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 ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$→(b ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$, and ${\mathit{c}}^3$${\mathrm{\Pi }}_{\mathit{u}}$) transitions in ${\mathrm{H}}_2$. The integral cross sections for excitation of the ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and ${\mathit{c}}^3$${\mathrm{\Pi }}_{\mathit{u}}$ states from the ground state are found to be significantly different from earlier two-state calculations. The ${\mathit{a}}^3$${\mathrm{\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° and 180°, 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.

• Received 17 August 1990

DOI:https://doi.org/10.1103/PhysRevA.43.3514