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Manuscript Title: A program for deriving recoupling coefficients formulae.
Authors: P.M. Lima
Program title: RECOUP
Catalogue identifier: ABZR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 66(1991)89
Programming language: Fortran.
Computer: VAX 11/780.
Operating system: VAX/VMS.
RAM: 30K words
Word size: 32
Keywords: General purpose, Rotation group, Elements matrix, Angular momentum, Recoupling coefficients, Ls-coupling, Momentum diagrams.
Classification: 4.1.

Nature of problem:
In atomic calculations one needs to evaluate the matrix elements of the Hamiltonian operator with respect to a basis set of configuration wave functions. This program derives the formulae needed to evaluate the recoupling coefficients which arise in the calculation of matrix elements by the methods of Racach algebra.

Solution method:
The program uses the graphical methods introduced by Jucys and El-Baz. The recoupling coefficients are represented by diagrams, which are stored in the computer memory under the form of arrays. These diagrams are transformed, according to given rules, so that any diagram may be decomposed on a product of simple standard diagrams. Using this method method, any given recoupling coefficient may be expressed as a weighted sum of products of 6j-symbols multiplied by phase factors. The obtained formulae are stored in such a form that they may be directly used by another program to calculate the concrete values of the coefficients.

The submitted program may derive formulae for any recoupling coefficient, satisfying the following condition - in the corresponding diagram a part may be separated, having no more than 4 vertices, which is linked to the rest of the diagram by no more than four edges. Practically all the coefficients arising in the calculation of real atomic systems satisfy this condition.

Running time:
0.3 s for the test run