On irregular oscillatory structures in resonant vibrational excitation cross-sections in diatomic molecules

We examine in detail the origin of irregular oscillatory structures in the cross-sections of low-energy resonant vibrational excitation of several diatomic molecules by electron impact. We show that these irregularities are caused by a combination of two phenomena: enhancing of the magnitude of the nuclear wave function in the vicinity of poles in the complex energy plane corresponding to quasi-bound vibrational states of the molecular anion, and energy variations of the phase of the nuclear wave function which corresponds to the reflection in the potential well of the molecular anion and which are sometimes called boomerang oscillations. These two phenomena are usually both involved in the nuclear dynamics. The former one is usually dominant at lower energies (NO molecule) and in systems where the potential energy of the molecular anion (H2 in high rotational states) possesses an outer potential well. The latter one dominates if the width of the quasi-bound vibrational states of the molecular anion is relatively large (e.g. at higher energies for NO and N2 molecule, H2 in ground state).