Maple procedures for the coupling of angular momenta. VI. LS–jj transformations

Abstract
Transformation matrices between different coupling schemes are required, if a reliable classification of the level structure is to be obtained for open-shell atoms and ions. While, for instance, relativistic computations are traditionally carried out in jj-coupling, a LSJ coupling notation often occurs much more appropriate for classifying the valence-shell structure of atoms. Apart from the (known) transformation of single open shells, however, further demand on proper transformation coeffic...

Title of program: RACAH
Catalogue Id: ADFV_v6_0 [ADQP]

Nature of problem
For open-shell atoms and ions, a reliable classification of the level structure often requires the knowledge of the LS-jj transformation matrices in order to find the main components of the wave functions as well as their proper spectroscopic notation. Apart from the transformation of individual (sub-)shell states, matrices of much larger complexity arise for the transformation of symmetry-adapted configuration state functions which are constructed from the coupling of two or more open shells.

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
若要对开壳层原子和离子的能级结构实现可靠分类，需用到不同耦合方案间的变换矩阵。例如，尽管相对论计算传统上采用jj耦合（jj-coupling）方案开展，但LSJ耦合标记（LSJ coupling notation）往往更适用于原子价层结构的分类。除已知的单开壳层变换之外，目前对恰当的变换系数仍存在进一步的需求……

程序名称：RACAH
目录号：ADFV_v6_0 [ADQP]

问题本质
对于开壳层原子和离子，要可靠分类其能级结构，通常需要掌握LS-jj变换矩阵，以便确定波函数的主要分量及其恰当的光谱标记。除单个（亚）壳层态的变换外，由两个或多个开壳层耦合构建的对称适配组态态函数的变换，会涉及复杂度更高的矩阵。

存放在Mendeley Data中的CPC程序仓库的本程序版本如下：
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馆藏的CPC程序库（1969-2018年）