Linear-algebraic approach to electron-molecule collisions: Separable exchange approximations

The linear-algebraic method for electron-molecule collisions developed by Schneider and Collins is generalized to include separable expansions of the exchange kernel. These separable expansions are constructed using bound-state integral programs and spherical-harmonic projections which may be performed by analytic methods. The short-range nature of the exchange operator obviates the need for large basis sets in the separable expansion and allows for a very efficient construction of the required integrals. The method is applied to $e+{\mathrm{H}}_2$ and $e+\mathrm{LiH}$ scattering in the static-exchange approximation. Comparison of the separable expansion with more standard numerical techniques for exchange is excellent (