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Manuscript Title: Evaluation of a general three-denominator Lewis integral.
Authors: U. Roy, L.J. Dube, P. Mandal, N.C. Sil
Program title: LEWIS
Catalogue identifier: ADCO_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 92(1995)277
Programming language: Fortran.
Computer: PC Pentium-100.
Operating system: MS DOS v. 6.2, SOLARIS v. 2.x.
Word size: 64
Keywords: Three-denominator lewis Integrals, Dalitz integration, Variational and Collisional calculations, General purpose, Quadrature, Analytic, Contour integration.
Classification: 4.11.

Nature of problem:
Structural and collisional studies in atomic, molecular and nuclear physics often encounter a certain type of 3-denominator integrals in the course of the calculations [1]. These integrals (called here general Lewis integrals [2]) appear naturally whenever two or more centres of force are present and relative coordinates of the interacting particles are involved. We derive a closed analytic form for these integrals and demonstrate by a few examples the usefulness of the results.

Solution method:
Expressions for a general class of 3-denominator Lewis integrals are obtained by contour integration as a sum of two finite series, thereby avoiding parametric differentiation of a complicated closed form. Analytical methods are employed throughout, thus enabling high accuracy and efficiency of the calculations.

The highest order of the derivatives of the Lewis integrals is limited to 3 and the parameters (mu0,mu1,mu2) and variables (q1,q2) are taken to be real.

[1] C.J. Joachain, Quantum collision theory (North-Holland, Amsterdam, 1983)
[2] R.R. Lewis, Phys Rev A102 (1956) 537