Separable approximations have been used in electron-molecule scattering calculations to avoid the computation of two-electron matrix elements involving continuum functions. We show that such matrix elements involving one continuum function (proportional to a spherical Bessel function at large distances) and three Gaussian functions can be reduced to a single numerical quadrature of an integral involving ordinary two-election integrals over only Gaussian functions. Using these integrals in the Kohn variational method for electron-molecule scattering allows one to avoid the limitations of a primitive separable approximation for exchange interactions by replacing it with a more stable Schwinger separable expansion. The procedure is demonstrated for electron scattering from the 2 ${}_{}{}^3{}_{}{}^{}$S state of helium.

• Received 9 March 1992

DOI:https://doi.org/10.1103/PhysRevA.46.255