Electronic excitation of H2 by electron impact: Close-coupling calculations using the complex Kohn variational method.

Abstract

The complex Kohn variational method is employed in four-state close-coupling calculations to generate integral and differential cross sections for low-energy electron-impact excitation of the $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$\ensuremath{\rightarrow}(b $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$, $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$, and ${\mathit{c}}^{3}$${\mathrm{\ensuremath{\Pi}}}_{\mathit{u}}$) transitions in ${\mathrm{H}}_{2}$. The integral cross sections for excitation of the $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and ${\mathit{c}}^{3}$${\mathrm{\ensuremath{\Pi}}}_{\mathit{u}}$ states from the ground state are found to be significantly different from earlier two-state calculations. The ${\mathit{a}}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ cross sections are also larger than the most recent experimental results. This discrepancy is traced to the behavior of the differential cross sections at scattering angles near 0\ifmmode^\circ\else\textdegree\fi{} and 180\ifmmode^\circ\else\textdegree\fi{}, where measurements have not been carried out. The differential cross sections we find for ${\mathrm{H}}_{2}$ are strikingly similar to cross sections for analogous transitions in He. Previous theoretical studies of these transitions in He have also shown the two-state approximation to be inadequate.