Born Inelastic Differential Cross Sections in H2

Abstract

First Born differential cross sections are calculated for inelastic electron scattering of 300-eV electrons off H2 for excitations from the ground electronic—vibrational state into the vibrational levels of the B, B′, C, D, and D′ Rydberg states. The initial and final state electronic wavefunctions were approximated by Hartree—Fock functions. In order to facilitate the calculation, the molecular orbitals were expanded in a linear combination of Gaussian-type atomic orbitals. The variation of the electronic scattering amplitude was examined as a function of molecular orientation, internuclear separation, and scattering angle (or electron momentum transfer). It is shown that the use of the Franck—Condon factors to determine relative intensities for scattering into different vibrational levels yields errors of less than 20%, and hence these factors are a good approximation to the relative intensities. The theoretical differential cross section for zero-angle scattering is in good agreement with the most recent experimental data, and transition moments extracted from electron scattering experiments within the context of the Franck—Condon principle are in agreement with the theoretical values.