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Manuscript Title: A procedure to evaluate the cross section for electron-hydrogen collisions in the Bethe approximation to the reactance matrix.
Authors: A. Burgess, C.T. Whelan
Program title: BETRT
Catalogue identifier: AAXK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 47(1987)295
Programming language: Fortran.
Computer: IBM 3081.
Operating system: MVS.
Keywords: Atomic physics, Electron-neutral atom, Collisions, Partial wave analysis, Weber Schafheitlin integrals, Legendre functions of The second kind, Seaton coefficients, Born approximation to Reactance matrix (born Ii), Burgess sum rules, Bethe approximation to Reactance matrix.
Classification: 2.4.

Nature of problem:
The calculation of cross sections for electron impact excitation of neutrals in the intermediate energy range is greatly complicated by the large number of partial waves which contribute. It has been argued that the unitarised Born approximation gives an adequate representation of all but the partial cross sections corresponding to the smallest values of L, the total angular momentum. Further for L large the Born Reactance matrix may be approximated to a high degree of accuracy by the Bethe. The program presented here is restricted to the electron- hydrogen problem; however it is trivial to modify for use with any target which can be represented as a single electron outside a closed shell (for electron-lithium scattering), further many of the subroutines can be equally well applied to the scattering of an electron from any neutral system. In particular the method of evaluating the important special case of the Weber-Schafheitlin integral presented here will lead to a significant reduction in the computer time needed in all problems where a high L approximation to the Born integrals is required. Given the channel analysis the Bethe reactance matrix elements are calculated for the specified L-range LMIN LE. L .LE. LMAX, unitarised cross sections produced and the Burgess sum rules applied to calculate the cross sections in the weak coupling Bethe approximation for L .GE. LMAX.