A “canonical functions” approach to the solution of two coupled differential equations of scattering theory

H. Kobeissi; K. Fakhreddine

doi:doi:10.1051/jp2:1991115

Numéro		J. Phys. II France Volume 1, Numéro 8, August 1991


Page(s)		899 - 908
DOI		https://doi.org/10.1051/jp2:1991115

DOI: 10.1051/jp2:1991115
J. Phys. II France 1 (1991) 899-908

A "canonical functions" approach to the solution of two coupled differential equations of scattering theory

H. Kobeissi and K. Fakhreddine

Faculty of science, Lebanese University and the Group of Molecular and Atomic Physics at the National Research Council, Beirut, Lebanon

(Received 3 December 1990, revised 16 April 1991, accepted 30 April 1991)

Abstract
The system of two coupled Schrödinger differential equations (CE) arising in the close-coupling description of electron-atom scattering is considered. A "canonical functions" approach is used. This approach replaces the integration of CE for the eigenvector with unknown initial values by the integration of CE for "canonical" functions having well-defined initial values at an arbitrary origin $r_0(0 < r_0 < \infty$ ). The terms of the reactance matrix are then deduced from these canonical functions. The results are independent from the choice of r₀. It is shown that many conventional difficulties in the numerical application are avoided, mainly that of the choice of the starting boundary variable $r_{\rm s}\sim 0$ which is automatically determined. The results of the present method are compared to those of other methods and show excellent agreement with previous accurate results.