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
本文介绍了一款用于生成通用角动量再耦合系数的6-j系数（6-j coefficients）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（文献来源：[Comput. Phys. Commun. 1 (1970) 241]）。本研究着重于寻找求和变量数量最少的最优求和公式，以此优化NJSYM的计算结果。本文所得结果至少不逊于（且通常优于……

程序名称：NJFORMULA
目录编号：ACVV_v1_0

问题本质
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相位因子与平方根因子的6-j系数乘积的多重求和式。后续可针对给定的角动量数值对该求和公式进行求值（为此我们将提供程序NJSUMMATION[5]）。

本程序收录于Mendeley数据平台的CPC程序库中，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馆藏的CPC程序库（1969-2019）