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The Library for Integration Over Spin-Angular variables in Atomic Theory

Gediminas Gaigalas
Institute of Theoretical Physics and Astronomy,
A. Goštauto 12, Vilnius 2600, LITHUANIA

Charlotte Froese Fischer
Department of Computer Science, Box 1679 B,
Vanderbilt University, Nashville, TN 37235, USA

In this paper a library for spin-angular integration in LS -coupling is presented. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin), and the graphical technique of angular momentum. This implementation extends applications in atomic theory capabilities to partially filled f - shells and has lead to faster execution of angular integration codes. The possibility of using some library routines for solving various angular momentum problems in atomic physics, is also discussed.

Theoretical determination of atomic energy levels, orbitals and radiative transition data requires the calculation of matrix elements of physical operators ( see the multiconfiguration Hartree-Fock method [1], for example). The matrix elements of arbitrary operator can generally be expressed as

$\sum_{i,j} coef(i,j) <\gamma_{i}L_{i}S_{i}\vert\vert T^{k_l k_s}\vert\vert\gamma_{j}L_{j}S_{j}>$ where $T^{k_l k_s}$ is a tensor operator of ranks $k_l$, $k_s$. The program calculates the spin-angular part for matrix elements $<\gamma_{i}L_{i}S_{i}\vert\vert T^{k_l k_s}\vert\vert\gamma_{j}L_{j}S_{j}>$ of one- and/or two-particle operator $T^{k_l k_s}$.

Method of solution
This program is created involving the angular methodology of [2-5]. It has been extended to include partially filled f - subshells in wavefunction expansions. The classification of terms is identical to that described in [5].

Restrictions on the complexity of the problem
The restrictions are similar to those described in [6] except that non-orthogonal orbitals are not supported. The initial and final state must constitute one orthonormal set for MLTPOL, LSTR and LSJTR.

Unusual features of the program
Some of the subroutines described in the libraries may be used separately, as electronic tables of standard quantities.

References

C. Froese Fischer, T. Brage and P. Jönsson, Computational Atomic Structure. An MCHF Approach (Institute of Physics Publishing, Bristol/Philadelphia, 1997).

G. Gaigalas and Z. Rudzikas, J. Phys. B: At. Mol. Phys. 29 (1996) 3303.

G. Gaigalas, Z. Rudzikas and C. Froese Fischer, J. Phys. B: At. Mol. Phys. 30 (1997) 3747.

G. Gaigalas, A. Bernotas, Z. Rudzikas and C. Froese Fischer, Physica Scripta 57 (1998) 207.

G. Gaigalas, Z. Rudzikas and C. Froese Fischer, Atomic Data and Nuclear Data Tables 70 (1998) 1.

C. Froese Fischer and B. Liu, Comput. Phys. Commun. 64 (1991) 406.




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Next: Introduction
2001-12-07