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Manuscript Title: JAHN - A program for representing atomic and nuclear states within an isospin basis
Authors: G. Gaigalas, S. Fritzsche, E. Gaidamauskas, G. Kirsanskas, T. Zalandauskas
Program title: JAHN
Catalogue identifier: ADXA_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 175(2006)52
Programming language: Maple, Release 8 and 9.
Computer: All computers with a valid license for the computer algebra package Maple which is a registred trademark of Waterloo Maple Inc.
Operating system: Linux 8.1+.
RAM: 30 MB
Keywords: Angular momentum theory, Atomic shell model, Atomic structure theory, Coefficients of fractional grandparentage, Coefficients of fractional parentage, Complex atom and spectra, Isospin basis, Isospin formalism, LS-coupling, Nuclear theory, Racah algebra within three spaces (orbital, spin and isospin space), Subshell state, Symmetry-adapted function.
PACS: 3.65F, 2.90+p..
Classification: 2.9.

External routines: requires RACAH (Catalogue Id. ADFV)

Nature of problem:
The accurate computation of atomic (nuclear) properties and level structures requires a good understanding and implementation of the atomic (nuclear) shell model and, hence, a fast and reliable access to its classification, the coefficients of fractional parentage and the coefficients of fractional grandparentage. For open-shell atoms and ions, moreover, a reliable classification of the level structure often requires the knowledge of some transformation matrices in order to find the main components of the wave functions as well as their proper spectroscopic notation. In particular, the transformation from a LS-coupled to an isospin-coupled basis is important for atoms and ions with the two open shells n1lN1n2lN2.

Solution method:
The concept of the isospin formalism is used and explained in refs [1, 2, 3]. The coefficients of fractional parentage (CFP) in the isospin basis, the coefficients of fractional grandparentage (CFGP) in the isospin basis and the transformation matrices from a LS-coupled to an isospin-coupled basis are provided for s, p, d, shells. These matrices are utilized to transform symmetry-adapted configuration state functions (CSF) as obtained from the coupling of two open shells n1lN1n2lN2. Moreover, a simple notation is introduced to handle such symmetry functions interactively.

The classification of the n1lN1n2lN2 electron configurations provides support for the subshell angular momentum l = 0,...,2 and for the occupation numbers N1 , and N2 where N1 and N2 must be in the range N1 = 0,...,(2l+1) and N2 = 0,...,(2l+1), respectively. The program provides the CFP and CFGP for isospin-coupled subshell states for the orbital angular momenta l = 0,1 and occupation numbers N ≤ 2(2l+1) and for l = 2 with N ≤ 4, respectively. It also evaluates the transformation matrices 〈lN1lN2w1L1S1w2L2S2LS |lN1lN2wTLS〉 for l = 0,1 and occupation numbers N1, N2 and N in the range N1 = 0,..,2l; N2 = 1,2; N = N1 + N2 ≤ 2(2l+1) and for l = 2 and occupation numbers N1, N2 and N in the range N1 = 0,..,3; N2 = 1,2; N = N1 + N2 ≤ 4, respectively. The transformation of an atomic state function (ASF) or configuration state function (CSF) from an LS-coupled to an isospin-coupled basis can be obtained for these orbital momenta and occupation numbers.

Unusual features:
The program is designed as an interactive environment for the (symbolic) manipulation and computation of expressions from theory of atomic and nuclear shell model. Here we provide the user with a simple access to the coefficients of fractional parentage as well as to the transformation matrices 〈lN1lN2w1L1S1w2L2S2LS |lN1lN2wTLS〉. A complete transformation of LS-coupled CSF or ASF into an isospin-coupled basis can be carried out just by typing a few lines at Maple's prompt. These coefficients and transformation matrices enable the user to make a more detailed analysis of matrix elements of the operators of physical quantities within the isospin basis. The (main) commands of the JAHN program are described in detail in the appendices A and B of the manuscript..

Running time:
The program replies promptly on most requests. Even large tabulations of CFP or transformation matrices can be obtained within a few seconds.

[1] V. Šimonis, PhD Thesis, (Institute of Physiscs, Vilnius, 1982) (in Russian).
[2] Z. Rudzikas and J. Kaniauskas, Quasispin and Isospin in the Theory of Atom (Mokslas, Vilnius, 1984) (in Russian).
[3] J.M. Kaniauskas, V. C. Šimonis and Z.B. Rudzikas, J. Phys. B: At. Mol. Phys. 20 (1987) 3267.