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Manuscript Title: NJGRAF: an efficient program for calculation of general recoupling coefficients by graphical analysis, compatible with NJSYM.
Authors: A. Bar-Shalom, M. Klapisch
Program title: NJGRAF
Catalogue identifier: ABBY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 50(1988)375
Programming language: Fortran.
Computer: CDC CYBER 72.
Operating system: NOS/BE.
RAM: 22K words
Word size: 60
Keywords: General purpose, Rotation group, Atomic physics, Nuclear physics, Scattering, Recoupling coefficients, Racah coefficients, 3nj-symbol, Theory graph, Angular momentum, Sum rules.
Classification: 4.1.

Other versions:
Cat Id Title Reference
AAGD_v1_0 NJSYM CPC 1(1969)241
AAGD_v2_0 A NEW VERSION OF NJSYM CPC 8(1974)151
AAGD_v3_0 NJSYM - A MORE EFFICIENT VERSION CPC 28(1982)189

Nature of problem:
This program calculates a general recoupling coefficient for an arbitrary number of integer or half-integer angular momenta.

Solution method:
The recoupling coefficient is first transformed into a structureless graph, from which zero-valued angular momenta are taken out. Then one or more "flat diagrams" are created and searched for minimal "n-loops" so as to generate the optimal expression as a sum over products of 6j coefficients. The latter are evaluated by a subroutine of Scott and Hibbert. Due attention has been paid to minimalizing the number of values that summation variables are given.

Restrictions:
The number of angular momenta is limited only by the dimensions of the arrays; in the present version: 60.

Unusual features:
NJGRAF is compatible with NJSYM package, including the use of separate calls to GENSUM, provided minor changes in the calling program are made. A logical array FREE is defined; if the value of a given angular momentum J, may change (is "free") between calls to GENSUM, then FREE(J) should be given the value TRUE as input. In that case, the formula is established in NJGRAF without taking into account any particular value of this angular momentum, e.g. O.

Running time:
The test case took 0.05 seconds on CDC Cyber 72. The gain of time with respect to the original NJSYM is a factor between 5 and 50.