Low-energy electron-impact excitation of the hydrogen molecule

We present cross sections for the excitation of the two lowest ($b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $a{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$) triplet states of molecular hydrogen by electron impact for incident electron energies ≤ 20 eV. The cross sections are calculated using the distorted-wave approximation with the inelastic transition density obtained in the random-phase approximation. An efficient expansion technique using Gaussian basis functions allows us to avoid numerical integrations and to treat accurately the noncentral nature of the scattering process with full allowance for electron exchange. The sum of the two triplet cross sections is found to be in good agreement with the experimental cross section for dissociation of ${\mathrm{H}}_2$ into 2H.