PROGRAM SUMMARY
Title of program:
RACAH
Catalogue identifier:
ADNM
Ref. in CPC:
135(2001)219
Distribution format: gzip file
Operating system: Linux, Windows
High speed store required:
2MK words
Number of lines in distributed program, including test data, etc:
21742
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.
Programming language used: Maple V Release 4 and 5
Other versions of this program:
Cat. Id. Title Ref. in CPC ADFV Racah 103(1997)51 ADHW Racah 111(1998)167
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.
Method of solution:
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.
Restrictions:
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.
Typical 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.
References:
[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).