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Manuscript Title: Unified approach for exact calculation of angular momentum coupling and recoupling coefficients.
Authors: L. Wei
Program title: 369j
Catalogue identifier: ADKL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 120(1999)222
Programming language: Fortran.
Computer: DEC 3000/400 alpha.
Operating system: UNIX (Digital).
Word size: 64
Keywords: Rotation group, Angular momentum coupling and recoupling coefficients, 3j-symbol, 6j-symbol, 9j-symbol, Binomial coefficients, Recursive relation, Prime number Representation, 32768-base number Representation.
Classification: 4.1.

Nature of problem:
Angular momentum coupling and recoupling coefficients occur in almost all of the areas using quantum mechanics. The accurate and fast calculation of 3j, 6j and 9j symbols is required in a variety of situations in nuclear physics, atomic physics, molecular physics, and astrophysics, etc.

Solution method:
The algebraic expressions of 3j, 6j and 9j symbols have all been reformulated as the summation of products of binomial coefficients. The programs calculate the binomial recursively at every stage instead of evaluating factorials of integers. We also use two different number representations in the calculation: prime number representation for the prefactor, and 32768-base number representation for the summation terms.

Running time:
The time taken for calculating 3j, 6j and 9j symbols of small angular momenta is almost instantaneous. It is still less than 0.1 second for 3j symbols, and 0.2 second for 6j symbols, when angular momenta reach 200. For 9j symbols, it is less than 1.0 second when angular momenta approach 100.