Differential cross sections for the electron-impact ionization of molecular hydrogen in the distorted-wave Born approximation

Differential cross sections for electron-impact ionization of molecular hydrogen are presented in the factorized first Born, fixed-nuclei, frozen-core Hartree-Fock approximation. The wave function of the ejected electron is described by a Coulomb wave distorted by the static-exchange potential of the frozen ionic core. Transition matrix elements are evaluated in both the length and velocity forms using Padé-approximant corrections to initial estimates based on the Schwinger variational principle. For high-energy incident electrons, the length form is in excellent agreement with experimental Compton defects but the magnitude of the doubly differential cross section is too large. The magnitude of the doubly differential cross section in the velocity form is generally in good agreement with experiment; however, the maxima occur at energy losses which are too large, particularly for small linear-momentum transfers. Results of calculations of the triply differential cross section are also presented. The agreement with experiment is only fair for 250-eV incident electrons because of the breakdown of the first Born approximation.