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Manuscript Title: Maple procedures for the coupling of angular momenta. III. Standard quantities for evaluating many-particle matrix elements.
Authors: G. Gaigalas, S. Fritzsche, B. Fricke
Program title: RACAH
Catalogue identifier: ADFV_v3_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 135(2001)219
Programming language: Maple V Release 4 and 5.
Operating system: Linux, Windows.
RAM: 2M words
Keywords: General purpose, Rotation group, Angular momentum, Atomic many-body perturbation theory, Complex atom, jj-coupling, LS-coupling, Recoupling coefficient, Reduced coefficient of fractional parentage, Reduced matrix element, Standard unit tensor, Tensor operator, Computer algebra.
Classification: 4.1, 5.

Nature of problem:
In atomic and nuclear structure theory, the evaluation and spin-angular integration of many-particle matrix elements is typically based on standard quantities like the matrix elements of the unit tensor, the (reduced) coefficients of fractional parentage as well as a number of other reduced matrix elements concerning various products of creation and annihilation operators. These quantities arise very frequently both in configuration interaction approaches and the derivation of perturbation expansions for many-particle systems using symmetry-adapted configuration state functions.

Solution method:
In the framework of the RACAH program [2], we provide a set of procedures for the manipulation and computation of such standard quantities in atomic theory. Different classifications of the antisymmetrized (sub-) shell states are supported for both, LS- and jj-coupling. The currently provided set of entities includes the coefficients of fractional parentage, the reduced coefficients of fractional parentage, and the reduced matrix elements of the operators U^(k), V^(k1) and W^(kqklks) in LS-coupling and of the operators T^(k) and W^(kqkj) in jj-coupling, respectively.

Coefficients and reduced matrix elements can be obtained for all shells with l <= 3 in LS-coupling, i.e. including open f-shells, and for all subshells with j <= 9/2 in jj-coupling (i.e. up to f9/2 and g9/2 subshells).

Unusual features:
The interactive use of the procedures within the RACAH program [2] allows a quick and reliable 'electronic reference' to these quantities for evaluating general matrix elements. The concept and functionality of MAPLE [1] can easily be exploited to combine these coefficients in any other (useful) form than supported by the program in order to support the evaluation of complex expressions. The definitions and relations which are relevant for the computation of those quantities are displayed in Appendix A. For quick reference, Appendix B lists the additional or extended commands to the RACAH program.

Running time:
The program replies promptly on all requests. Even lengthy tabulations of (reduced) coefficients and matrix elements can easily be carried out within a few (tens of) seconds.

[1] Maple is a registered trademark of Waterloo Maple Inc.
[2] S. Fritzsche, Comp. Phys. Commun. 103, 51 (1997); S. Fritzsche, S. Varga, D. Geschke and B. Fricke, Comp. Phys. Commun. 111, 167 (1998).