# Calculation of general recoupling coefficients using graphical methods

## Description

Abstract A new program to generate a summation in terms of 6-j coefficients for a general angular momentum recoupling coefficient is described. This algorithm makes use of the graphical techniques as developed by Yutsis, Levinson and Vanagas Attention is paid to providing an appropriate data structure for the graph representing a general recoupling coefficient, and to reducing the coefficient to a summation formula with a minimum number of summation variables. Our results are compared to those of Bar-... Title of program: NEWGRAPH Catalogue Id: ADFJ_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 use the program NJSUMMATION [4]). Versions of this program held in the CPC repository in Mendeley Data ADFJ_v1_0; NEWGRAPH; 10.1016/S0010-4655(96)00170-1 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)