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Manuscript Title: Solution of differential equations for exchange matrix elements in heavy particle collisions.
Authors: L.A. Parcell
Program title: SOLVE D.E. FOR MATRIX ELEMENTS
Catalogue identifier: AAGU_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)283
Programming language: Fortran.
Computer: IBM 370.
Operating system: OS/370.
RAM: 18K words
Word size: 32
Keywords: Molecular, Exchange matrix element, Heavy particle collision, Impact parameter Approximation, Linear coupled Differential equations, Charge transfer.
Classification: 16.8.

Nature of problem:
In calculating cross sections for atomic collisions employing the impact parameter approximation, exchange matrix elements arise as coefficients of the differential equations for the transition amplitudes. Their evaluation is complicated by phase factors due to electron transfer momentum. The program calculates a general one- electron two-centre exchange integral in terms of which the matrix elements can be expressed.

Solution method:
These general exchange integrals may be found by solving a set of coupled differential equations. The program uses a method described by Parcell where the solutions are expressed in terms of a simple quadrature and which allows a step by step evaluation of the solutions along the collision path.

Restrictions:
The program restricts the general exchange integral to contain s or p angular functions. It could be extended to higher angular functions.

Unusual features:
The program is written to overcome the effect of certain parameters which, for large values, lead to oscillating factors.

Running time:
The time required to compute solutions will depend on parameter values, the step interval, and the number of solutions. For the test run with velocity 1.5 a.u., to find the values of 52 functions with at least 7- figure accuracy at 180 points between t=-30 and t=0 took 80 s CPU using the G compiler.