SLATEC Routines --- RC3JM ---
*DECK RC3JM
SUBROUTINE RC3JM (L1, L2, L3, M1, M2MIN, M2MAX, THRCOF, NDIM, IER)
C***BEGIN PROLOGUE RC3JM
C***PURPOSE Evaluate the 3j symbol g(M2) = (L1 L2 L3 )
C (M1 M2 -M1-M2)
C for all allowed values of M2, the other parameters
C being held fixed.
C***LIBRARY SLATEC
C***CATEGORY C19
C***TYPE SINGLE PRECISION (RC3JM-S, DRC3JM-D)
C***KEYWORDS 3J COEFFICIENTS, 3J 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 L1, L2, L3, M1, M2MIN, M2MAX, THRCOF(NDIM)
C INTEGER NDIM, IER
C
C CALL RC3JM (L1, L2, L3, M1, M2MIN, M2MAX, THRCOF, NDIM, IER)
C
C *Arguments:
C
C L1 :IN Parameter in 3j symbol.
C
C L2 :IN Parameter in 3j symbol.
C
C L3 :IN Parameter in 3j symbol.
C
C M1 :IN Parameter in 3j symbol.
C
C M2MIN :OUT Smallest allowable M2 in 3j symbol.
C
C M2MAX :OUT Largest allowable M2 in 3j symbol.
C
C THRCOF :OUT Set of 3j coefficients generated by evaluating the
C 3j symbol for all allowed values of M2. THRCOF(I)
C will contain g(M2MIN+I-1), I=1,2,...,M2MAX-M2MIN+1.
C
C NDIM :IN Declared length of THRCOF in calling program.
C
C IER :OUT Error flag.
C IER=0 No errors.
C IER=1 Either L1.LT.ABS(M1) or L1+ABS(M1) non-integer.
C IER=2 ABS(L1-L2).LE.L3.LE.L1+L2 not satisfied.
C IER=3 L1+L2+L3 not an integer.
C IER=4 M2MAX-M2MIN not an integer.
C IER=5 M2MAX less than M2MIN.
C IER=6 NDIM less than M2MAX-M2MIN+1.
C
C *Description:
C
C Although conventionally the parameters of the vector addition
C coefficients satisfy certain restrictions, such as being integers
C or integers plus 1/2, the restrictions imposed on input to this
C subroutine are somewhat weaker. See, for example, Section 27.9 of
C Abramowitz and Stegun or Appendix C of Volume II of A. Messiah.
C The restrictions imposed by this subroutine are
C 1. L1.GE.ABS(M1) and L1+ABS(M1) must be an integer;
C 2. ABS(L1-L2).LE.L3.LE.L1+L2;
C 3. L1+L2+L3 must be an integer;
C 4. M2MAX-M2MIN must be an integer, where
C M2MAX=MIN(L2,L3-M1) and M2MIN=MAX(-L2,-L3-M1).
C If the conventional restrictions are satisfied, then these
C restrictions are met.
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 g(M2) = (0.75 1.50 1.75 )
C (0.25 M2 -0.25-M2)
C for M2=-1.5,-0.5,0.5,1.5 but none of the symmetry properties of the
C 3j symbol, set forth on page 1056 of Messiah, is satisfied.
C
C The subroutine generates g(M2MIN), g(M2MIN+1), ..., g(M2MAX)
C where M2MIN and M2MAX are defined above. The sequence g(M2) 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 3j 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. Abramowitz, M., and Stegun, I. A., Eds., Handbook
C of Mathematical Functions with Formulas, Graphs
C and Mathematical Tables, NBS Applied Mathematics
C Series 55, June 1964 and subsequent printings.
C 2. Messiah, Albert., Quantum Mechanics, Volume II,
C North-Holland Publishing Company, 1963.
C 3. 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 4. 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 5. 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; MMATCH (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 THRCOF expanded. These changes were done by
C D. W. Lozier.
C***END PROLOGUE RC3JM