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Manuscript Title: Fast routine for the evaluation of two-centre integrals in heavy particle collisions.
Authors: A. Dubois
Program title: JANPET
Catalogue identifier: ABZM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 64(1991)300
Programming language: Fortran.
Computer: AMDAHL VP1100.
Operating system: TSO.
RAM: 700K words
Word size: 8
Peripherals: disc.
Keywords: Molecular physics, Wave function, Heavy particle collision, Two-centre matrix Element, Electron translational Factor, Slater-type orbital.
Classification: 16.10.

Nature of problem:
A convenient description of heavy particle collisions is provided by the coupled-channel impact parameter method. For systems where electron capture channels are open, the overlap and coupling matrices are partly composed by two-centre integrals. These latter cannot be expressed in a compact analytical form when the scattering state is expanded on Slater- type orbitals, modified by electron translational factors to insure Galilean invariance of the theory. These exchange matrix elements are then dependent on velocity, impact parameter and internuclear distance and their evaluation particularly time-consuming.

Solution method:
The exchange integrals are evaluated by the integration of a set of first-order coupled differential equations along the trajectory path. This method, introduced by Chesire is reformulated for convenience in the natural coordinate frame where the quantisation axis is perpendicular to the collision plane. This feature does not alter the general applicability of the routine since standard transformations to other reference frames can be readily applied.

Restrictions:
The present version of the routine is restricted to integrals involving s-, p- and d- states.

Running time:
The three test runs provided require less than 0.5 sec. Note that the running time is nearly independent of the number of mesh points required along the trajectory.