Angular Dependence of Differential Cross Sections for Electron Excitation of Singlet→Triplet Transitions

Abstract

The failure of previous calculations to predict the correct “forward‐peaking” angular dependence of the electron‐impact differential cross section for the helium $1^1{\text{S\hspace{0.17em}→\hspace{0.17em}2}}^{3}S$ transition is shown to be due to the neglect of the core contribution. Even a simple approximation to the full Born–Oppenheimer transition amplitude based on an expansion in inverse powers of the incident electron momentum predicts the correct angular dependence of this transition for electron energies to within 40 eV of threshold. For electron‐impact excitation of the lowest singlet→triplet transition in molecular hydrogen, the peaking of the differential cross section away from zero scattering angle is due mainly to a molecular diffraction effect, and the success of Ochkur's approximation in predicting this dependence is shown to be merely a consequence of the relatively small contribution made by the core terms for this particular transition and cannot be generalized. For higher singlet→triplet transitions in H₂, the angular dependence of the differential cross section and the magnitude of the core contribution are shown to depend importantly on the separated atom state with which the molecular wavefunction correlates at infinite separation.