Programs in Physics & Physical Chemistry
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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.|
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.
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.
The program restricts the general exchange integral to contain s or p angular functions. It could be extended to higher angular functions.
The program is written to overcome the effect of certain parameters which, for large values, lead to oscillating factors.
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.
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