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Manuscript Title: Maple procedures for the coupling of angular momenta. VII. Extended and accelerated computations.
Authors: S. Fritzsche, T. Inghoff, M. Tomaselli
Program title: RACAH
Catalogue identifier: ADFV_v7_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 153(2003)424
Programming language: Maple 7 and 8.
Operating system: Linux 7.1+, Windows 2000.
RAM: 50M words
Keywords: Angular momentum, Bipolar harmonic, Clebsch-Gordan coefficient, Coefficient of fractional parentage, Condon-Shortley coefficient, Cruzan's algorithm, Gaunt coefficient, Racah's W-coefficient, Reduced matrix element, Rotation matrix, Sharp's symbol, Spherical harmonic, Spinor spherical harmonic, Tensor spherical harmonic, Tripolar harmonic, Unit tensor, Vector spherical harmonic, Wigner D-function, Wigner n-j symbol, Computational methods.
Classification: 4.1, 5.

Nature of problem:
The theories of angular momentum and spherical tensor operators provide a very powerful calculus for the study of (quantum) many-particle systems, sometimes known also as Racah's algebra. The efficient use of these theories, however, require - apart from the knowledge of a great deal of algebraic transformations and rules - a fast and reliable access to their standard quantities such as the Wigner n-j symbols and Clebsch-Gordan coefficients, spherical harmonics of various kinds, the rotation matrices, and many others.

Solution method:
A set of MAPLE [1] procedures has been developed and maintained over the last years which supports both, algebraic manipulations as well as fast computations of the standard expressions from the theory of angular momentum.

Of course, the full power of the angular momentum theory is given by a large set of (group-theoretical and often rather sophisticated) relations between its standard quantities, which may help simplify and reduce the "numerical costs" in the theoretical treatment of (quantum) many-particle systems dramatically. In fact, many details of such systems can be understood only if the proper algebraic relations are found and applied. In the present version of RACAH, however, symbolic manipulations are supported so far only for those expressions which include the Wigner n-j symbols (n<=9), Clebsch-Gordan coefficients and/or spherical harmonics. For all other quantities, we currently just facilitate fast numerical computations, by making use also of MAPLE's recently implemented hardware floating-point model.

Unusual features:
The RACAH program provides an interactive environment which apart from the standard symbols and fuctions of the theory of angular momentum, also supports the evaluation of recoupling coefficients, various coefficients and matrix elements from the atomic shell model as well as transformtion matrices between different coupling schemes [2].

Running time:
Although the program replies 'promptly' on most requests, the running time depends strongly on the complexity of the expressions.

[1] Maple is a registered trademark of Waterloo Maple Inc.
[2] S. Fritzsche, Comp. Phys. Commun. 103 (1997) 51; G. Gaigalas, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 135 (2001) 219; S. Fritzsche, T. Inghoff, T. Bastug, M. Tomaselli, Comp. Phys. Commun. 139 (2001) 314.