PROGRAM SUMMARY
Title of program:
RACAH
Catalogue identifier:
ADRW
Ref. in CPC:
153(2003)422
Distribution format: tar gzip file
Operating system: Linux 7.1+, Windows 2000
High speed store required:
50MK words
Number of lines in distributed program, including test data, etc:
73719
Keywords:
Angular momentum, Bipolar harmonic, Clebsch-Gordan coefficient,
Coefficient of fractional parentage, Condon-Shortley coefficient,
Cruzan's algorithm, Gaunt coefficient, Racah's W-coefficient,
Element reduced matrix, 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.
Programming language used: Maple 7 and 8
Other versions of this program:
Cat. Id. Title Ref. in CPC ADOS RACAH 139(2001)314 ADQP RACAH 149(2002)39
Nature of physical 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.
Method of solution:
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.
Restrictions:
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].
Typical running time:
Although the program replies 'promptly' on most requests, the running
time depends strongly on the complexity of the expressions.
References:
[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.