Asymptotic completeness in dissipative scattering theory

Abstract

We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form $H = H_V - i C^* C$, where $H_V = H_0 + V$ is self-adjoint and $C$ is a bounded operator. We study the wave operators associated to $H$ and $H_0$. We prove that they are asymptotically complete if and only if $H$ does not have spectral singularities on the real axis. For Schr\"odinger operators, the spectral singularities correspond to real resonances.