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Manuscript Title: Atomic integral containing three odd powers of interelectronic separation coordinates.
Authors: A.H. Moussa, H.M.A. Radi
Program title: ATOMINT
Catalogue identifier: ACRO_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 6(1973)89
Programming language: Fortran.
Computer: IBM 360/30.
Operating system: SYSTEM / 360 (DOS).
RAM: 72K words
Word size: 8
Keywords: Atomic physics, Hylleraas functions, Bound state, Wave function, Variational method.
Classification: 2.7.

Nature of problem:
The subroutine ATOMINT evaluates an atomic integral, containing 3 odd powers of interelectronic separation coordinates, which appears in bound state variational calculations of three electron atoms, and in phase shift variational calculation of scattering of electron (or positrons) by two electron atoms.

Solution method:
The integral is expanded as infinite sums of Legendre polynomials, and these angular terms are reduced, by applying the coupling rules of spherical harmonics, to simple integrals which are easily integrated. The orthogonal properties keep one infinite sum only to do. The limits of the radial integrals are divided into six parts, and the resulting integrals are evaluated in closed forms in most cases and in a convergent sum in one case. On the average, five terms lead to a reasonable accuracy.

Running time:
The time depends on the input values, and on the number of terms in the infinite sum; the average time is between 5-10 min approximately.