A simple model for the resonant vibrational excitation of a molecule by electron impact is proposed in which the potential curves of the electronic states of the molecule and its resonant anion are replaced by those of linear harmonic oscillators of arbitrary frequencies and equilibrium internuclear separations. A closed-form expression for the excitation amplitude is derived. Useful recursion relations among amplitudes are obtained which allow convenient evaluation of cross sections for any inelastic or superelastic vibrational transition. The model is used to generate the cross sections for vibrational excitation of Li_2 and N_2 by the impact of low-energy electrons.
Wadehra JM, Drallos PJ. Simple model for the resonant vibrational excitation of molecules and its application to Li2 and N2. Phys. Rev. A. 1987;36(3):1148-1155. doi: 10.1103/PhysRevA.36.1148