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Manuscript Title: Hyperfine structure parametrization in Maple
Authors: O. Scharf, S. Fritzsche, G. Gaigalas
Program title: Hfs
Catalogue identifier: ADXD_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 174(2006)202
Programming language: Maple, Release 7, 8 and 9.
Computer: All computers with a license for the computer algebra package Maple [1].
Operating system: Linux 9.0.
Keywords: hyperfine structure, electric quadrupole interaction, magnetic dipole interaction, spin-angular coefficients for hyperfine structure operators, parametrization of the A and B factors, semiempirical hyperfine structure analysis.
PACS: 3.65F, 2.90+p.
Classification: 2.9.

Nature of problem:
Atomic state functions of an many configuration many electron atom with several open shells are defined by a number of quantum numbers, by their coupling and selection rules such as the Pauli exclusion principal and parity conservation. The matrix elements of any one-particle operator acting on these wave functions can be analytical integrated up to the radial part [3]. The decoupling of the interacting electrons is general, the obtained submatrix element holds all the peculiarities of the operator in question. These submatrix elements are the key to do hyperfine structure calculations. The interaction between the electrons and the atomic nucleus leads to an additional splitting of the fine structure lines, the hyperfine structure. The leading components are the magnetic dipole interaction defining the A factor and the electric quadrupole interaction, defining the B factor. They express the energetic splitting of the spectral lines. Moreover, they are obtained directly by experiments and can be calculated theoretical in an ab initio approach. A semiempirical approach allows to least square fit the radial parts of the wave function to the experimental obtained A and B factors.

Solution method:
The atomic environment is defined in Maple by extending the existing procedures csf_LS() and asf_LS() to several open shells and implementing a data structure level_LS() for the fine structure level. A general approach to decouple the interacting shells for any one-particle operator is implemented leading to the so-called submatrix element. The submatrix elements for the magnetic dipole and electric quadrupole interaction are implemented, allowing to calculate the A and B factors up to the radial part. Several procedures for standard quantities of the hyperfine structure are defined, too. The calculations are accelerated by using a hyper-geometric approach for three, six and ninej symbols.

Restrictions:
Only atomic state functions in nonrelativistic LS-coupling with states having l ≤ 3 are supported.

Running time:
The program replies promptly on most requests. The least square fit depends heavily on the number of levels and can take a few minutes.

References:
[1] Maple is a registered trademark of Waterloo Maple Inc.
[2] S. Fritzsche, Computer Physics Communication 103, 51 (1997).
[3] G. Gaigalas, Z. Rudzikas, O. Scharf, Central European Journal of Physics 2, 720 (2004).