Therefore, the computation of angular coefficients for different coupling schemes, (grand) coefficients of fractional parentage as well as the matrix elements (of various irreducible tensors from the shell model) is to be maintained from now on independently within the Jucys module (iii) a number of bugs and inconsistencies have been reported to us and corrected in the present version.

Reasons for new version: A revision of the Racah module became necessary for mainly three reasons: (i) Since the last extension of the Racah procedures, which was developed within the framework of Maple 8, several updates of Maple were distributed by the vendors (currently Maple 13) and required a number of adaptations to the source code (ii) the increasing size and program structure of the Racah module made it advisible to separate the (procedures for the treatment of the) atomic shell model from the manipulation and computation of Racah expressions. In particular the algebraic manipulation of complex ( Racah) expressions may result in considerable simplifications, thus reducing the ‘numerical costs’, and often help obtain further insight into the behaviour of physical systems. These procedures are based on a sizeable set of group-theoretical (and often rather sophisticated) relations which has been discussed and proven in the literature see the monograph by Varshalovich et al.

Solution method: A set of Maple procedures has been developed and maintained during the last decade which supports both, algebraic manipulations as well as fast computations of the standard expressions and symbols from the theory of angular momentum. For an efficient use of these theories, however, one requires not only a reliable handling of a large number of algebraic transformations and rules but, more often than not, also a fast access to their standard quantities, such as the Wigner n - j symbols, Clebsch–Gordan coefficients, spherical harmonics of various kinds, the rotation matrices, and many others. Nature of problem: The theories of angular momentum and spherical tensor operators, sometimes known also as Racah's algebra, provide a powerful calculus for studying spin networks and (quantum) many-particle systems. 174 (2006) 616ĭoes the new version supersede the previous version?: Yes Journal reference of previous version: Comput. Operating system: Suse Linux 10.2+ and Ubuntu 8.10Ĭatalogue identifier of previous version: ADFV_v9_0 of bytes in distributed program, including test data, etc.: 544 866Ĭomputer: All computers with a license for the computer algebra package Maple of lines in distributed program, including test data, etc.: 30 436 Licensing provisions: Standard CPC licence, Program obtainable from: CPC Program Library, Queen's University, Belfast, N.

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