Vibration-induced narrowing of electron scattering resonances near threshold

Resonant scattering of electrons from molecules is discussed in the context of an exactly solvable model. There is a strong non-adiabatic entanglement of electronic and nuclear motions for resonances near threshold. The calculations show that the interaction of the electronic and vibrational motions can lead to a dramatic reduction of the resonance width. The limits of applicability of the so-called compound state formula, which has been used so far to analyse low-lying shape resonances in molecules, are pointed out.