U112: Clebsch-Gordan Coefficients in Rational Form

Author(s): K.S. Kölbig Library: MATHLIB
Submitter: Submitted: 15.10.1994
Language: Fortran Revised:

Function subprogram RTCLGN calculates the (signed) square of the Clebsch-Gordan coefficient in rational form and in powers of prime numbers. In terms of the Wigner-3j symbol, this coefficient is defined by

eqnarray41

All tex2html_wrap_inline96 and tex2html_wrap_inline98 must have integral or half-integral values (see Notes). For definitions and notations see Ref. 1.

On computers other than CDC and Cray, only the double-precision version DTCLGN is available. On CDC and Cray computers, only the single-precision version RTCLGN is available.

Structure:

SUBROUTINE subprogram
User Entry Names: RTCLGN
Files Referenced: Unit 6

Usage:

For tex2html_wrap_inline100 (type REAL), tex2html_wrap_inline102 (type DOUBLE PRECISION), 

    CALL tTCLGN(JJ1,JJ2,JJ3,MM1,MM2,MM3,RNUM,RDEN,KPEX)
JJ1,JJ2,JJ3
(INTEGER) The j-parameters multiplied by two, i.e. JJ1 tex2html_wrap_inline106 etc.
MM1,MM2,MM3
(INTEGER) The m-parameters multiplied by two, i.e. MM1 tex2html_wrap_inline110 etc.
RNUM
(type according to t) Contains, on exit, the signed numerator of tex2html_wrap_inline112 .
RDEN
(type according to t) Contains, on exit, the denominator of tex2html_wrap_inline114 .
KPEX
(INTEGER) Array of length 40 at least. Contains, on exit, the exponents tex2html_wrap_inline116 in the expression

eqnarray67

where tex2html_wrap_inline118 are the first 40 prime numbers.

Notes:

A Clebsch-Gordan coefficient tex2html_wrap_inline120 is considered to be zero unless simultaneously
(i) tex2html_wrap_inline122 and tex2html_wrap_inline124 have both either integral or half-integral values (each i),
(ii) tex2html_wrap_inline128 (each i),
(iii) tex2html_wrap_inline132 ,
(iv) tex2html_wrap_inline134 is an integer and \ tex2html_wrap_inline136 .

In this case, tex2html_wrap_inline138 , tex2html_wrap_inline140 or tex2html_wrap_inline142 , tex2html_wrap_inline144 , respectively, and tex2html_wrap_inline146 .

This subroutine is based on an earlier version by H. Yoshiki.

Error handling:

Error U112.1: The calculation requires a prime number tex2html_wrap_inline148 with n>40.
In this case, tex2html_wrap_inline152 , tex2html_wrap_inline154 , tex2html_wrap_inline156 . A message is written on Unit 6 unless subroutine MTLSET (N002) has been called.

References:

  1. R.D. Cowan, The theory of atomic structure and spectra, (Univ. of California Press, Berkeley CA 1981) 142-144
tex2html_wrap_inline158

Michel Goossens Wed Jun 5 08:15:33 METDST 1996