Electron-Impact Excitation Cross Section for the Two Lowest Triplet States of Molecular Hydrogen

Calculations for the electron-impact excitation cross sections of molecular hydrogen from its ground ($X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$) to its first ($b{{}_{}{}^3{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$) and second ($a{{}_{}{}^3{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$) triplet states were performed using the Ochkur (O) and Ochkur-Rudge (OR) approximations. All nuclear motions were taken into account. It was found that the first triplet cross section is sensitive to the choice of the ground-state wave function whereas the second one is not. The former is also sensitive to the excited-state wave function used. The results using the O approximation are significantly larger than those of the OR approximation, and the maximum cross section occurs at a somewhat lower energy. Use of the separated-atom approximation produced results significantly lower than those arising from inclusion of all the multicenter terms in the scattering amplitude. The sum of the first and second OR triplet cross sections agrees well with a recent approximate experimental determination of the cross section for the electron-impact dissociation of ${\mathrm{H}}_2$ into 2H. More accurate experiments are now needed to further test the OR approximation.