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Manuscript Title: Exact computation of the 9-j symbols.
Authors: S.-T. Lai, Y.-N. Chiu
Program title: W9J
Catalogue identifier: ACHW_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 70(1992)544
Programming language: Fortran.
Computer: VAX 8650.
Operating system: VMS version 5.4-1.
Word size: 32
Keywords: General purpose, Rotation group, Nuclear, Atomic, Molecular angular Momentum, Nuclear structure, Nuclear reaction, Recoupling coefficient, 9j-symbol, Wigner 9j-symbol, 3-photon transition.
Classification: 4.1.

Nature of problem:
The program calculates the exact 9-j (for low angular momentum j up to j=10) and the approximate 9-j coefficient (for high j up to j=90 or higher), using the triple sum formula due to Jucys and Bandzaitis (rewritten for exact computational use by authors). This coefficient arises in the recoupling of four angular momenta, which can be coupled by different schemes. It is of fundamental importance in the evaluation of matrix elements in nuclear, atomic, molecular physics and molecular reaction dynamics calculations (multiphoton transitions).

Solution method:
The simplest known form of the 9-j symbols due to Jucys-Bandzaitis has been rewritten for the convenient use in a computer. The program decomposes the large number of factorial and the integer number which arise in the triple sum into a product of prime factors with certain powers.

Running time:
The execution time required on the VAX 8650 to compute a given 9-j symbol depends mainly on the number of terms to be summed. It could be varied from less than one second to more than one minute CPU time since the program uses REAL*16. The results are more accurate than other numerical computations especially when angular momentum quantum number becomes large (e.g. j=90 or higher).