C #RACAH V1A 15-FEB-72. C LAST UPDATE: C FUNCTION RACAH(J1,J2,J3,J4,J5,J6) C C *PURPOSE. C TO EVALUATE THE RACAH OR "6-J" RECOUPLING COEFFICIENT C AS DEFINED IN ANY STANDARD WORK ON ANGULAR MOMENTUM. C C *PARAMETERS: C C J1 - INTEGER FIRST ANGULAR MOMENTUM QUANTUM NUMBER C J2 - THE SECOND C J3 - THE THIRD C J4 - THE FOURTH C J5 - THE FIFTH C J6 - THE SIXTH. C C NOTE!! BY CONVENTION ALL ANGULAR MOMENTUM QUANTUM NUMBERS ARE C INTEGERS WITH TWICE THEIR PHYSICAL VALUES. THIS APPLIES TO ALL C THE PARAMETERS ABOVE. THE RACHA COEFFICIENT RETURNED BY THE C ABOVE CALL IS WRITTEN C C W(J1, J2, J3, J4; J5, J6) C C INPUT PARAMETERS: C J1, J2, J3, J4, J5, J6 C OUTPUT PARAMETERS: C (REAL FUNCTION VALUE ONLY) C C *METHOD. C THE FORMULA ORIGINALLY DUE TO G.RACAH, PHYS REV 62(1942)438 C GIVES THE COEFFICIENT AS A PRODUCT OF TRIANGLE FUNCTIONS AND A C SUM OF TERMS INVOLVING FACTORIALS. C THE SUM IS EVALUATED BY DOING THE FIRST TERM AND THEN C GETTING SUCCESSIVE TERMS BY A SIMPLE RECURRENCE RELATION. C C *ACCURACY. C C *RESTRICTIONS. C C *ERROR CONDITIONS. C IF THE INPUT "J"S ARE NOT PHYSICALLY POSSIBLE THE VALUE C RETURNED WILL BE ZERO. C C *NON STANDARD ROUTINES CALLED. C TRIANG - TRAINGLE FUNCTION OF FACTORIALS - MRMLIB. C FAC2 - FACTORIAL OF HALF ITS ARGUMENT - MRMLIB. C C *TYPICAL TIMES. C C *ORIGIN. M.R.MANNING. C C *COMMENTS. C C #END. C IR1=J1+J2+J3+J4 IR2=J1+J4+J5+J6 IR3=J2+J3+J5+J6 JR1=J1+J2+J5 JR2=J3+J4+J5 JR3=J1+J3+J6 JR4=J2+J4+J6 J=MAX0(JR1,JR2,JR3,JR4) IND=MIN0(IR1,IR2,IR3) RACAH=SQRT(TRIANG(J1,J2,J5)*TRIANG(J3,J4,J5)*TRIANG(J1,J3,J6)* X TRIANG(J2,J4,J6) ) SUM=0. TRM=PARITY((IR1+J)/2)*FAC2(J+2)/( FAC2(J-JR1)*FAC2(J-JR2)* X FAC2(J-JR3)*FAC2(J-JR4)*FAC2(IR1-J)*FAC2(IR2-J)*FAC2(IR3-J) ) 10 I=J SUM=SUM+TRM IF(I-IND) 12,20,20 12 J=I+2 TRM=-TRM*FLOAT( (J+2)*(IR1-I)*(IR2-I)*(IR3-I))/FLOAT( (J-JR1)* X (J-JR2)*(J-JR3)*(J-JR4)) GO TO 10 C 20 RACAH= RACAH*SUM RETURN END