Nonlocal potentials and resonances of narrow width

Abstract

This paper discusses resonances of narrow width in the context of bound states embedded in the continuum spectrum of nonlocal potentials. Feshbach's theory of nuclear reactions leads directly to resonance theory, and we base our discussion here on the techniques he developed for shifting nuclear many-body aspects into effective single-particle nonlocal potentials. In our formulation, the many-body state of the compound nucleus is represented by a single-particle state. The basis for our discussion is a two channel model of a resonance of zero width, with a continuum bound state originating from the coupling of a bound state to the single-particle scattering state. We give a specific example of a model which leads to an arbitrarily narrow (nonzero width) resonance, and demonstrate that the width of the resonance produced by breaking the continuum bound state is proportional to ${(\ensuremath{\Lambda}\ensuremath{-}1)}^{2}$, where the parameter $\ensuremath{\Lambda}$ is such that $\ensuremath{\Lambda}=1$ corresponds to the condition necessary for the existence of a continuum bound state.NUCLEAR REACTIONS Compound nucleus resonances, coupled channels, nonlocal potentials, coutinuum bound states, Breit-Wigner formula.