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Manuscript Title: Generalized transformation brackets for the harmonic oscillator functions.
Authors: M. Sotona, M. Gmitro
Catalogue identifier: ABGH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 3(1972)53
Programming language: Fortran.
Computer: IBM 7040.
Operating system: IBSYS.
RAM: 3K words
Word size: 36
Keywords: Nuclear physics, Oscillator bracket, Reaction, Matrix element, Talmi coefficient, Brody-moshinsky bracket, Angular momentum, Harmonic oscillator.
Classification: 17.17.

Nature of problem:
The program calculates the transformation coefficient in the expansion of two coupled harmonic oscillator wavefunctions (for particles 1 and 2) into coupled pairs of relative and centre-of-mass functions. It will thus be of general use in almost any calculation using harmonic oscillator bases.

Solution method:
The formula used for computation is essentially of a recursive type. It starts with the l=0 case and is therefore especially suited for the brackets with one small angular momentum as required in modern nuclear structure calculations with realistic nucleon-nucleon potentials.

The only restrictions come from the core area assigned to store logarithms of factorials and gamma functions calculated once and for all at the beginning of execution. Since the core requirements are very modest an enlargement of the corresponding arrays is always possible.

Running time:
The running time strongly depends on the smallest angular momentum that appears in a given coefficient and on the nodal quantum numbers. Only the relative angular momenta l=0, 1 and 2 are usually needed, then the average time to calculate one such coefficient is about 50, 100, 200 ms respectively on an IBM 7040. See also table 1 of the long write-up.