X-ray and Electron Scattering by Molecular Hydrogen

Abstract

A theoretical study has been made of the x-ray and electron scattering to be expected from molecular hydrogen. The methods of calculation have the common feature that they are based on expansions of the wave function, density and potential in Legendre polynomials. Simple self-consistent field wave functions having spherical symmetry are presented and, while the binding energy thereby obtained is poor, it is found nevertheless that they may be utilized with success in both the x-ray and the electron scattering calculations. The x-ray scattering is also discussed on the basis of an lcao molecular-orbital function and the `floating' function of Gurnee and Magee. It is found that the results of the various approximations used agree well among themselves and also with experiment, and some conclusions regarding the charge distribution in the hydrogen molecule may be drawn. For the elastic scattering of slow electrons, it is found that there is good agreement between the present results and earlier work of Massey and Ridley if exchange is neglected in both cases. However, it is found that electron exchange markedly affects the scattering cross sections, thus confirming the essential conclusions of Massey and Ridley, although the method employed in the present work is probably not sufficiently reliable to enable the precise effect of exchange to be determined.