Resonant states for a three-body problem under an external field

Here we consider one of the basic models for many-body problems under an external field: the molecule ion H₂⁺ under the effect of an external Stark-type potential. If we consider the vibrational energy levels of the first two electronic states of the molecule ion H₂⁺ then, in the semiclassical limit and by means of a suitable modified Born–Oppenheimer method, we can prove that they switch to sharp resonances localized in the same interval of energy of the vibrational levels when an external Stark-type field, with the same direction of the nuclear axis, occurs.