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

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)

摘要
本文描述了一款用于为通用角动量再耦合系数生成基于6-j系数 (6-j coefficients) 的求和公式的程序。该算法采用了Burke在程序NJSYM中提出的二叉树变换方法[《计算机物理学报》(Comput. Phys. Commun.) 1 (1970) 241]。本程序着重于寻找含最少求和变量的最优求和公式，以此改进NJSYM的计算结果。本文所得结果至少与NJSYM的结果相当，且通常更优（原文此处存在截断）。

程序名称：NJFORMULA
目录编号：ACVV_v1_0

问题描述
将任意数量（整数或半整数）角动量的通用再耦合系数表示为包含6-j系数乘积的多重求和式，其中涵盖相位因子与平方根因子。针对给定的角动量参数值，可对该求和公式进行数值求值（为此我们将提供程序NJSUMMATION[5]）。

本程序存放在门德雷数据 (Mendeley Data) 的CPC资源库中的版本信息为：ACVV_v1_0; NJFORMULA; 10.1016/0010-4655(94)90055-8

本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019年）。