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Manuscript Title: Integral of a product of three 6-dimensional spherical harmonics.
Authors: A. Amaya, E. Chacon
Program title: HHMTX
Catalogue identifier: ACHX_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 71(1992)159
Programming language: Fortran.
Computer: HP-9000 (SERIES 500).
Operating system: UNIX V.2, MicroVMS 4.7.
RAM: 146K words
Keywords: General purpose, Algebras, Hyperspherical harmonics, Three-body systems, Collective model, O(6).
Classification: 4.2.

Nature of problem:
Approximate eigenvalues and eigenfunctions for a Schrodinger equation H Psi = E Psi may be obtained by diagonalization of a truncated matrix of the intrinsic Hamiltonian H with respect to a complete set of functions depending on the relative vectors. In a system of three interacting bodies the matrix elements involve integrals of a product of two and three Dragt harmonics when the relative vectors are transformed to a set of 6-dimensional spherical coordinates and the harmonics are used as basis for the angular part. The program calculates the integral over five angular coordinates of two and three Dragt harmonic functions classified by the chain of groups O(6)>SO(2) X SU(3)>SO(3).

Solution method:
First, sets of labels for the possible irreducible representations allowed by group theory and consistent with the input data are generated and stored. For each set, a Dragt harmonic is calculated by a direct implementation of the realization given. A detailed description for the procedure by which integrals over each angular coordinate are performed is given in the long write up.

Restrictions:
For large quantum numbers it may be necessary to shift from 8 to 16 bytes of storage for numeric data in SUMSIG and DSL subroutines.

Running time:
For exapmles 1, 2, 3 and 5 it takes on hp-9000 (series 500) 0.2 seconds, 0.7 seconds, 4.1 seconds and 10.9 seconds, respectively.