SLATEC Routines --- RC6J ---
*DECK RC6J
SUBROUTINE RC6J (L2, L3, L4, L5, L6, L1MIN, L1MAX, SIXCOF, NDIM,
+ IER)
C***BEGIN PROLOGUE RC6J
C***PURPOSE Evaluate the 6j symbol h(L1) = {L1 L2 L3}
C {L4 L5 L6}
C for all allowed values of L1, the other parameters
C being held fixed.
C***LIBRARY SLATEC
C***CATEGORY C19
C***TYPE SINGLE PRECISION (RC6J-S, DRC6J-D)
C***KEYWORDS 6J COEFFICIENTS, 6J SYMBOLS, CLEBSCH-GORDAN COEFFICIENTS,
C RACAH COEFFICIENTS, VECTOR ADDITION COEFFICIENTS,
C WIGNER COEFFICIENTS
C***AUTHOR Gordon, R. G., Harvard University
C Schulten, K., Max Planck Institute
C***DESCRIPTION
C
C *Usage:
C
C REAL L2, L3, L4, L5, L6, L1MIN, L1MAX, SIXCOF(NDIM)
C INTEGER NDIM, IER
C
C CALL RC6J(L2, L3, L4, L5, L6, L1MIN, L1MAX, SIXCOF, NDIM, IER)
C
C *Arguments:
C
C L2 :IN Parameter in 6j symbol.
C
C L3 :IN Parameter in 6j symbol.
C
C L4 :IN Parameter in 6j symbol.
C
C L5 :IN Parameter in 6j symbol.
C
C L6 :IN Parameter in 6j symbol.
C
C L1MIN :OUT Smallest allowable L1 in 6j symbol.
C
C L1MAX :OUT Largest allowable L1 in 6j symbol.
C
C SIXCOF :OUT Set of 6j coefficients generated by evaluating the
C 6j symbol for all allowed values of L1. SIXCOF(I)
C will contain h(L1MIN+I-1), I=1,2,...,L1MAX-L1MIN+1.
C
C NDIM :IN Declared length of SIXCOF in calling program.
C
C IER :OUT Error flag.
C IER=0 No errors.
C IER=1 L2+L3+L5+L6 or L4+L2+L6 not an integer.
C IER=2 L4, L2, L6 triangular condition not satisfied.
C IER=3 L4, L5, L3 triangular condition not satisfied.
C IER=4 L1MAX-L1MIN not an integer.
C IER=5 L1MAX less than L1MIN.
C IER=6 NDIM less than L1MAX-L1MIN+1.
C
C *Description:
C
C The definition and properties of 6j symbols can be found, for
C example, in Appendix C of Volume II of A. Messiah. Although the
C parameters of the vector addition coefficients satisfy certain
C conventional restrictions, the restriction that they be non-negative
C integers or non-negative integers plus 1/2 is not imposed on input
C to this subroutine. The restrictions imposed are
C 1. L2+L3+L5+L6 and L2+L4+L6 must be integers;
C 2. ABS(L2-L4).LE.L6.LE.L2+L4 must be satisfied;
C 3. ABS(L4-L5).LE.L3.LE.L4+L5 must be satisfied;
C 4. L1MAX-L1MIN must be a non-negative integer, where
C L1MAX=MIN(L2+L3,L5+L6) and L1MIN=MAX(ABS(L2-L3),ABS(L5-L6)).
C If all the conventional restrictions are satisfied, then these
C restrictions are met. Conversely, if input to this subroutine meets
C all of these restrictions and the conventional restriction stated
C above, then all the conventional restrictions are satisfied.
C
C The user should be cautious in using input parameters that do
C not satisfy the conventional restrictions. For example, the
C the subroutine produces values of
C h(L1) = { L1 2/3 1 }
C {2/3 2/3 2/3}
C for L1=1/3 and 4/3 but none of the symmetry properties of the 6j
C symbol, set forth on pages 1063 and 1064 of Messiah, is satisfied.
C
C The subroutine generates h(L1MIN), h(L1MIN+1), ..., h(L1MAX)
C where L1MIN and L1MAX are defined above. The sequence h(L1) is
C generated by a three-term recurrence algorithm with scaling to
C control overflow. Both backward and forward recurrence are used to
C maintain numerical stability. The two recurrence sequences are
C matched at an interior point and are normalized from the unitary
C property of 6j coefficients and Wigner's phase convention.
C
C The algorithm is suited to applications in which large quantum
C numbers arise, such as in molecular dynamics.
C
C***REFERENCES 1. Messiah, Albert., Quantum Mechanics, Volume II,
C North-Holland Publishing Company, 1963.
C 2. Schulten, Klaus and Gordon, Roy G., Exact recursive
C evaluation of 3j and 6j coefficients for quantum-
C mechanical coupling of angular momenta, J Math
C Phys, v 16, no. 10, October 1975, pp. 1961-1970.
C 3. Schulten, Klaus and Gordon, Roy G., Semiclassical
C approximations to 3j and 6j coefficients for
C quantum-mechanical coupling of angular momenta,
C J Math Phys, v 16, no. 10, October 1975,
C pp. 1971-1988.
C 4. Schulten, Klaus and Gordon, Roy G., Recursive
C evaluation of 3j and 6j coefficients, Computer
C Phys Comm, v 11, 1976, pp. 269-278.
C***ROUTINES CALLED R1MACH, XERMSG
C***REVISION HISTORY (YYMMDD)
C 750101 DATE WRITTEN
C 880515 SLATEC prologue added by G. C. Nielson, NBS; parameters
C HUGE and TINY revised to depend on R1MACH.
C 891229 Prologue description rewritten; other prologue sections
C revised; LMATCH (location of match point for recurrences)
C removed from argument list; argument IER changed to serve
C only as an error flag (previously, in cases without error,
C it returned the number of scalings); number of error codes
C increased to provide more precise error information;
C program comments revised; SLATEC error handler calls
C introduced to enable printing of error messages to meet
C SLATEC standards. These changes were done by D. W. Lozier,
C M. A. McClain and J. M. Smith of the National Institute
C of Standards and Technology, formerly NBS.
C 910415 Mixed type expressions eliminated; variable C1 initialized;
C description of SIXCOF expanded. These changes were done by
C D. W. Lozier.
C***END PROLOGUE RC6J