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if( k1 == -100. || k2 == -100. || k3 == -100. || k4 == -100. || k5 == -100. ) temp = 0.;
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//printf(" %d | %.12f | %.12f | %.12f | %.12f | %.12f | %.12f, %f \n", k, k1, k2, k3, k4, k5, temp, factorial(k) );
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CG += temp;
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}
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return s0*s*CG;
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}
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double ThreeJSymbol(double J1, double m1, double J2, double m2, double J3, double m3){
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// ( J1 J2 J3 ) = (-1)^(J1-J2 - m3)/ sqrt(2*J3+1) * CGcoeff(J3, -m3, J1, m1, J2, m2)
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// ( m1 m2 m3 )
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return pow(-1, J1 - J2 - m3)/sqrt(2*J3+1) * CGcoeff(J3, -m3, J1, m1, J2, m2);
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}
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double SixJSymbol(double J1, double J2, double J3, double J4, double J5, double J6){
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// coupling of j1, j2, j3 to J-J1
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// J1 = j1
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// J2 = j2
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// J3 = j12 = j1 + j2
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// J4 = j3
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// J5 = J = j1 + j2 + j3
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// J6 = j23 = j2 + j3
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//check triangle condition
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if( J3 < abs(J1 - J2 ) || J1 + J2 < J3 ) return 0;
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if( J6 < abs(J2 - J4 ) || J2 + J4 < J6 ) return 0;
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if( J5 < abs(J1 - J6 ) || J1 + J6 < J5 ) return 0;
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if( J5 < abs(J3 - J4 ) || J3 + J4 < J5 ) return 0;
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double sixJ = 0;
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for( float m1 = -J1; m1 <= J1 ; m1 = m1 + 1){
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for( float m2 = -J2; m2 <= J2 ; m2 = m2 + 1){
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for( float m3 = -J3; m3 <= J3 ; m3 = m3 + 1){
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for( float m4 = -J4; m4 <= J4 ; m4 = m4 + 1){
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for( float m5 = -J5; m5 <= J5 ; m5 = m5 + 1){
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for( float m6 = -J6; m6 <= J6 ; m6 = m6 + 1){
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double f = (J1 - m1) + (J2 - m2) + (J3 - m3) + (J4 - m4) + (J5 - m5) + (J6 - m6);
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double a1 = ThreeJSymbol( J1, -m1, J2, -m2, J3, -m3); // J3 = j12
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double a2 = ThreeJSymbol( J1, m1, J5, -m5, J6, m6); // J5 = j1 + (J6 = j23)
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double a3 = ThreeJSymbol( J4, m4, J2, m2, J6, -m6); // J6 = j23
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double a4 = ThreeJSymbol( J4, -m4, J5, m5, J3, m3); // J5 = j3 + j12
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double a = a1 * a2 * a3 * a4;
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//if( a != 0 ) printf("%4.1f %4.1f %4.1f %4.1f %4.1f %4.1f | %f \n", m1, m2, m3, m4, m5, m6, a);
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sixJ += pow(-1, f) * a1 * a2 * a3 * a4;
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}
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}
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}
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}
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}
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}
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return sixJ;
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}
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double NineJSymbol( double J1, double J2, double J3, double J4, double J5, double J6, double J7, double J8, double J9){
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double gMin = min( min (min( abs(J1 - J2 ), abs(J4 - J5)) , abs( J4 - J6 )) , abs(J7 - J8));
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double gMax = max( max (max( J1+J2, J4+J5), J3+J6), J7+J8);
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//printf(" gMin, gMax = %f %f \n", gMin, gMax);
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double nineJ = 0;
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for( float g = gMin; g <= gMax ; g = g + 1){
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double f = pow(-1, 2*g) * (2*g+1);
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double s1 = SixJSymbol(J1, J4, J7, J8, J9, g);
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if( s1 == 0 ) continue;
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double s2 = SixJSymbol(J2, J5, J8, J4, g, J6);
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if( s2 == 0 ) continue;
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double s3 = SixJSymbol(J3, J6, J9, g, J1, J2);
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if( s3 == 0 ) continue;
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nineJ += f* s1*s2*s3;
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}
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return nineJ;
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}
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