Separable approximation for exchange interactions in electron-molecule scattering

We have formulated and applied a separable approximation for treating the nonlocal exchange interactions that arise in electron-molecule collision problems. A separable representation of the exchange terms in the electron-molecule interaction potential is obtained by projection onto a finite set of Cartesian Gaussian functions and is combined with a single-center expansion of the direct potential terms that accurately treats the long-range, multipolar forces. An integral-equation method is used to obtain a solution of the set of coupled equations obtained in a body-frame formulation of the collision problem. The method is illustrated by application to low-energy $e^{-}-{\mathrm{H}}_2$ and $e^{-}-\mathrm{L}\mathrm{i}\mathrm{H}$ scattering in the static-exchange approximation.