Disappearance of continuum exchange integrals from algebraic variational calculations of electron scattering

We show how it is possible to systematically eliminate, with little resulting error, all ‘‘free-free’’ and ‘‘bound-free’’ exchange integrals needed to implement electron scattering calculations with algebraic variational techniques, such as the Kohn method. This elimination is rigorous within the framework of the separable approximation for exchange interactions and follows from certain invariance properties of the scattering wave function. The procedure is illustrated for the case of $e^{\mathrm{-}}$+He and $e^{\mathrm{-}}$+H scattering in the static-exchange approximation.