Dispersion Relations for Electron Scattering from Atomic Helium

Abstract

Dispersion relations are deduced appropriate to the scattering of electrons by helium atoms either in their ground state or in their first excited metastable state. The analysis extends earlier work on dispersion relations for potential scattering and electron-hydrogen scattering and points out that in the case of scattering from excited He the dispersion relation generally involves an integral over unphysical energies, as well as residue contributions from bound states of ${\mathrm{He}}^{\ensuremath{-}}$ embedded in the continuum. The symmetries of those ${\mathrm{He}}^{\ensuremath{-}}$ bound states making nonvanishing residue contributions, and the form of the optical theorem when the exclusion principle is taken into account, are also discussed.