A Numerical Approach to the Solution of Coupled Equations Involved in Electron-Ion and Electron-Atom Scattering Problems

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 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 long-range potential terms are taken into account at r_t 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.