Elastic scattering of fast electrons by ${\mathrm{H}}_2$(${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$) and ${\mathrm{N}}_2$(X${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$)

The differential cross section (DCS) d${\sigma }^{\mathrm{el}}$/dΩ for the elastic scattering of electrons by homonuclear diatomic molecules in the first Born approximation at scattering angles equal or near zero is derived here by an expansion method. This method gives d${\sigma }^{\mathrm{el}}$/dΩ=α+β$K^2$+γ$K^4$+.. ., where α,β,γ are constants, and K is the momentum transfer. For ${\mathrm{H}}_2$, the value α with vibrational corrections is calculated with use of the most accurate wave function given by Kolos and Wolniewicz (KW) and the values for the constants β and γ are evaluated from the Davidson and Jones (DJ) wave function. The resulting DCS’s at small scattering angles are given for comparison with experiment. The disagreement between theory and experiment for ${\mathrm{H}}_2$ is found when the scattering angle is less than 15 mrad at 25 keV (i.e., K=0.6 a.u.). The disagreement is very similar to the ones reported in the studies of Compton scattering and (e,2e) reaction spectroscopy. The disagreement between theory and experiment at scattering angles near zero for ${\mathrm{N}}_2$ are also reported. New experimental data for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ at very small scattering angles may be needed in order to establish the disagreements reported here. The DCS for ${\mathrm{N}}_2$ at large scattering angles is also calculated using an accurate multiconfiguration self-consistent-field first-order configuration-interaction (MCSCF-FOCI) wave function. Good agreement within experimental resolution at large scattering angles is found for ${\mathrm{N}}_2$ for the difference function ΔN(K) and for the DCS. This is contrary to the recent study of ${\mathrm{H}}_2$ where discrepancies were reported at large scattering angles. The calculated total cross sections for ${\mathrm{N}}_2$ are in good agreement with the experimental data at low incident energies is the hundred-electron-volt range.