$R$-matrix theory for electron-molecule collisions using analytic basis set expansions. II. Electron-${\mathrm{H}}_2$ scattering in the static-exchange model

The $R$-matrix formalism developed by the author to treat scattering from nonspherically symmetric potentials is applied to the scattering of electrons from ${\mathrm{H}}_2$ in the static exchange approximation. Calculations were performed for ${\Sigma }_g$, ${\Sigma }_u$, ${\Pi }_g$, and ${\Pi }_u$ symmetries and phase shifts extracted for $s$, $p$, and $d$ partial waves. The inclusion of $p$ orbitals on each center was found to be essential in representing $d$-wave contributions to the phase shift and to have a non-negligible effect on $p$-wave scattering. The results are in good agreement with other calculations based on the static-exchange model using entirely different numerical techniques. We conclude by discussing the outlook for the method and how it may be extended to treat polarization, correlation, and inelastic processes.