Improvement in the First Born Theory of Electron Scattering by Molecular Systems. II. Example of the1sσg−2pσuTransition inH2+

Abstract

The asymptotic closure cross section, derived in I of this series, is calculated for the $1s{\sigma }_g-2p{\sigma }_u$ excitation of $\mathrm{H}_2^{}{}_{}{}^{+}$ by fast electrons. These data are compared with earlier treatments of this system which were based on a less rigorous theory. The earlier data are observed to be surprisingly accurate. The Bethe cross section for exciting discrete vibrational modes in the $2p{\sigma }_u$ orbital of $\mathrm{H}_2^{}{}_{}{}^{+}$ is calculated. This cross section is then used, along with the asymptotic closure cross section, to generate the Bethe cross section for all continuum modes of nuclear motion in the $2p{\sigma }_u$ orbital of $\mathrm{H}_2^{}{}_{}{}^{+}$. Two approximations are considered for this partitioning of the asymptotic closure cross section and they are not found to be, in general, very useful.