Perturbation of embedded eigenvalue by a nearly resonance

The case of quantum-mechanical system (including electronic molecules) is considered where the Hamiltonian admits a separation, in particular by the Faddeev method, of a weakly coupled channel. 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 part of the Hamiltonian gives rise to another resonance. It is shown that if real parts of these resonances coincide and while a coupling between the separated and main channels is sufficiently small then the width of the resonance generated by the separated (molecular) channel is inversely proportional to the width of the main (nuclear) channel resonance. This phenomenon being a kind of a universal law may play an important role increasing the nuclear fusion probability in electronic molecules whose nuclear constituents have narrow pre-threshold resonances.