Theory of resonance and threshold effects in the electronic excitation of molecules by electron impact

A simple model of electron scattering resonances near electronic excitation thresholds is discussed. The model consists of a single discrete electronic state coupled to several electronic continua. The vibrational dynamics in the resonance state is treated, taking proper account of non-Born-Oppenheimer effects in near-threshold electron-molecule scattering. The effect of long-range potentials is included via the threshold expansion of the partial decay widths of the resonance. The analytic properties of the fixed-nuclei $S$ matrix are analyzed in detail for two special cases ($s$-wave scattering in the absence of long-range potentials and scattering from a strongly polar target molecule). The dipole potential is shown to lead to a qualitatively new behavior of the trajectories of resonance poles near excitation thresholds. The model yields a qualitative description of the measured excitation function of the $B^1{\Sigma }^{+}$ state of the CO molecule, where a strong and narrow threshold peak is observed.