SLATEC Routines --- DRC6J ---


*DECK DRC6J
      SUBROUTINE DRC6J (L2, L3, L4, L5, L6, L1MIN, L1MAX, SIXCOF, NDIM,
     +   IER)
C***BEGIN PROLOGUE  DRC6J
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      DOUBLE 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        DOUBLE PRECISION L2, L3, L4, L5, L6, L1MIN, L1MAX, SIXCOF(NDIM)
C        INTEGER NDIM, IER
C
C        CALL DRC6J(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  D1MACH, 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 D1MACH.
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  DRC6J