A Numerical Approach to the Solution of Coupled Equations Involved in Electron-Ion and Electron-Atom Scattering Problems
Abstract
A numerical procedure is outlined which treats the coupled equations involved in electron-ion scattering, as well as electron-atom scattering, within the close-coupling formalism. The coupled integrodifferential equations of the scattering problem are solved by a two-step process. First, the equations are separated into auxiliary equations which are then solved numerically in the interior region from zero out to some transformation point rt. Any convenient numerical technique can be used to integrate the equations; in this work, a noniterative integral equation method is used. Next, the long-range potential terms are taken into account at rt via an open-channel projection technique. This technique simply projects the reactance matrix to its asymptotic value. The numerical procedure is then tested by applying it to e-He + scattering. Finally, two specific disadvantages of the procedure related to the treatment of closed channels are discussed in detail.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- June 1975
- DOI:
- 10.1016/0021-9991(75)90029-7
- Bibcode:
- 1975JCoPh..18..201S
- Keywords:
-
- Atomic Collisions;
- Electron Scattering;
- Green'S Functions;
- Integral Equations;
- Ion Scattering;
- Numerical Integration;
- Asymptotic Methods;
- Boundary Value Problems;
- Matrices (Mathematics);
- Particle Interactions;
- Projection;
- Transformations (Mathematics);
- Nuclear and High-Energy Physics