The application of variational methods to atomic scattering problems - IV. The excitation of the 2 1 S and 2 3 S states of helium by electron impact

Abstract

The zero-order partial cross-sections for the excitation of the and 2 1 S and 2 3 S states of helium by electron impact are calculated with full allowance for distortion of the initial and final electron waves by potential and exchange interaction with the atom in its initial and final state respectively. The distorted waves are determined by a variational method. Allowance for distortion reduces the cross-sections by a factor of 10 or more and brings them into good agreement with the rather meagre observational data. In particular, a near-resonance effect in the distortion of the electron wave by the potential and exchange interaction with a helium atom in the 2 3 S state, near the zero-energy limit, leads to a very sharp maximum in the excitation cross-section for this state for electron energies within a fraction of an electron-volt of the threshold. This agrees quite closely with the observations of Maier-Liebnitz. At electron energies of a few electron-volts beyond the threshold the contribution of the first-order partial cross-section is not negligible. It has been estimated neglecting distortion, which is certainly much less important than for the zero-order cross-sections. Comparison has then been made between the calculated total cross-sections at energies of 4 to 20 eV beyond the threshold and those deduced by indirect methods from the observations of Dorrestein. Agreement is good in view of the neglect of distortion in the first-order cross-section, the neglect of the higher order cross-sections in the theoretical curve, and the uncertainties involved in the analysis of the observed data. The Born-Oppenheimer cross-sections, neglecting distortion in the zero order as well as all higher order cross-sections, are at least 20 times too large for electron energies up to 40 eV.