Impact-parameter method for electronic excitation of molecules by electron impact

The semiclassical impact-parameter method is extended to study the electronic excitation of molecules by electron impact. The formalism describes the molecular electrons quantum mechanically but treats the collision classically using straight-line trajectories. The expression for the integrated cross section satisfies reciprocity. The method is applicable to spin-allowed transitions at intermediate and high impact energies where electron exchange is negligible. Theoretical excitation cross sections are presented for the $X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}\to B{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ transition in ${\mathrm{H}}_2$, $X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}\to 1{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$, $3{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ in ${\mathrm{F}}_2$, and $X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}\to b^{\prime }$, $c^{\prime }{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ in ${\mathrm{N}}_2$. Below 50-eV impact energies, the method gives more accurate integrated cross sections than the Born approximation.