# New efficient programs to calculate general recoupling coefficients Part I: Generation of a summation formula

## Description

Abstract A program to generate a summation formula in terms of 6-j coefficients for a general angular momentum recoupling coefficient is described. This algorithms makes use of binary tree transformations as introduced by Burke [Comput. Phys. Commun. 1 (1970) 241] in the program NJSYM. Due attention is paid to finding an optimal summation formula with a minimal number of summation variables, thereby improving the results of NJSYM. The results obtained here are at least as good as (and often better tha... Title of program: NJFORMULA Catalogue Id: ACVV_v1_0 Nature of problem A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta is expressed as a multiple sum over products of 6-j coefficients, including phase factors and square root factors. This summation formula can then be evaluated for given values of the angular momenta (for this purpose we will provide a program NJSUMMATION [5]). Versions of this program held in the CPC repository in Mendeley Data ACVV_v1_0; NJFORMULA; 10.1016/0010-4655(94)90055-8 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)