Perturbation of an embedded eigenvalue by a nearby resonance

Abstract

Quantum-mechanical systems (including molecules), whose Hamiltonians admit the separation (in particular, by the Faddeev method) of a weakly coupled channel, are considered. The width (i.e., the imaginary part) of the resonance generated by a discrete spectrum eigenvalue of the separated channel is studied in the case where the main component of the Hamiltonian gives rise to another resonance. It is shown that if the real parts of these resonances coincide and these two channels are weakly correlated, then the width of the resonance corresponding to the separated (molecular) channel is inversely proportional to the width of the main (nuclear) channel resonance. This phenomenon, which is a kind of universal law, may play an important role in increasing the nuclear fusion probability in molecules whose nuclear constituents have narrow pre-threshold resonances.