Jahn—A program for representing atomic and nuclear states within an isospin basis

A computer program is presented to deal with atomic and nuclear state functions within an isospin-coupled basis. Apart from the classification of the isospin bases states, the program Jahn supports the computation of the corresponding coefficients of fractional parentage as well as of the transformation matrices going from a LS-coupled to an isospin-coupled basis. In the future, these features may facilitate the treatment of atomic systems in order to obtain a deeper insight into the coupling of open-shell atoms and ions. The Jahn program has been designed for interactive work and is distributed as a Maple module.Program summaryTitle of program:JahnCatalogue identifier:ADXA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXA_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:NoneComputers for which the program is designed: All computers with a valid license of the computer algebra package Maple which is a registered trademark of Waterloo Maple Inc.Installations: University of Kassel (Germany)Operating systems under which the program has been tested: Linux 8.1+Program language used:Maple, Release 8 and 9Memory required to execute with typical data: 30 MBNumber of lines in distributed program, including test data, etc.: 38 158Number of bytes in distributed program, including test data, etc.: 743 689Distribution format: tar.gzNature of the physical 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 n1lN1n2lN2n1lN1n2lN2.Method of solution: The concept of the isospin formalism is used and explained in [V. Šimonis, PhD Thesis, Institute of Physics, Vilnius, 1982 (in Russian); Z. Rudzikas, J. Kaniauskas, Quasispin and Isospin in the Theory of Atom, Mokslas, Vilnius, 1984 (in Russian); J.M. Kaniauskas, V.Č. Šimonis, Z.B. Rudzikas, J. Phys. B: At. Mol. Phys. 20 (1987) 3267]. 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 n1lN1n2lN2n1lN1n2lN2. Moreover, a simple notation is introduced to handle such symmetry functions interactively.Restrictions onto the complexity of the problem:   The classification of the n1lN1n2lN2n1lN1n2lN2 electron configurations provides support for the subshell angular momentum l=0,…,2l=0,…,2 and for the occupation numbers N1N1 and N2N2, where N1N1 and N2N2 must be in the range N1=0,…,(2l+1)N1=0,…,(2l+1) and N2=0,…,(2l+1)N2=0,…,(2l+1), respectively. The program provides the CFP and CFGP for isospin-coupled subshell states for the orbital angular momenta l=0,1l=0,1 and occupation numbers N⩽2(2l+1)N⩽2(2l+1) and for l   = 2 with N⩽4N⩽4, respectively. It also evaluates the transformation matrices 〈lN1lN2w1L1S1w2L2S2LS|lN1lN2wTLS〉 for l=0,1l=0,1 and occupation numbers N1N1, N2N2 and N   in the range N1=0,…,2lN1=0,…,2l; N2=1,2N2=1,2; N=N1+N2⩽2(2l+1)N=N1+N2⩽2(2l+1) and for l=2l=2 and occupation numbers N1N1, N2N2 and N   in the range N1=0,…,3N1=0,…,3; N2=1,2N2=1,2; N=N1+N2⩽4N=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 of the program:   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 Appendices A and B.Typical running time: The program replies promptly on most requests. Even large tabulations of CFP or transformation matrices can be obtained within a few seconds.