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

Abstract

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 $X{^{1}\ensuremath{\Sigma}_{g}}^{+}\ensuremath{\rightarrow}B{^{1}\ensuremath{\Sigma}_{u}}^{+}$ transition in ${\mathrm{H}}_{2}$, $X{^{1}\ensuremath{\Sigma}_{g}}^{+}\ensuremath{\rightarrow}1{^{1}\ensuremath{\Sigma}_{u}}^{+}$, $3^{1}\ensuremath{\Pi}_{u}$ in ${\mathrm{F}}_{2}$, and $X{^{1}\ensuremath{\Sigma}_{g}}^{+}\ensuremath{\rightarrow}{b}^{\ensuremath{'}}$, ${c}^{\ensuremath{'}}{^{1}\ensuremath{\Sigma}_{u}}^{+}$ in ${\mathrm{N}}_{2}$. Below 50-eV impact energies, the method gives more accurate integrated cross sections than the Born approximation.