Elastic Scattering of Low-Energy Electrons from Molecular Hydrogen

The cross sections for elastic scattering of low-energy electrons by molecular hydrogen are calculated by solving numerically the continuum Hartree—Fock equations for an electron moving in the potential field of the neutral homonuclear diatomic hydrogen molecule. Hartree—Fock equations make full allowance for electron exchange. The cross sections for elastic scattering of electrons by molecular hydrogen are calculated with and without the inclusion of electron exchange. The agreement in the exchange approximation with experimental data is very good but disappears completely if exchange is neglected. The method of calculation is based on an expansion of the continuum orbitals up to fourth order as a product of a series of spherical harmonics and radial wavefunctions about the molecular midpoint of the molecule. The potential field of the incident electron due to the nuclei of the neutral molecule is expanded in spherical harmonics up to the eighth order. The continuum orbitals are substituted into the Hartree—Fock equations, integration is performed over angular coordinates, and the resulting infinite set of coupled differential—integral equations is truncated and solved numerically to a self-consistent solution, by an iterative technique for three radial continuum functions.