Elastic Scattering of Low-Energy Electrons from Atomic Helium

Abstract

Scattering phase shifts have been computed for elastic electron scattering from neutral helium for an energy range from 0 to 50 eV. These computations were based upon an extension of Hartree-Fock theory in which the distortion induced in the atom by the incident electron is considered in the adiabatic approximation and developed in a perturbation expansion in the interaction between incident and atomic electrons. This expansion contains terms describing both the adiabatic polarization interaction and velocity-dependent corrections to it. The effects of these two interactions are examined by calculating the scattering in two approximations: first, a pure adiabatic-exchange calculation using the total polarization potential consistent with second-order perturbation theory; and second, a "dynamic-exchange" calculation in which all the dynamic terms consistent with second-order perturbation theory are included along with the polarization potential. An additional dynamic-exchange calculation in which only the dipole components of all the distortion terms are included is also considered. The computed phase shifts were used to determine the scattering cross sections and these are compared with other calculations and experimental data. Scattering lengths were also calculated by iteration of the pertinent equations at zero energy, and resulted in the values $1.097a_0$ for the adiabatic-exchange approximation and $1.186a_0$ and $1.181a_0$ for the dynamic-exchange approximations using, respectively, the total-distortion terms and the dipole components of these terms only. The dynamic-exchange values for the scattering length compare very favorably with the experimental value $1.18a_0$ determined independently from experimental data by Frost and Phelps and by Crompton and Jory. The dynamic-exchange approximation for the total scattering cross section agrees quite closely with the experimental data of Ramsauer and Kollath, while the corresponding diffusion cross section agrees quite well with the data of Crompton and Jory. These calculations show that best agreement with experiment is obtained when only the dipole components of all of the distortion terms are included in the formalism.