Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] adrm_v1_0.tar.gz(109 Kbytes)
Manuscript Title: New heuristic approach to the calculation of general recoupling coefficients.
Authors: D. Van Dyck, V. Fack
Program title: CycleCostAlgorithm, GYutsis
Catalogue identifier: ADRM_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 151(2003)354
Programming language: Java 1.2.
Computer: Pentium II-350.
Operating system: Linux.
Keywords: Angular momentum, General recoupling coefficient, Racah coefficient, Wigner n-j symbols, Graphical rules, Yutsis graph, Computational methods, Rotation group.
Classification: 4.1.

Nature of problem:
A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta can be expressed as a formula consisting of products of 6-j coefficients summed over a certain number of variables. Such a formula can be generated using the program GYutsis (with a graphical user front end) or CycleCostAlgorithm (with a text-mode user front end).

Solution method:
Using the graphical techniques of Yutsis, Levinson and Vanagas [1] a summation formula for a general recoupling coefficient is obtained by representing the coefficient as a Yutsis graph and by performing a selection of reduction rules valid for such graphs. Each reduction rule contributes to the final summation formula by a numerical factor or by an additional summation variable. Whereas an optimal summation formula (i.e. with a minimum number of summation variables) is hard to obtain, we present here a new heuristic approach for selecting an edge from a k-cycle in order to transform it into an (k-1)-cycle (k>3) in such a way that a 'good' summation formula is obtained.

Running time:
From instantaneously for the typical problems to a few seconds for the heaviest problems on a Pentium II-350 Linux-system with 256 MB RAM.

References:
[1] A.P. Yutsis, I.B. Levinson and V.V. Vanagas, Mathematical Apparatus of the Theory of Angular Momentum (Israel Program for Scientific Translation, Jerusalem, 1962).