Spectroscopic LSJ notation for atomic levels obtained from relativistic calculations

Abstract

Listen

Translate article

Today, relativistic calculations are known to provide a very successful means in the study of open-shell atoms and ions. But although accurate atomic data are obtained from these computations, they are traditionally carried out in jj-coupling and, hence, do often not allow for a simple LSJ classification of the atomic levels as needed by experiment. In fact, this lack of providing a proper spectroscopic notation from relativistic structure calculations has recently hampered not only the spectroscopy of medium and heavy elements, but also the interpretation and analysis of inner-shell processes, for which the occurrence of additional vacancies usually leads to a very detailed fine structure. Therefore, in order to facilitate the classification of atomic levels from such computations, here we present a program (within the Ratip environment) which help transform the atomic wave functions from jj-coupled multiconfiguration Dirac–Fock computations into a LS-coupled representation. Beside of a proper LSJ assignment to the atomic levels, the program also supports the full transformation of the wave functions if required for (nonrelativistic) computations. Program summary Title of program: Lsj Catalogue number: ADTL Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADTL Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the new version has been tested: IBM RS 6000, PC Pentium III Installations: University of Kassel (Germany) Operating systems: IBM AIX 4.1.2+, Linux 7.1.+ Program language used in the new version: ANSI standard Fortran 90/95 Memory required to execute with typical data: Memory requirements depend on the shell structure and the size of the wave function expansion which is used to represent the atomic levels No. of bits in a word: All real variables are parametrized by a selected kind parameter and, thus, can easily be adapted to any required precision as supported by the compiler. Presently, the kind parameter is set to double precision (two 32-bit words) in the module rabs_constant No. of lines in distributed program, including test data, etc.: 225 242 No. of bytes in distributed program, including test data, etc.: 3 646 630 CPU time required to execute test data: 5 s on a 1 GHz Pentium III processor Distribution format: tar gzip file Keywords: Atomic, LSJ spectroscopic notation, LS− jj transformation, multiconfiguration Dirac–Fock, recoupling of angular momenta, relativistic Nature of the physical problem: The spectroscopic LSJ notation is determined for atomic levels which were calculated previously in the framework of the jj-coupled multiconfiguration Dirac–Fock (MCDF) model. This notation is based on a complete jj− LS transformation of the leading jj-coupled configuration state functions (CSF) in the wave function representation of the selected levels. Restrictions onto the complexity of the problem: The jj→ LS transformation of the ( jj-coupled) CSF is supported for all shell structures including open s-, p-, d-, and f-shells. For shells with l>3 (i.e. beyond the f-subshells), however, a proper transformation of the antisymmetrized subshell states can be carried out only for the case of one or two equivalent electrons. This restriction also applies for the transformation of the g 7/2 and g 9/2 subshell states which are otherwise supported by the Ratip package [Fritzsche, J. Elec. Spec. Rel. Phen. 114–116 (2001) 1155]. The jj↔ LS transformation matrices, which are applied internally by the program, are consistent with the definition of the (reduced) coefficients of fractional parentage [Gaigalas et al., At. Data Nucl. Data Tables 70 (1998) 1; Gaigalas et al., At. Data Nucl. Data Tables 76 (2000) 235] as published previously. Unusual features of the program: The Lsj program is designed as a part of the Ratip package [Fritzsche, Elec. Spec. Rel. Phen. 114–116 (2001) 1155] for the computation of (relativistic) atomic transition and ionization properties. This (new) component therefore supports the transformation of all atomic states which are generated either with Ratip or by means of the Grasp92 code [Parpia et al., Comput. Phys. Comm. 94 (1996) 249]. Moreover, the normalization of the transformed states is tested within the LSJ-coupled basis.