Total Inelastic Cross Section for Collisions of ${\mathrm{H}}_2$ with Fast Charged Particles

A sum rule due to Inokuti et al. for the Bethe inelastic cross section for fast-charged-particle collisions with atoms and molecules has been applied to ${\mathrm{H}}_2$. Using an accurate two-center configuration-interaction wave function, the formula for nonrelativistic incident particles was found to be given as ${\sigma }_{\mathrm{tot}}=4\mathrm{}\pi a_0^{}{}_{}{}^2{z}^2\left(\frac{R}{T}\right)\left[1.5487\mathrm{}\ln \right(\frac{T}{R})+2.2212]$ to within an error of 0.5% in ${\sigma }_{\mathrm{tot}}$ for incident-electron energies above 1 keV. Although the theoretical values are in good agreement with the summed experimental (i) total ionization (including dissociation ionization), (ii) total dissociative excitation, and (iii) most important discrete excitation cross sections, an apparent systematic trend suggests that one or more of the current experimental total cross sections for electron impact on ${\mathrm{H}}_2$ may not be accurate and that omitted processes should be included for comparison in the incident energy range above 1 keV.