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sixj.f90
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sixj.f90
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SUBROUTINE SIXJ(I,J,K,L,M,N,ITIK,SI)
!*******************************************************************
! *
! THIS PACKAGE DETERMINES THE VALUES OF 6j COEFFICIENT *
! *
! | I/2 J/2 K/2 | *
! | L/2 M/2 N/2 | (29.1A) [J.B.77] *
! *
! This restructured package uses the CONTAINS keyword to group *
! related subroutines together into self-contained blocks, *
! rather than relying on calls to subroutines in separate files. *
! The ultimate aim is to reduce the size and complexity of the *
! "librang90" library. *
! *
! Written by G. Gaigalas, *
! Vanderbilt University, Nashville October 1996 *
! Transform to fortran 90/95 by G. Gaigalas December 2012 *
! The last modification made by G. Gaigalas October 2017 *
! Reststructured by A. Senchuk May 2019 *
! *
!*******************************************************************
!
!-----------------------------------------------
! M o d u l e s
!-----------------------------------------------
USE vast_kind_param, ONLY: DOUBLE
USE CONS_C, ONLY: ZERO, ONE
!-----------------------------------------------
! I n t e r f a c e B l o c k s
!-----------------------------------------------
USE ixjtik_I
USE dracah_I
IMPLICIT NONE
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER :: I, J, K, L, M, N
INTEGER, INTENT(IN) :: ITIK
REAL(DOUBLE) :: SI
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: IFA
REAL(DOUBLE), DIMENSION(0:4,0:4,0:4,0:4,0:4,0:4) :: RACA
REAL(DOUBLE) :: UNDEF, A
LOGICAL :: SAVE
!-----------------------------------------------
DATA RACA/ 15625*1.D-20/
DATA UNDEF/ 1.D-20/
SI = ZERO
IF (ITIK /= 0) THEN
!
! CHESKED TRIANGULAR CONDITIONS
!
IF (IXJTIK(I,J,K,L,M,N) == 0) RETURN
ENDIF
SAVE = .FALSE.
IF (MAX0(I,J,K,L,M,N) <= 4) THEN
SI = RACA(I,J,K,L,M,N)
IF (SI == UNDEF) THEN
SAVE = .TRUE.
ELSE
RETURN
ENDIF
ENDIF
!
! CALCULATED IN CASE WHEN ONE OF PERAMETERS EQUAL 0
!
IF (I*J*K*L*M*N == 0) THEN
IF (I == 0) THEN
A = DBLE((M + 1)*(K + 1))
IFA = L + M + K
ELSE IF (J == 0) THEN
A = DBLE((L + 1)*(K + 1))
IFA = I + M + N
ELSE IF (K == 0) THEN
A = DBLE((I + 1)*(L + 1))
IFA = I + M + N
ELSE IF (L == 0) THEN
A = DBLE((J + 1)*(K + 1))
IFA = I + J + K
ELSE IF (M == 0) THEN
A = DBLE((I + 1)*(K + 1))
IFA = I + J + K
ELSE
A = DBLE((I + 1)*(J + 1))
IFA = I + J + K
ENDIF
SI = ONE/DSQRT(A)
IF (MOD(IFA,4) /= 0) SI = -SI
!
! THE CASE 1/2
!
ELSE IF (MIN0(I,J,K,L,M,N) == 1) THEN
IF (I == 1) THEN
CALL SIXJ5 (M, K, L, J, N, 0, SI)
ELSE IF (J == 1) THEN
CALL SIXJ5 (I, N, M, L, K, 0, SI)
ELSE IF (K == 1) THEN
CALL SIXJ5 (I, M, N, L, J, 0, SI)
ELSE IF (L == 1) THEN
CALL SIXJ5 (J, K, I, M, N, 0, SI)
ELSE IF (M == 1) THEN
CALL SIXJ5 (I, K, J, L, N, 0, SI)
ELSE
CALL SIXJ5 (I, J, K, L, M, 0, SI)
ENDIF
!
! THE CASE 1
!
ELSE IF (MIN0(I,J,K,L,M,N) == 2) THEN
IF (I == 2) THEN
CALL SIXJ1 (M, K, L, J, N, 0, SI)
ELSE IF (J == 2) THEN
CALL SIXJ1 (I, N, M, L, K, 0, SI)
ELSE IF (K == 2) THEN
CALL SIXJ1 (I, M, N, L, J, 0, SI)
ELSE IF (L == 2) THEN
CALL SIXJ1 (J, K, I, M, N, 0, SI)
ELSE IF (M == 2) THEN
CALL SIXJ1 (I, K, J, L, N, 0, SI)
ELSE
CALL SIXJ1 (I, J, K, L, M, 0, SI)
ENDIF
!
! THE CASE 3/2
!
ELSE IF (MIN0(I,J,K,L,M,N) == 3) THEN
IF (I == 3) THEN
CALL SIXJ35 (M, K, L, J, N, 0, SI)
ELSE IF (J == 3) THEN
CALL SIXJ35 (I, N, M, L, K, 0, SI)
ELSE IF (K == 3) THEN
CALL SIXJ35 (I, M, N, L, J, 0, SI)
ELSE IF (L == 3) THEN
CALL SIXJ35 (J, K, I, M, N, 0, SI)
ELSE IF (M == 3) THEN
CALL SIXJ35 (I, K, J, L, N, 0, SI)
ELSE
CALL SIXJ35 (I, J, K, L, M, 0, SI)
ENDIF
!
! THE CASE 2
!
ELSE IF (MIN0(I,J,K,L,M,N) == 4) THEN
IF (I == 4) THEN
CALL SIXJ2 (M, K, L, J, N, 0, SI)
ELSE IF (J == 4) THEN
CALL SIXJ2 (I, N, M, L, K, 0, SI)
ELSE IF (K == 4) THEN
CALL SIXJ2 (I, M, N, L, J, 0, SI)
ELSE IF (L == 4) THEN
CALL SIXJ2 (J, K, I, M, N, 0, SI)
ELSE IF (M == 4) THEN
CALL SIXJ2 (I, K, J, L, N, 0, SI)
ELSE
CALL SIXJ2 (I, J, K, L, M, 0, SI)
ENDIF
!
! THE CASE 5/2
!
ELSE IF (MIN0(I,J,K,L,M,N) == 5) THEN
CALL DRACAH (I, J, M, L, K, N, SI)
IF (MOD(I + J + M + L,4) /= 0) SI = -SI
!
! CASES 3
!
ELSE IF (MIN0(I,J,K,L,M,N) == 6) THEN
IF (I == 6) THEN
CALL SIXJ3 (M, K, L, J, N, 0, SI)
ELSE IF (J == 6) THEN
CALL SIXJ3 (I, N, M, L, K, 0, SI)
ELSE IF (K == 6) THEN
CALL SIXJ3 (I, M, N, L, J, 0, SI)
ELSE IF (L == 6) THEN
CALL SIXJ3 (J, K, I, M, N, 0, SI)
ELSE IF (M == 6) THEN
CALL SIXJ3 (I, K, J, L, N, 0, SI)
ELSE
CALL SIXJ3 (I, J, K, L, M, 0, SI)
ENDIF
!
! THE CASE 7/2
!
ELSE IF (MIN0(I,J,K,L,M,N) == 7) THEN
CALL DRACAH (I, J, M, L, K, N, SI)
IF (MOD(I + J + M + L,4) /= 0) SI = -SI
!
! CASES 4
!
ELSE IF (MIN0(I,J,K,L,M,N) == 8) THEN
IF (I == 8) THEN
CALL SIXJ4 (M, K, L, J, N, 0, SI)
ELSE IF (J == 8) THEN
CALL SIXJ4 (I, N, M, L, K, 0, SI)
ELSE IF (K == 8) THEN
CALL SIXJ4 (I, M, N, L, J, 0, SI)
ELSE IF (L == 8) THEN
CALL SIXJ4 (J, K, I, M, N, 0, SI)
ELSE IF (M == 8) THEN
CALL SIXJ4 (I, K, J, L, N, 0, SI)
ELSE
CALL SIXJ4 (I, J, K, L, M, 0, SI)
ENDIF
!
! THE CASE 9/2
!
ELSE IF (MIN0(I,J,K,L,M,N) == 9) THEN
CALL DRACAH (I, J, M, L, K, N, SI)
IF (MOD(I + J + M + L,4) /= 0) SI = -SI
!
! CALCULATED OTHER CASES
!
ELSE
CALL DRACAH(I,J,M,L,K,N,SI)
IF (MOD(I + J + M + L,4) /= 0) SI = -SI
ENDIF
IF (SAVE) RACA(I,J,K,L,M,N) = SI
RETURN
CONTAINS
SUBROUTINE SIXJ5(J,K,L,M,N,ITIK,SI)
!*******************************************************************
! THIS PACKAGE DETERMINES THE VALUES OF 6j COEFFICIENT *
! *
! | J/2 K/2 L/2 | *
! | M/2 N/2 1/2 | [B.M.X. 75] *
! *
! Written by G. Gaigalas, *
! Vilnius, Lithuania March 1995 *
! Transform to fortran 90/95 by G. Gaigalas December 2012 *
! The last modification made by G. Gaigalas October 2017 *
! Restructed by C. Froese Fischer May 2019 *
! *
!*******************************************************************
!
IMPLICIT NONE
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER :: J, K, L, M, N
INTEGER, INTENT(IN) :: ITIK
REAL(DOUBLE), INTENT(OUT) :: SI
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: I1
REAL(DOUBLE) :: AS, A, B, C, AKA
!-----------------------------------------------
SI = ZERO
IF (ITIK /= 0) THEN
!
! CHESKED TRIANGULAR CONDITIONS
!
IF (IXJTIK(J,K,L,M,N,1) == 0) RETURN
ENDIF
I1 = (J + K + L)/2
AS = DBLE(I1)
A = DBLE(L)
B = DBLE(K)
C = DBLE(J)
AKA = ONE
IF (MOD(I1,2) /= 0) AKA = -AKA
IF (K < M) THEN
IF (J < N) THEN
! M > K, J < N.
SI = -AKA*DSQRT((AS + TWO)*(AS - A + ONE)/((B + ONE)*(B + TWO)*(C &
+ ONE)*(C + TWO)))
ELSE IF (J > N) THEN
! M > K, J > N.
SI = AKA*DSQRT((AS - C + ONE)*(AS - B)/((B + ONE)*(B + TWO)*C*(C + &
ONE)))
ENDIF
ELSE IF (K > M) THEN
IF (J < N) THEN
! M < K, J < N.
SI = AKA*DSQRT((AS - C)*(AS - B + ONE)/(B*(B + ONE)*(C + ONE)*(C + &
TWO)))
ELSE IF (J > N) THEN
! M < K, J > N.
SI = AKA*DSQRT((AS + ONE)*(AS - A)/(B*(B + ONE)*C*(C + ONE)))
ENDIF
ENDIF
RETURN
END SUBROUTINE SIXJ5
!
!##############################################################################
!
SUBROUTINE SIXJ1(I,J,K,L,M,ITIK,SI)
!*******************************************************************
! THIS PACKAGE DETERMINES THE VALUES OF 6j COEFFICIENT *
! *
! | I/2 J/2 K/2 | *
! | L/2 M/2 1 | [B.M.X. 75]. *
! *
! Written by G. Gaigalas, *
! Vilnius, Lithuania March 1995 *
! Transform to fortran 90/95 by G. Gaigalas December 2012 *
! The last modification made by G. Gaigalas October 2017 *
! Restructed by A. Senchuk September 2019 *
! *
!*******************************************************************
!
IMPLICIT NONE
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER :: I, J, K, L, M
INTEGER, INTENT(IN) :: ITIK
REAL(DOUBLE), INTENT(OUT) :: SI
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: IFA
REAL(DOUBLE) :: AS, AKA, A, B, C
!-----------------------------------------------
SI = ZERO
IF (ITIK /= 0) THEN
!
! CHESKED TRIANGULAR CONDITIONS
!
IF (IXJTIK(I,J,K,L,M,2) == 0) RETURN
ENDIF
IFA = (I + J + K)/2
AS = DBLE(IFA)
AKA = ONE
IF (MOD(IFA,2) /= 0) AKA = -AKA
A = DBLE(K)
B = DBLE(J)
C = DBLE(I)
IF (I < M) THEN
IF (J < L) THEN
! M > I, L > J.
SI = AKA*DSQRT((AS + TWO)*(AS + THREE)*(AS - A + ONE)*(AS - A + TWO &
)/((B + ONE)*(B + TWO)*(B + THREE)*(C + ONE)*(C + TWO)*(C + &
THREE)))
ELSE IF (J == L) THEN
! M > I, L = J.
SI = (-AKA)*DSQRT(TWO*(AS + TWO)*(AS - C)*(AS - B + ONE)*(AS - A + &
ONE)/(B*(B + ONE)*(B + TWO)*(C + ONE)*(C + TWO)*(C + THREE)))
ELSE
! M > I, L < J.
SI = AKA*DSQRT((AS - C - ONE)*(AS - C)*(AS - B + ONE)*(AS - B + TWO &
)/((B - ONE)*B*(B + ONE)*(C + ONE)*(C + TWO)*(C + THREE)))
ENDIF
ELSE IF (I == M) THEN
IF (J < L) THEN
! M = L, L > J.
SI = (-AKA)*DSQRT((AS + TWO)*(AS - C + ONE)*(AS - B)*(AS - A + ONE) &
*TWO/((B + ONE)*(B + TWO)*(B + THREE)*C*(C + ONE)*(C + TWO)))
ELSE IF (J == L) THEN
! M = I, L = J.
SI = (-AKA)*((B*B + C*C - A*A)*HALF + B + C - A)/DSQRT(B*(B + ONE)* &
(B + TWO)*C*(C + ONE)*(C + TWO))
ELSE
! M = I, L < J.
SI = AKA*DSQRT((AS + ONE)*(AS - C)*(AS - B + ONE)*(AS - A)*TWO/((B &
- ONE)*B*(B + ONE)*C*(C + ONE)*(C + TWO)))
ENDIF
ELSE
IF (J < L) THEN
! M < I, L > J.
SI = AKA*DSQRT((AS - C + ONE)*(AS - C + TWO)*(AS - B - ONE)*(AS - B &
)/((B + ONE)*(B + TWO)*(B + THREE)*(C - ONE)*C*(C + ONE)))
ELSE IF (J == L) THEN
! M < I, L = J.
SI = AKA*DSQRT((AS + ONE)*(AS - C + ONE)*(AS - B)*(AS - A)*TWO/(B*( &
B + ONE)*(B + TWO)*(C - ONE)*C*(C + ONE)))
ELSE
! M < I, L < J.
SI = AKA*DSQRT(AS*(AS + ONE)*(AS - A - ONE)*(AS - A)/((B - ONE)*B*( &
B + ONE)*(C - ONE)*C*(C + ONE)))
ENDIF
ENDIF
RETURN
END SUBROUTINE SIXJ1
!
!##############################################################################
!
SUBROUTINE SIXJ35(J,K,L,M,N,ITIK,SI)
!*******************************************************************
! THIS PACKAGE DETERMINES THE VALUES OF 6j COEFFICIENT *
! *
! | J/2 K/2 L/2 | *
! | M/2 N/2 3/2 | [B.M.X. 75] *
! *
! Written by G. Gaigalas, *
! Vanderbilt University, Nashville October 1996 *
! Transform to fortran 90/95 by G. Gaigalas December 2012 *
! The last modification made by G. Gaigalas October 2017 *
! *
! Restructed by C. Froese Fischer May 2019 *
!*******************************************************************
!
IMPLICIT NONE
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER :: J, K, L, M, N
INTEGER, INTENT(IN) :: ITIK
REAL(DOUBLE), INTENT(OUT) :: SI
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: I1
REAL(DOUBLE) :: AS, A, B, C, AKA
!-----------------------------------------------
SI = ZERO
IF (ITIK /= 0) THEN
!
! CHESKED TRIANGULAR CONDITIONS
!
IF (IXJTIK(J,K,L,M,N,3) == 0) RETURN
ENDIF
I1 = (J + K + L)/2
AS = DBLE(I1)
A = DBLE(L)
B = DBLE(J)
C = DBLE(K)
AKA = ONE
IF (MOD(I1,2) /= 0) AKA = -AKA
IF (J - N == 3) THEN
! -3
IF (K - M == 3) THEN
! I -3/2 -3/2
SI = AKA*DSQRT((AS - ONE)*AS*(AS + ONE)*(AS - A - TWO)*(AS - A - &
ONE)*(AS - A)/((B - TWO)*(B - ONE)*B*(B + ONE)*(C - TWO)*(C - &
ONE)*C*(C + ONE)))
ELSE IF (M - K == 3) THEN
! IV P(12) 3/2 -3/2
SI = AKA*DSQRT((AS - C - TWO)*(AS - C - ONE)*(AS - C)*(AS - B + ONE &
)*(AS - B + TWO)*(AS - B + THREE)/((C + 1)*(C + TWO)*(C + THREE) &
*(C + FOUR)*(B - TWO)*(B - ONE)*B*(B + ONE)))
ELSE IF (K - M == 1) THEN
! II P(12) -1/2 -3/2
SI = AKA*DSQRT(THREE*AS*(AS + ONE)*(AS - A - ONE)*(AS - A)*(AS - C) &
*(AS - B + ONE)/((C - ONE)*C*(C + ONE)*(C + TWO)*(B - TWO)*(B - &
ONE)*B*(B + ONE)))
ELSE IF (M - K == 1) THEN
! III P(12) 1/2 -3/2
SI = AKA*DSQRT(THREE*(AS + ONE)*(AS - A)*(AS - C - ONE)*(AS - C)*( &
AS - B + ONE)*(AS - B + TWO)/(C*(C + ONE)*(C + TWO)*(C + THREE)* &
(B - TWO)*(B - ONE)*B*(B + ONE)))
ENDIF
ELSE IF (N - J == 3) THEN
! 3
IF (K - M == 3) THEN
! IV -3/2 3/2
SI = AKA*DSQRT((AS - B - TWO)*(AS - B - ONE)*(AS - B)*(AS - C + ONE &
)*(AS - C + TWO)*(AS - C + THREE)/((B + ONE)*(B + TWO)*(B + &
THREE)*(B + FOUR)*(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 3) THEN
! 2 pataisyta 3/2 3/2
SI = -AKA*DSQRT((AS + TWO)*(AS + THREE)*(AS + FOUR)*(AS - A + ONE)* &
(AS - A + TWO)*(AS - A + THREE)/((B + ONE)*(B + TWO)*(B + THREE) &
*(B + FOUR)*(C + ONE)*(C + TWO)*(C + THREE)*(C + FOUR)))
ELSE IF (K - M == 1) THEN
! 1 P(12) pataisytas -1/2 3/2
SI = -AKA*DSQRT(THREE*(AS + TWO)*(AS - A + ONE)*(AS - C + ONE)*(AS &
- C + TWO)*(AS - B - ONE)*(AS - B)/((C - ONE)*C*(C + ONE)*(C + &
TWO)*(B + ONE)*(B + TWO)*(B + THREE)*(B + FOUR)))
ELSE IF (M - K == 1) THEN
! 3 P(12) taisyta 1/2 3/2
SI = AKA*DSQRT(THREE*(AS + TWO)*(AS + THREE)*(AS - A + ONE)*(AS - A &
+ TWO)*(AS - B)*(AS - C + ONE)/(C*(C + ONE)*(C + TWO)*(C + &
THREE)*(B + ONE)*(B + TWO)*(B + THREE)*(B + FOUR)))
ENDIF
! -1
ELSE IF (J - N == 1) THEN
IF (K - M == 3) THEN
! II -3/2 -1/2
SI = AKA*DSQRT((THREE*AS*(AS + ONE)*(AS - A - ONE)*(AS - A)*(AS - B &
)*(AS - C + ONE))/((B - ONE)*B*(B + ONE)*(B + TWO)*(C - TWO)*(C &
- ONE)*C*(C + ONE)))
ELSE IF (M - K == 3) THEN
! 1 3/2 -1/2
SI = -AKA*DSQRT(THREE*(AS + TWO)*(AS - A + ONE)*(AS - B + ONE)*(AS &
- B + TWO)*(AS - C - ONE)*(AS - C)/((B - ONE)*B*(B + ONE)*(B + &
TWO)*(C + ONE)*(C + TWO)*(C + THREE)*(C + FOUR)))
ELSE IF (K - M == 1) THEN
! V -1/2 -1/2
SI = AKA*(TWO*(AS - B)*(AS - C) - (AS + TWO)*(AS - A - ONE))*DSQRT( &
(AS + ONE)*(AS - A)/((B - ONE)*B*(B + ONE)*(B + TWO)*(C - ONE)*C &
*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 1) THEN
! VI P(12) 1/2 -1/2
SI = AKA*((AS - B + TWO)*(AS - C + ONE) - TWO*(AS - A + ONE)*(AS + &
ONE))*DSQRT((AS - C)*(AS - B + ONE)/(C*(C + ONE)*(C + TWO)*(C + &
THREE)*(B - ONE)*B*(B + ONE)*(B + TWO)))
ENDIF
! 1
ELSE IF (N - J == 1) THEN
IF (K - M == 3) THEN
! III -3/2 1/2
SI = AKA*DSQRT(THREE*(AS + ONE)*(AS - A)*(AS - B - ONE)*(AS - B)*( &
AS - C + ONE)*(AS - C + TWO)/(B*(B + ONE)*(B + TWO)*(B + THREE)* &
(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 3) THEN
! 3 pataisyta 3/2 1/2
SI = AKA*DSQRT(THREE*(AS + TWO)*(AS + THREE)*(AS - A + ONE)*(AS - A &
+ TWO)*(AS - B + ONE)*(AS - C)/(B*(B + ONE)*(B + TWO)*(B + &
THREE)*(C + ONE)*(C + TWO)*(C + THREE)*(C + FOUR)))
ELSE IF (K - M == 1) THEN
! VI -1/2 1/2
SI = AKA*((AS - C + TWO)*(AS - B + ONE) - TWO*(AS - A + ONE)*(AS + &
ONE))*DSQRT((AS - B)*(AS - C + ONE)/(B*(B + ONE)*(B + TWO)*(B + &
THREE)*(C - ONE)*C*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 1) THEN
! 4 pataisyta 1/2 1/2
SI = -AKA*(TWO*(AS - B)*(AS - C) - (AS + THREE)*(AS - A))*DSQRT((AS &
+ TWO)*(AS - A + ONE)/(B*(B + ONE)*(B + TWO)*(B + THREE)*C*(C &
+ ONE)*(C + TWO)*(C + THREE)))
ENDIF
ENDIF
RETURN
END SUBROUTINE SIXJ35
!
!################################################################################
!
SUBROUTINE SIXJ2(J,K,L,M,N,ITIK,SI)
!*******************************************************************
! THIS PACKAGE DETERMINES THE VALUES OF 6j COEFFICIENT *
! *
! | J/2 K/2 L/2 | *
! | M/2 N/2 2 | [B.M.X. 75] *
! *
! Written by G. Gaigalas, *
! Vanderbilt University, Nashville October 1996 *
! Transform to fortran 90/95 by G. Gaigalas December 2012 *
! The last modification made by G. Gaigalas October 2017 *
! Restructed by A. Senchuk September 2019 *
! *
!*******************************************************************
IMPLICIT NONE
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER :: J, K, L, M, N
INTEGER, INTENT(IN) :: ITIK
REAL(DOUBLE), INTENT(OUT) :: SI
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: I1
REAL(DOUBLE) :: AS, A, B, C, AKA, X1, X2, X3
!-----------------------------------------------
SI = ZERO
IF (ITIK /= 0) THEN
!
! CHESKED TRIANGULAR CONDITIONS
!
IF (IXJTIK(J,K,L,M,N,4) == 0) RETURN
ENDIF
I1 = (J + K + L)/2
AS = DBLE(I1)
A = DBLE(L)
B = DBLE(J)
C = DBLE(K)
AKA = ONE
IF (MOD(I1,2) /= 0) AKA = -AKA
IF (J - N == 4) THEN
! -2
IF (K - M == 4) THEN
! I -2 -2
SI = AKA*DSQRT((AS - TWO)*(AS - ONE)*AS*(AS + ONE)/((B - THREE)*(B &
- TWO)*(B - ONE)*B*(B + ONE)))
SI = SI*DSQRT((AS - A - THREE)*(AS - A - TWO)*(AS - A - ONE)*(AS - &
A)/((C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 4) THEN
! V P(12) 2 -2
SI = AKA*DSQRT((AS - C - THREE)*(AS - C - TWO)*(AS - C - ONE)*(AS &
- C)/((C + ONE)*(C + TWO)*(C + THREE)*(C + FOUR)*(C + TWO + &
THREE)))
SI = SI*DSQRT((AS - B + ONE)*(AS - B + TWO)*(AS - B + THREE)*(AS - &
B + FOUR)/((B - THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)))
ELSE IF (K - M == 2) THEN
! II P(12) -1 -2
SI = AKA*TWO*DSQRT((AS - ONE)*AS*(AS + ONE)/((C - TWO)*(C - ONE)*C* &
(C + ONE)*(C + TWO)))
SI = SI*DSQRT((AS - A - TWO)*(AS - A - ONE)*(AS - A)*(AS - C)*(AS &
- B + ONE)/((B - THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)))
ELSE IF (M - K == 2) THEN
! IV P(12) 1 -2
SI = AKA*TWO*DSQRT((AS + ONE)*(AS - A)*(AS - C - TWO)*(AS - C - ONE &
)*(AS - C)/(C*(C + ONE)*(C + TWO)*(C + THREE)*(C + FOUR)))
SI = SI*DSQRT((AS - B + ONE)*(AS - B + TWO)*(AS - B + THREE)/((B - &
THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)))
ELSE IF (K - M == 0) THEN
! III P(12) 0 -2
SI = AKA*DSQRT(TWO*THREE*AS*(AS + ONE)*(AS - A - ONE)*(AS - A)/((C &
- ONE)*C*(C + ONE)*(C + TWO)*(C + THREE)))
SI = SI*DSQRT((AS - C - ONE)*(AS - C)*(AS - B + ONE)*(AS - B + TWO) &
/((B - THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)))
ENDIF
! 2
ELSE IF (N - J == 4) THEN
IF (K - M == 4) THEN
! V -2 2
SI = AKA*DSQRT((AS - B - THREE)*(AS - B - TWO)*(AS - B - ONE)*(AS &
- B)/((B + ONE)*(B + TWO)*(B + THREE)*(B + FOUR)*(B + TWO + &
THREE)))
SI = SI*DSQRT((AS - C + ONE)*(AS - C + TWO)*(AS - C + THREE)*(AS - &
C + FOUR)/((C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 4) THEN
! 1 2 2
SI = AKA*DSQRT((AS - A + FOUR)*(AS - A + THREE)*(AS - A + TWO)*(AS &
- A + ONE)/((B + THREE + TWO)*(B + FOUR)*(B + THREE)*(B + TWO)* &
(B + ONE)))
SI = SI*DSQRT((AS + THREE + TWO)*(AS + FOUR)*(AS + THREE)*(AS + TWO &
)/((C + THREE + TWO)*(C + FOUR)*(C + THREE)*(C + TWO)*(C + ONE)) &
)
ELSE IF (K - M == 2) THEN
! 3 -1 2
SI = -AKA*DSQRT((AS - A + ONE)*(AS + TWO)*(AS - B - TWO)*(AS - B - &
ONE)*(AS - B)/((B + TWO + THREE)*(B + FOUR)*(B + THREE)*(B + TWO &
)*(B + ONE)))
SI = SI*TWO*DSQRT((AS - C + THREE)*(AS - C + TWO)*(AS - C + ONE)/(( &
C - TWO)*(C - ONE)*C*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 2) THEN
! 2 1 2
SI = -AKA*DSQRT((AS - B)*(AS - C + ONE)*(AS - A + THREE)*(AS - A + &
TWO)*(AS - A + ONE)/((B + THREE + TWO)*(B + FOUR)*(B + THREE)*(B &
+ TWO)*(B + ONE)))
SI = SI*TWO*DSQRT((AS + FOUR)*(AS + THREE)*(AS + TWO)/((C + FOUR)*( &
C + THREE)*(C + TWO)*(C + ONE)*C))
ELSE IF (K - M == 0) THEN
! 5 0 2
SI = AKA*DSQRT(THREE*TWO*(AS - B)*(AS - B - ONE)*(AS - C + TWO)*(AS &
- C + ONE)/((B + THREE + TWO)*(B + FOUR)*(B + THREE)*(B + TWO)* &
(B + ONE)))
SI = SI*DSQRT((AS - A + TWO)*(AS - A + ONE)*(AS + THREE)*(AS + TWO) &
/((C + THREE)*(C + TWO)*(C + ONE)*C*(C - ONE)))
ENDIF
ELSE IF (J - N == 2) THEN
! -1
IF (K - M == 4) THEN
! II P(12) -2 -1
SI = AKA*TWO*DSQRT((AS - ONE)*AS*(AS + ONE)/((B - TWO)*(B - ONE)*B* &
(B + ONE)*(B + TWO)))
SI = SI*DSQRT((AS - A - TWO)*(AS - A - ONE)*(AS - A)*(AS - B)*(AS &
- C + ONE)/((C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 4) THEN
! 3 P(12) 2 -1
SI = -AKA*DSQRT((AS - A + ONE)*(AS + TWO)*(AS - C - TWO)*(AS - C - &
ONE)*(AS - C)/((C + TWO + THREE)*(C + FOUR)*(C + THREE)*(C + TWO &
)*(C + ONE)))
SI = SI*TWO*DSQRT((AS - B + THREE)*(AS - B + TWO)*(AS - B + ONE)/(( &
B - TWO)*(B - ONE)*B*(B + ONE)*(B + TWO)))
ELSE IF (K - M == 2) THEN
! VI -1 -1
SI = AKA*((A + B)*(A - B + TWO) - (C - TWO)*(C - B + TWO))/DSQRT((B &
- TWO)*(B - ONE)*B*(B + ONE)*(B + TWO))
SI = SI*DSQRT(AS*(AS + ONE)*(AS - A - ONE)*(AS - A)/((C - TWO)*(C &
- ONE)*C*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 2) THEN
! VIII P(12) 1 -1
SI = AKA*((A + C + FOUR)*(A - C - TWO) - (B - TWO)*(B + C + FOUR))/ &
DSQRT(C*(C + ONE)*(C + TWO)*(C + THREE)*(C + FOUR))
SI = SI*DSQRT((AS - C - ONE)*(AS - C)*(AS - B + ONE)*(AS - B + TWO) &
/((B - TWO)*(B - ONE)*B*(B + ONE)*(B + TWO)))
ELSE IF (K - M == 0) THEN
! VII P(12) 0 -1
SI = AKA*HALF*((A + C + TWO)*(A - C) - B*B + FOUR)/DSQRT((C - ONE)* &
C*(C + ONE)*(C + TWO)*(C + THREE))
SI = SI*DSQRT(THREE*TWO*(AS + ONE)*(AS - A)*(AS - C)*(AS - B + ONE) &
/((B - TWO)*(B - ONE)*B*(B + ONE)*(B + TWO)))
ENDIF
ELSE IF (N - J == 2) THEN
! 1
IF (K - M == 4) THEN
! IV -2 1
SI = AKA*TWO*DSQRT((AS + ONE)*(AS - A)*(AS - B - TWO)*(AS - B - ONE &
)*(AS - B)/(B*(B + ONE)*(B + TWO)*(B + THREE)*(B + FOUR)))
SI = SI*DSQRT((AS - C + ONE)*(AS - C + TWO)*(AS - C + THREE)/((C - &
THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 4) THEN
! 2 P(12) 2 1
SI = -AKA*DSQRT((AS - C)*(AS - B + ONE)*(AS - A + THREE)*(AS - A + &
TWO)*(AS - A + ONE)/((C + THREE + TWO)*(C + FOUR)*(C + THREE)*(C &
+ TWO)*(C + ONE)))
SI = SI*TWO*DSQRT((AS + FOUR)*(AS + THREE)*(AS + TWO)/((B + FOUR)*( &
B + THREE)*(B + TWO)*(B + ONE)*B))
ELSE IF (K - M == 2) THEN
! VIII -1 1
SI = AKA*((A + B + FOUR)*(A - B - TWO) - (C - TWO)*(B + C + FOUR))/ &
DSQRT(B*(B + ONE)*(B + TWO)*(B + THREE)*(B + FOUR))
SI = SI*DSQRT((AS - B - ONE)*(AS - B)*(AS - C + ONE)*(AS - C + TWO) &
/((C - TWO)*(C - ONE)*C*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 2) THEN
! 4 1 1
SI = AKA*(THREE*(AS - B)*(AS - C) - (AS - A)*(AS + FOUR))/DSQRT((B &
+ FOUR)*(B + THREE)*(B + TWO)*(B + ONE)*B)
SI = SI*DSQRT((AS - A + TWO)*(AS - A + ONE)*(AS + THREE)*(AS + TWO) &
/((C + FOUR)*(C + THREE)*(C + TWO)*(C + ONE)*C))
ELSE IF (K - M == 0) THEN
! 6 P(12) 0 1
SI = -AKA*((AS - B - ONE)*(AS - C) - (AS - A)*(AS + THREE))/DSQRT(( &
B + FOUR)*(B + THREE)*(B + TWO)*(B + ONE)*B)
SI = SI*DSQRT(THREE*TWO*(AS - B)*(AS - C + ONE)*(AS - A + ONE)*(AS &
+ TWO)/((C + THREE)*(C + TWO)*(C + ONE)*C*(C - ONE)))
ENDIF
ELSE IF (N - J == 0) THEN
! 0
IF (K - M == 4) THEN
! III -2 0
SI = AKA*DSQRT(THREE*TWO*AS*(AS + ONE)*(AS - A - ONE)*(AS - A)/((B &
- ONE)*B*(B + ONE)*(B + TWO)*(B + THREE)))
SI = SI*DSQRT((AS - B - ONE)*(AS - B)*(AS - C + ONE)*(AS - C + TWO) &
/((C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 4) THEN
! 5 2 0
SI = AKA*DSQRT(THREE*TWO*(AS - C)*(AS - C - ONE)*(AS - B + TWO)*(AS &
- B + ONE)/((C + THREE + TWO)*(C + FOUR)*(C + THREE)*(C + TWO)* &
(C + ONE)))
SI = SI*DSQRT((AS - A + TWO)*(AS - A + ONE)*(AS + THREE)*(AS + TWO) &
/((B + THREE)*(B + TWO)*(B + ONE)*B*(B - ONE)))
ELSE IF (K - M == 2) THEN
! VII -1 0
SI = AKA*HALF*((A + B + TWO)*(A - B) - C*C + FOUR)/DSQRT((B - ONE)*&
B*(B + ONE)*(B + TWO)*(B + THREE))
SI = SI*DSQRT(THREE*TWO*(AS + ONE)*(AS - A)*(AS - B)*(AS - C + ONE)&
/((C - TWO)*(C - ONE)*C*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 2) THEN
! 6 1 0
SI = -AKA*((AS - C - ONE)*(AS - B) - (AS - A)*(AS + THREE))/DSQRT((&
C + FOUR)*(C + THREE)*(C + TWO)*(C + ONE)*C)
SI = SI*DSQRT(THREE*TWO*(AS - C)*(AS - B + ONE)*(AS - A + ONE)*(AS&
+ TWO)/((B + THREE)*(B + TWO)*(B + ONE)*B*(B - ONE)))
ELSE IF (K - M == 0) THEN
! IX 0 0
X1 = (AS - B)*(AS - B - ONE)*(AS - C)*(AS - C - ONE)
X2 = FOUR*(AS - B)*(AS - C)*(AS - A)*(AS + TWO)
X3 = (AS - A)*(AS - A - ONE)*(AS + THREE)*(AS + TWO)
SI = AKA*(X1 - X2 + X3)/DSQRT((B - ONE)*B*(B + ONE)*(B + TWO)*(B + &
THREE)*(C - ONE)*C*(C + ONE)*(C + TWO)*(C + THREE))
ENDIF
ENDIF
RETURN
END SUBROUTINE SIXJ2
!
!################################################################################
!
SUBROUTINE SIXJ3(J, K, L, M, N, ITIK, SI)
!*******************************************************************
! THIS PACKAGE DETERMINES THE VALUES OF 6j COEFFICIENT *
! *
! | J/2 K/2 L/2 | *
! | M/2 N/2 2 | [B.M.X. 75] *
! *
! Written by G. Gaigalas, *
! Vanderbilt University, Nashville October 1996 *
! Transform to fortran 90/95 by G. Gaigalas December 2012 *
! The last modification made by G. Gaigalas October 2017 *
! Restructed by A. Senchuk September 2019 *
! *
!*******************************************************************
IMPLICIT NONE
!-----------------------------------------------
! D u m m y A r g u m e n t s
!-----------------------------------------------
INTEGER :: J, K, L, M, N
INTEGER, INTENT(IN) :: ITIK
REAL(DOUBLE), INTENT(OUT) :: SI
!-----------------------------------------------
! L o c a l V a r i a b l e s
!-----------------------------------------------
INTEGER :: I1
REAL(DOUBLE) :: AS, A, B, C, AKA
!-----------------------------------------------
SI = ZERO
IF (ITIK /= 0) THEN
!
! CHESKED TRIANGULAR CONDITIONS
!
IF (IXJTIK(J,K,L,M,N,6) == 0) RETURN
ENDIF
I1 = (J + K + L)/2
AS = DBLE(I1)
A = DBLE(L)
B = DBLE(J)
C = DBLE(K)
AKA = ONE
IF (MOD(I1,2) /= 0) AKA = -AKA
IF (J - N == 6) THEN
! -3
IF (K - M == 6) THEN
! -3 -3
SI = AKA*DSQRT((AS + ONE)*AS*(AS - ONE)*(AS - TWO)*(AS - THREE)*(AS&
- FOUR)/((B + ONE)*B*(B - ONE)*(B - TWO)*(B - THREE)*(B - FOUR)&
*(B - THREE - TWO)))
SI = SI*DSQRT((AS - A - THREE - TWO)*(AS - A - FOUR)*(AS - A - &
THREE)*(AS - A - TWO)*(AS - A - ONE)*(AS - A)/((C + ONE)*C*(C - &
ONE)*(C - TWO)*(C - THREE)*(C - FOUR)*(C - THREE - TWO)))
ELSE IF (M - K == 6) THEN
! 3 -3
SI = AKA*DSQRT((AS - C)*(AS - C - ONE)*(AS - C - TWO)*(AS - C - &
THREE)*(AS - C - FOUR)*(AS - C - THREE - TWO)/((B + ONE)*B*(B - &
ONE)*(B - TWO)*(B - THREE)*(B - FOUR)*(B - THREE - TWO)))
SI = SI*DSQRT((AS - B + THREE + THREE)*(AS - B + THREE + TWO)*(AS&
- B + FOUR)*(AS - B + THREE)*(AS - B + TWO)*(AS - B + ONE)/((C&
+ FOUR + THREE)*(C + THREE + THREE)*(C + THREE + TWO)*(C + FOUR&
)*(C + THREE)*(C + TWO)*(C + ONE)))
ELSE IF (K - M == 4) THEN
! -2 -3
SI = AKA*DSQRT(TWO*THREE*(AS - C)*(AS - B + ONE)*(AS - THREE)*(AS&
- TWO)*(AS - ONE)*AS*(AS + ONE)/((B - THREE - TWO)*(B - FOUR)*(&
B - THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)))
SI = SI*DSQRT((AS - A - FOUR)*(AS - A - THREE)*(AS - A - TWO)*(AS&
- A - ONE)*(AS - A)/((C - FOUR)*(C - THREE)*(C - TWO)*(C - ONE)&
*C*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 4) THEN
! 2 -3
SI = AKA*DSQRT(TWO*THREE*(AS + ONE)*(AS - A)*(AS - C - FOUR)*(AS - &
C - THREE)*(AS - C - TWO)*(AS - C - ONE)*(AS - C)/((C + THREE + &
THREE)*(C + THREE + TWO)*(C + FOUR)*(C + THREE)*(C + TWO)*(C + &
ONE)*C))
SI = SI*DSQRT((AS - B + THREE + TWO)*(AS - B + FOUR)*(AS - B + &
THREE)*(AS - B + TWO)*(AS - B + ONE)/((B - THREE - TWO)*(B - &
FOUR)*(B - THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)))
ELSE IF (K - M == 2) THEN
! -1 -3
SI = AKA*DSQRT(THREE*(THREE + TWO)*(AS - C)*(AS - C - ONE)*(AS - B&
+ TWO)*(AS - B + ONE)*(AS - TWO)*(AS - ONE)*AS*(AS + ONE)/((B&
- THREE - TWO)*(B - FOUR)*(B - THREE)*(B - TWO)*(B - ONE)*B*(B&
+ ONE)))
SI = SI*DSQRT((AS - A - THREE)*(AS - A - TWO)*(AS - A - ONE)*(AS - &
A)/((C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)*(C + TWO)*(C + &
THREE)))
ELSE IF (M - K == 2) THEN
! 1 -3
SI = AKA*DSQRT(THREE*(THREE + TWO)*(AS + ONE)*AS*(AS - A - ONE)*(AS&
- A)*(AS - C - THREE)*(AS - C - TWO)*(AS - C - ONE)*(AS - C)/((&
B - THREE - TWO)*(B - FOUR)*(B - THREE)*(B - TWO)*(B - ONE)*B*(B&
+ ONE)))
SI = SI*DSQRT((AS - B + FOUR)*(AS - B + THREE)*(AS - B + TWO)*(AS&
- B + ONE)/((C + THREE + TWO)*(C + FOUR)*(C + THREE)*(C + TWO)*&
(C + ONE)*C*(C - ONE)))
ELSE IF (M - K == 0) THEN
! 0 -3
SI = AKA*TWO*DSQRT((THREE + TWO)*(AS + ONE)*AS*(AS - ONE)*(AS - A&
- TWO)*(AS - A - ONE)*(AS - A)/((B - THREE - TWO)*(B - FOUR)*(B&
- THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)))
SI = SI*DSQRT((AS - C - TWO)*(AS - C - ONE)*(AS - C)*(AS - B + &
THREE)*(AS - B + TWO)*(AS - B + ONE)/((C + FOUR)*(C + THREE)*(C&
+ TWO)*(C + ONE)*C*(C - ONE)*(C - TWO)))
ENDIF
ELSE IF (N - J == 6) THEN
! 3
IF (K - M == 6) THEN
! -3 3
SI = AKA*DSQRT((AS - B)*(AS - B - ONE)*(AS - B - TWO)*(AS - B - &
THREE)*(AS - B - FOUR)*(AS - B - THREE - TWO)/((C + ONE)*C*(C - &
ONE)*(C - TWO)*(C - THREE)*(C - FOUR)*(C - THREE - TWO)))
SI = SI*DSQRT((AS - C + THREE + THREE)*(AS - C + THREE + TWO)*(AS&
- C + FOUR)*(AS - C + THREE)*(AS - C + TWO)*(AS - C + ONE)/((B&
+ FOUR + THREE)*(B + THREE + THREE)*(B + THREE + TWO)*(B + FOUR&
)*(B + THREE)*(B + TWO)*(B + ONE)))
ELSE IF (M - K == 6) THEN
! 3 3
SI = AKA*DSQRT((AS - A + THREE + THREE)*(AS - A + THREE + TWO)*(AS&
- A + FOUR)*(AS - A + THREE)*(AS - A + TWO)*(AS - A + ONE)/((B&
+ SEVEN)*(B + THREE + THREE)*(B + THREE + TWO)*(B + FOUR)*(B + &
THREE)*(B + TWO)*(B + ONE)))
SI = SI*DSQRT((AS + SEVEN)*(AS + THREE + THREE)*(AS + THREE + TWO)*&
(AS + FOUR)*(AS + THREE)*(AS + TWO)/((C + SEVEN)*(C + THREE + &
THREE)*(C + THREE + TWO)*(C + FOUR)*(C + THREE)*(C + TWO)*(C + &
ONE)))
ELSE IF (K - M == 4) THEN
! -2 3
SI = -AKA*DSQRT(TWO*THREE*(AS - A + ONE)*(AS + TWO)*(AS - B - FOUR)&
*(AS - B - THREE)*(AS - B - TWO)*(AS - B - ONE)*(AS - B)/((B + &
SEVEN)*(B + THREE + THREE)*(B + THREE + TWO)*(B + FOUR)*(B + &
THREE)*(B + TWO)*(B + ONE)))
SI = SI*DSQRT((AS - C + THREE + TWO)*(AS - C + FOUR)*(AS - C + &
THREE)*(AS - C + TWO)*(AS - C + ONE)/((C - FOUR)*(C - THREE)*(C&
- TWO)*(C - ONE)*C*(C + ONE)*(C + TWO)))
ELSE IF (M - K == 4) THEN
! 2 3
SI = -AKA*DSQRT(TWO*THREE*(AS - B)*(AS - C + ONE)*(AS - A + THREE&
+ TWO)*(AS - A + FOUR)*(AS - A + THREE)*(AS - A + TWO)*(AS - A&
+ ONE)/((B + SEVEN)*(B + THREE + THREE)*(B + THREE + TWO)*(B + &
FOUR)*(B + THREE)*(B + TWO)*(B + ONE)))
SI = SI*DSQRT((AS + THREE + THREE)*(AS + THREE + TWO)*(AS + FOUR)*(&
AS + THREE)*(AS + TWO)/((C + THREE + THREE)*(C + THREE + TWO)*(C&
+ FOUR)*(C + THREE)*(C + TWO)*(C + ONE)*C))
ELSE IF (K - M == 2) THEN
! -1 3
SI = AKA*DSQRT(THREE*(THREE + TWO)*(AS - A + ONE)*(AS - A + TWO)*(&
AS + THREE)*(AS + TWO)*(AS - B - THREE)*(AS - B - TWO)*(AS - B&
- ONE)*(AS - B)/((B + SEVEN)*(B + THREE + THREE)*(B + THREE + &
TWO)*(B + FOUR)*(B + THREE)*(B + TWO)*(B + ONE)))
SI = SI*DSQRT((AS - C + FOUR)*(AS - C + THREE)*(AS - C + TWO)*(AS&
- C + ONE)/((C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)*(C + &
TWO)*(C + THREE)))
ELSE IF (M - K == 2) THEN
! 1 3
SI = AKA*DSQRT(THREE*(THREE + TWO)*(AS - B)*(AS - B - ONE)*(AS - C&
+ TWO)*(AS - C + ONE)*(AS - A + FOUR)*(AS - A + THREE)*(AS - A&
+ TWO)*(AS - A + ONE)/((B + SEVEN)*(B + THREE + THREE)*(B + &
THREE + TWO)*(B + FOUR)*(B + THREE)*(B + TWO)*(B + ONE)))
SI = SI*DSQRT((AS + THREE + TWO)*(AS + FOUR)*(AS + THREE)*(AS + TWO&
)/((C + THREE + TWO)*(C + FOUR)*(C + THREE)*(C + TWO)*(C + ONE)*&
C*(C - ONE)))
ELSE IF (M - K == 0) THEN
! 0 3
SI = -AKA*TWO*DSQRT((THREE + TWO)*(AS - B)*(AS - B - ONE)*(AS - B&
- TWO)*(AS - C + THREE)*(AS - C + TWO)*(AS - C + ONE)/((B + &
SEVEN)*(B + THREE + THREE)*(B + THREE + TWO)*(B + FOUR)*(B + &
THREE)*(B + TWO)*(B + ONE)))
SI = SI*DSQRT((AS - A + THREE)*(AS - A + TWO)*(AS - A + ONE)*(AS + &
FOUR)*(AS + THREE)*(AS + TWO)/((C + FOUR)*(C + THREE)*(C + TWO)*&
(C + ONE)*C*(C - ONE)*(C - TWO)))
ENDIF
ELSE IF (J - N == 4) THEN
! -2
IF (K - M == 6) THEN
! -3 -2
SI = AKA*DSQRT(TWO*THREE*(AS - B)*(AS - C + ONE)*(AS - THREE)*(AS&
- TWO)*(AS - ONE)*AS*(AS + ONE)/((C - THREE - TWO)*(C - FOUR)*(&
C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)))
SI = SI*DSQRT((AS - A - FOUR)*(AS - A - THREE)*(AS - A - TWO)*(AS&
- A - ONE)*(AS - A)/((B - FOUR)*(B - THREE)*(B - TWO)*(B - ONE)&
*B*(B + ONE)*(B + TWO)))
ELSE IF (M - K == 6) THEN
! 3 -2
SI = -AKA*DSQRT(TWO*THREE*(AS - A + ONE)*(AS + TWO)*(AS - C - FOUR)&
*(AS - C - THREE)*(AS - C - TWO)*(AS - C - ONE)*(AS - C)/((C + &
SEVEN)*(C + THREE + THREE)*(C + THREE + TWO)*(C + FOUR)*(C + &
THREE)*(C + TWO)*(C + ONE)))
SI = SI*DSQRT((AS - B + THREE + TWO)*(AS - B + FOUR)*(AS - B + &
THREE)*(AS - B + TWO)*(AS - B + ONE)/((B - FOUR)*(B - THREE)*(B&
- TWO)*(B - ONE)*B*(B + ONE)*(B + TWO)))
ELSE IF (K - M == 4) THEN
! -2 -2
SI = AKA*((TWO + THREE)*(AS - C)*(AS - B) - (AS + TWO)*(AS - A - &
FOUR))*DSQRT((AS - TWO)*(AS - ONE)*AS*(AS + ONE)/((B - FOUR)*(B&
- THREE)*(B - TWO)*(B - ONE)*B*(B + ONE)*(B + TWO)))
SI = SI*DSQRT((AS - A - THREE)*(AS - A - TWO)*(AS - A - ONE)*(AS - &
A)/((C - FOUR)*(C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)*(C + &
TWO)))
ELSE IF (M - K == 4) THEN
! 2 -2
SI = -AKA*((TWO + THREE)*(AS + ONE)*(AS - A + ONE) - (AS - C + ONE)&
*(AS - B + THREE + TWO))*DSQRT((AS - C - THREE)*(AS - C - TWO)*(&
AS - C - ONE)*(AS - C)/((B - FOUR)*(B - THREE)*(B - TWO)*(B - &
ONE)*B*(B + ONE)*(B + TWO)))
SI = SI*DSQRT((AS - B + FOUR)*(AS - B + THREE)*(AS - B + TWO)*(AS&
- B + ONE)/((C + THREE + THREE)*(C + THREE + TWO)*(C + FOUR)*(C&
+ THREE)*(C + TWO)*(C + ONE)*C))
ELSE IF (K - M == 2) THEN
! -1 -2
SI = AKA*(TWO*(AS - C - ONE)*(AS - B) - (AS + TWO)*(AS - A - THREE)&
)*DSQRT(TWO*(THREE + TWO)*(AS - C)*(AS - B + ONE)*(AS - ONE)*AS*&
(AS + ONE)/((B - FOUR)*(B - THREE)*(B - TWO)*(B - ONE)*B*(B + &
ONE)*(B + TWO)))
SI = SI*DSQRT((AS - A - TWO)*(AS - A - ONE)*(AS - A)/((C - THREE)*(&
C - TWO)*(C - ONE)*C*(C + ONE)*(C + TWO)*(C + THREE)))
ELSE IF (M - K == 2) THEN
! 1 -2
SI = -AKA*(TWO*AS*(AS - A + ONE) - (AS - C + ONE)*(AS - B + FOUR))*&
DSQRT(TWO*(THREE + TWO)*(AS + ONE)*(AS - A)*(AS - C - TWO)*(AS&
- C - ONE)*(AS - C)/((B - FOUR)*(B - THREE)*(B - TWO)*(B - ONE)&
*B*(B + ONE)*(B + TWO)))
SI = SI*DSQRT((AS - B + THREE)*(AS - B + TWO)*(AS - B + ONE)/((C + &
THREE + TWO)*(C + FOUR)*(C + THREE)*(C + TWO)*(C + ONE)*C*(C - &
ONE)))
ELSE IF (M - K == 0) THEN
! 0 -2
SI = -AKA*((AS - ONE)*(AS - A + ONE) - (AS - C + ONE)*(AS - B + &
THREE))*DSQRT(TWO*THREE*(THREE + TWO)*(AS + ONE)*AS*(AS - A - &
ONE)*(AS - A)/((B - FOUR)*(B - THREE)*(B - TWO)*(B - ONE)*B*(B&
+ ONE)*(B + TWO)))
SI = SI*DSQRT((AS - C - ONE)*(AS - C)*(AS - B + TWO)*(AS - B + ONE)&
/((C + FOUR)*(C + THREE)*(C + TWO)*(C + ONE)*C*(C - ONE)*(C - &
TWO)))
ENDIF
ELSE IF (N - J == 4) THEN
! 2
IF (K - M == 6) THEN
! -3 2
SI = AKA*DSQRT(TWO*THREE*(AS + ONE)*(AS - A)*(AS - B - FOUR)*(AS - &
B - THREE)*(AS - B - TWO)*(AS - B - ONE)*(AS - B)/((B + THREE + &
THREE)*(B + THREE + TWO)*(B + FOUR)*(B + THREE)*(B + TWO)*(B + &
ONE)*B))
SI = SI*DSQRT((AS - C + THREE + TWO)*(AS - C + FOUR)*(AS - C + &
THREE)*(AS - C + TWO)*(AS - C + ONE)/((C - THREE - TWO)*(C - &
FOUR)*(C - THREE)*(C - TWO)*(C - ONE)*C*(C + ONE)))
ELSE IF (M - K == 6) THEN
! 3 2
SI = -AKA*DSQRT(TWO*THREE*(AS - C)*(AS - B + ONE)*(AS - A + THREE&
+ TWO)*(AS - A + FOUR)*(AS - A + THREE)*(AS - A + TWO)*(AS - A&
+ ONE)/((C + SEVEN)*(C + THREE + THREE)*(C + THREE + TWO)*(C + &
FOUR)*(C + THREE)*(C + TWO)*(C + ONE)))
SI = SI*DSQRT((AS + THREE + THREE)*(AS + THREE + TWO)*(AS + FOUR)*(&
AS + THREE)*(AS + TWO)/((B + THREE + THREE)*(B + THREE + TWO)*(B&
+ FOUR)*(B + THREE)*(B + TWO)*(B + ONE)*B))