A Numerical Approach to the Solution of Coupled Equations Involved in ElectronIon and ElectronAtom Scattering Problems
Abstract
A numerical procedure is outlined which treats the coupled equations involved in electronion scattering, as well as electronatom scattering, within the closecoupling formalism. The coupled integrodifferential equations of the scattering problem are solved by a twostep 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 r_{t}. Any convenient numerical technique can be used to integrate the equations; in this work, a noniterative integral equation method is used. Next, the longrange potential terms are taken into account at r_{t} via an openchannel projection technique. This technique simply projects the reactance matrix to its asymptotic value. The numerical procedure is then tested by applying it to eHe ^{+} 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:
 10.1016/00219991(75)900297
 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 HighEnergy Physics