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Manuscript Title: Angular momentum coupling coefficients.
Authors: T. Tamura
Program title: GEOMETRICAL COEFFICIENT
Catalogue identifier: ABMA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 1(1970)337
Programming language: Fortran.
Computer: CDC 6600.
Operating system: CDC SCOPE.
RAM: 6K words
Word size: 60
Keywords: Nuclear physics, Atomic physics, General purpose, Nuclear spectra, Nuclear structure, Atomic spectra, Transformation matrices, Recoupling coefficient, Racah coefficient, Wigner coefficient, Fano coefficient, 3j-symbol, 6j-symbol, 9j-symbol, Clebsch-gordan, Angular momentum, Rotation group.
Classification: 4.1.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 19/01/71 See below

Nature of problem:
Calculates the geometrical coefficients, like Clebsch-Gordan coefficient, Racah coefficient, 9-j symbol and so forth, occurring in the quantum theory of angular momentum. The present program will thus be of universal use in almost any branch of physics that uses quantum mechanics.

Solution method:
Logarithms of factorials are calculated and are stored, once and for all in the beginning of the main routine. Symmetry properties of the coefficients are used to optimize the speed of the calculation.

Restrictions:
Restrictions come solely from the size of the core assigned to store the logarithms of factorials. Since the number of cores needed for that purpose is rather small in general, it does not mean in practice any real restriction. Also essentially there is no danger of over and underflow difficulties even when very large angular momenta are treated.

Running time:
The running time is the longer the larger is the smallest argument that appears in a given coefficient. For Clebsch-Gordan and Racah coefficients that are encountered in the usual calculations, with the values of arguments ranging from zero to twenty, say, the average time to calculate one of such coefficients is about one to two tenths of a millisecond on a CDC 6600.

CORRECTION SUMMARY
Manuscript Title: Angular momentum coupling coefficients. (C.P.C. 1(1970)337).
Authors: T. Tamura
Program title: 000A CORRECTION 19/01/71
Catalogue identifier: ABMA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)174
Classification: 4.1.