BOUND-STATE METHODS FOR LOW-ENERGY ELECTRON-ION SCATTERING

An effective-potential formalism, previously developed for electron sc attering by a neutral target, is extended to apply to electron-ion sca ttering, with the requirement of antisymmetrization now accounted for explicitly. A minimum principle for the effective potential is derived , valid for scattering below the ionization threshold and applicable w hen, as is usually the case, the target wave functions are imprecisely known. The basis for the minimum principle is the Rayleigh-Ritz prope rty that is satisfied by the modified Hamiltonian in terms of which th e effective potential is defined, An analysis of single-channel, zero- energy scattering for a particular partial wave is presented; it is ba sed on the effective-potential formalism and leads to an absolute defi nition of the zero-energy phase shift delta(0) of the form delta(0) = mu(infinity)pi, where mu(n) is the quantum defect of the nth energy le vel. This result may be thought of as an extension of Levinson's theor em for scattering by short-range potentials.