Total cross sections for high-energy electron scattering by ${\mathrm{H}}_2$ ${(}^1$${\Sigma }_g^{+}$), ${\mathrm{N}}_2$ ${(}^1$${\Sigma }_g^{+}$), and ${\mathrm{O}}_2$ ${(}^3$${\Sigma }_g^{\mathrm{-}}$)

Total inelastic cross sections are calculated for collisions of ground-state ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ with fast electrons according to the revised Bethe theory given by Inokuti et al. The asymptotic forms of the total elastic-scattering cross sections in the first Born approximation due to Inokuti and McDowell and including an electron exchange correction are also evaluated for these molecules. For ${\mathrm{H}}_2$, various accurate configuration-interaction wave functions are used to compute the total inelastic and the integral elastic-scattering cross sections. Good agreement between theory and experiment is found for the total cross sections (inelastic and elastic) for high incident energies as well as incident energies near 1 keV. The cross sections are also given for ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$. Since there are no experimental reports for the integral elastic cross section for ${\mathrm{N}}_2$ or ${\mathrm{O}}_2$ at very high incident energies, the comparison is made only for the experimental data at incident energies near 1 keV. It is found that the theoretical results overestimate the experimental data by about 30% for ${\mathrm{N}}_2$. However, the Bethe total inelastic cross sections are in good agreement with experiments. Since the Born-Bethe approximation may not be valid at lower incident energies, more accurate experimental data at very high incident energies are required for valid comparison with the theoretical results reported here.