Maple Procedures for the Coupling of Angular Momenta. Vi. Ls − Jj Transformations Program Summary Long Write–up

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 coefficients has recently arose from the study of open d− and f −shell elements, the analysis of multiple–excited levels, or the investigation on inner–shell phenomena. Therefore, in order to facilitate a simple access to LS ↔ jj transformation matrices, here we present an extension to the Racah program for the set–up and the transformation of symmetry–adapted functions. A flexible notation is introduced for defining and for manipulating open–shell configurations at different level of complexity which can be extended also to other coupling schemes and, hence, may help determine an optimum classification of atomic levels and processes in the future. Computers for which the program is designed: All computers with a license of the computer algebra package Maple [1]. Installations: University of Kassel (Germany). Operating systems under which the program has been tested: Linux 6.1+. Program language used: Maple V, Release 6 and 7. Memory required to execute with typical data: 30 MB. Nature of the physical 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. Method of solution: LS − jj transformation matrices are provided for all (sub–) shell states with orbital angular momenta l ≤ 3 in the framework of the Racah program [2]. These matrices are then utilized to transform symmetry–adapted configuration state functions (CSF), including the coupling of two open shells. Moreover, a simple notation is introduced to handle such symmetry functions interactively and to transform even atomic states which are given as a superposition of CSF. Restrictions onto the complexity of the problem: The program presently supports all shell states with l ≤ 3, i.e. up to open f −shells, in LS−coupling …