  Electrons coupled to local lattice deformations end up in selftrapped
localized molecular states involving their binding into bipolarons when the
coupling is stronger than a certain critical value. Below that value they exist
as essentially itinerant electrons. We propose that the abrupt crossover
between the two regimes can be described by resonant pairing similar to the
Feshbach resonance in binary atomic collision processes. Given the
intrinsically local nature of the exchange of pairs of itinerant electrons and
localized bipolarons, we demonstrate the occurrence of such a resonance on a
finite-size cluster made out of metallic atoms surrounding a polaronic ligand
center.
