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Manuscript Title: Maple procedures for the coupling of angular momenta. VI. LS-jj transformations.
Authors: G. Gaigalas, S. Fritzsche
Program title: RACAH
Catalogue identifier: ADFV_v6_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 149(2002)39
Programming language: Maple V Release 6 and 7.
Operating system: Linux 6.1+.
RAM: 30M words
Keywords: Angular momentum, Complex atom, Configuration state function, jj-coupling, LS-coupling, LS-jj transformation, LSJ and jjJ spectroscopic notation, Nonrelativistic, Relativistic, Subshell state, General purpose, Rotation group.
Classification: 4.1, 5.

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.

Solution method:
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:
The program presently supports all shell states with l<=3, i.e. up to open f-shells, in LS-coupling and with j<=7/2, i.e. up to open f7/2- and g7/2-subshells, in jj-coupling. For the transformation of configuration state functions, the coupling of two open LS-shells or, correspondingly, four jj-subshells are also supported. In jj-coupling, however, a standard order [cf. Section 2.2] is always assumed for the coupling sequence of the individual shells. Several simplifications are used on the basis of this standard order.

Unusual features:
Apart from the "interactive access" to the LS-jj transformation matrix elements between (sub-)shell states in LS- and jj-coupling, a complete transformation of the coupling scheme can be carried out also for configuration respectively atomic state functions, just by typing a few lines at MAPLE's prompt. To simplify the handling of the program, a short but very powerful notation has been introduced which help the user to construct stepwise symmetry-adapted functions of different complexity. But although the program presently supports only shell states in LS- and jj-coupling, the same notation can be extended also to incorporate further coupling schemes in the future. The main commands of the present extension are described in detail in Appendix B; for a quick reference on the current capabilities of the RACAH program, we refer the reader to Ref. [3] and to a list of all available commands in the file Racah-commands.ps which is appended to the code.

Running time:
The program replies promptly on most requests. Even large tabulations of LS-jj transformation matrices can be carried out in a few (tens of) seconds.

References:
[1] Maple is a registered trademark of Waterloo Maple Inc.
[2] S. Fritzsche, Comp. Phys. Commun. 103 (1997) 51; G. Gaigalas, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 135 (2001) 219.
[3] S. Fritzsche, T. Inghoff, T. Bastug and M. Tomaselli, Comp. Phys. Commun. 139 (2001) 314.