SLATEC Routines --- RC3JJ ---
*DECK RC3JJ
SUBROUTINE RC3JJ (L2, L3, M2, M3, L1MIN, L1MAX, THRCOF, NDIM, IER)
C***BEGIN PROLOGUE RC3JJ
C***PURPOSE Evaluate the 3j symbol f(L1) = ( L1 L2 L3)
C (-M2-M3 M2 M3)
C for all allowed values of L1, the other parameters
C being held fixed.
C***LIBRARY SLATEC
C***CATEGORY C19
C***TYPE SINGLE PRECISION (RC3JJ-S, DRC3JJ-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 L2, L3, M2, M3, L1MIN, L1MAX, THRCOF(NDIM)
C INTEGER NDIM, IER
C
C CALL RC3JJ (L2, L3, M2, M3, L1MIN, L1MAX, THRCOF, NDIM, IER)
C
C *Arguments:
C
C L2 :IN Parameter in 3j symbol.
C
C L3 :IN Parameter in 3j symbol.
C
C M2 :IN Parameter in 3j symbol.
C
C M3 :IN Parameter in 3j symbol.
C
C L1MIN :OUT Smallest allowable L1 in 3j symbol.
C
C L1MAX :OUT Largest allowable L1 in 3j symbol.
C
C THRCOF :OUT Set of 3j coefficients generated by evaluating the
C 3j symbol for all allowed values of L1. THRCOF(I)
C will contain f(L1MIN+I-1), I=1,2,...,L1MAX+L1MIN+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 L2.LT.ABS(M2) or L3.LT.ABS(M3).
C IER=2 Either L2+ABS(M2) or L3+ABS(M3) non-integer.
C IER=3 L1MAX-L1MIN not an integer.
C IER=4 L1MAX less than L1MIN.
C IER=5 NDIM less than L1MAX-L1MIN+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. L2 .GE. ABS(M2) and L3 .GE. ABS(M3);
C 2. L2+ABS(M2) and L3+ABS(M3) must be integers;
C 3. L1MAX-L1MIN must be a non-negative integer, where
C L1MAX=L2+L3 and L1MIN=MAX(ABS(L2-L3),ABS(M2+M3)).
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 f(L1) = ( L1 2.5 5.8)
C (-0.3 1.5 -1.2)
C for L1=3.3,4.3,...,8.3 but none of the symmetry properties of the 3j
C symbol, set forth on page 1056 of Messiah, is satisfied.
C
C The subroutine generates f(L1MIN), f(L1MIN+1), ..., f(L1MAX)
C where L1MIN and L1MAX are defined above. The sequence f(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 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; 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 THRCOF expanded. These changes were done by
C D. W. Lozier.
C***END PROLOGUE RC3JJ