Maple procedures for the coupling of angular momenta I. Data structures and numerical computations

Abstract The theory of angular momentum and of spherical tensor operators leads to algebraic expressions which are usually written in terms of generalized Clebsch-Gordan coefficients and/or Wigner n-j symbols. In principle, the evaluation and simplification of such expressions is a straightforward task but it can also become extremely cumbersome in more complex applications, for instance, in atomic and nuclear structure theory or in the study of angular dependent properties. In these fields, simplific... Title of program: Racah Catalogue Id: ADFV_v1_0 Nature of problem Computer algebra (CA) is used to evaluate Wigner n-j symbols and vector coupling coefficients and to simplify typical expressions which appear by using Racah algebra techniques. A set of Maple commands for interactive work is presented. Versions of this program held in the CPC repository in Mendeley Data ADFV_v1_0; Racah; 10.1016/S0010-4655(97)00032-5 ADFV_v2_0; Racah; 10.1016/S0010-4655(98)00021-6 ADFV_v3_0; RACAH; 10.1016/S0010-4655(00)00234-4 ADFV_v4_0; RACAH; 10.1016/S0010-4655(01)00218-1 ADFV_v5_0; RACAH; 10.1016/S0010-4655(01)00219-3 ADFV_v6_0; RACAH; 10.1016/S0010-4655(02)00591-X ADFV_v7_0; RACAH; 10.1016/S0010-4655(03)00227-3 ADFV_v8_0; RACAH; 10.1016/j.cpc.2004.11.003 ADFV_v9_0; RACAH; 10.1016/j.cpc.2005.12.008 ADFV_v10_0; RACAH; 10.1016/j.cpc.2009.06.018 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要 角动量与球张量算子理论可推导出代数表达式，这类表达式通常以广义克莱布希-高丹系数（generalized Clebsch-Gordan coefficients）和/或威格纳n-j符号（Wigner n-j symbols）的形式书写。原则上，对这类表达式进行求值与化简是一项直观的任务，但在更复杂的应用场景中，例如原子与核结构理论，或是角依赖特性研究中，该过程也会变得极为繁琐。在这些领域中，化简…… 程序名称：Racah 目录编号：ADFV_v1_0 问题本质 本程序采用计算机代数（Computer Algebra, CA）技术，对威格纳n-j符号与矢量耦合系数进行求值，并借助拉卡代数（Racah algebra）方法化简常见的相关表达式。本文还提供了一套用于交互式操作的Maple命令集。 存放在Mendeley Data中的CPC程序库的该程序版本如下： ADFV_v1_0; Racah; 10.1016/S0010-4655(97)00032-5 ADFV_v2_0; Racah; 10.1016/S0010-4655(98)00021-6 ADFV_v3_0; RACAH; 10.1016/S0010-4655(00)00234-4 ADFV_v4_0; RACAH; 10.1016/S0010-4655(01)00218-1 ADFV_v5_0; RACAH; 10.1016/S0010-4655(01)00219-3 ADFV_v6_0; RACAH; 10.1016/S0010-4655(02)00591-X ADFV_v7_0; RACAH; 10.1016/S0010-4655(03)00227-3 ADFV_v8_0; RACAH; 10.1016/j.cpc.2004.11.003 ADFV_v9_0; RACAH; 10.1016/j.cpc.2005.12.008 ADFV_v10_0; RACAH; 10.1016/j.cpc.2009.06.018 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018年）。