Energy-dependent Hamiltonian in a nuclear optical model

Abstract

We study the spectral properties of a 1D model of optical potential introduced by Morillon and Romain [21] in the context of nuclear reactions. We can localize the discrete spectrum and estimate the number of eigenvalues. We also study the continuous spectrum with possibly embedded spectral singularities and give an expansion formula for an arbitrary function on a set of generalized eigenfunctions. We briefly study the resonances of a related model.