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Manuscript Title: Parallel computation of recoupling coefficients using transputers.
Authors: V. Fack, J. Van der Jeugt, K. Srinivasa Rao
Program title: NINEJPAR
Catalogue identifier: ACJE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 71(1992)285
Programming language: C.
Computer: T800/20 MHZ TRANSPUTERS.
Operating system: MS-DOS.
Keywords: General purpose, Transputer, Parallel processing, Farming technique, Nuclear, Atomic, Molecular, Angular momentum, Nuclear structure, Nuclear reaction, Recoupling coefficient, 9-j coefficients, Ls-jj transformation Coefficient, Rotation group, Element matrix.
Classification: 4.1.

Nature of problem:
A parallel program calculates the 9-j coefficient (also called the ls-jj transformation coefficient) using the single sum over the product of three 6-j coefficients formula. This coefficient arises in the recoupl- ing of four angular momenta, which can be coupled either using the Russell-Saunders scheme or the jj-coupling scheme. It is of fundamental importance in the evaluation of matrix elements which occur in nuclear, atomic and molecular physics.

Solution method:
The classical formula for the 9-j coefficient is a single sum expression involving the product of three 6-j coefficients in every term. It is pointed out how such an expression is ideally suited for parallel computation, and can be executed on a network of transputers. A farming technique is used, whereby a master processor takes care of distributing work packets over worker processors calculating products of three 6-j coefficients, of receiving intermediate results from the worker processors, and of calculating the final result. The 6-j coefficient itself is computed by means of a single sum expression. This parallel program is compared with two sequential programs for the 9-j coefficient, one using the same single sum expression in terms of 6-j coefficients, and one using a triple sum series due to Jucys and Bandzaitis.

Running time:
The execution time required to compute a given 9-j coefficient, using either the single sum over the product of three 6-j coefficients or the triple sum series, depends mainly upon the values of the nine angular momenta. For a comparison between sequential programs based upon the single sum expression and the triple sum series, see Srinivasa Rao et al, (Comp. Phys. Commun. 56(1989)231). Here, we focus our attention on the advantage factor of the parallel program compared with the sequential program. With a network of 5 transputers, this advantage factor is of the order 4 for large values of angular momenta.