We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form H = HV −iC * C, where HV = H0 +V is self-adjoint and C is a bounded operator. We study the wave operators associated to H and H0. We prove that they are asymptotically complete if and only if H does not have spectral singularities on the real axis. For Schrödinger operators, the spectral singularities correspond to real resonances.

International audienc

Abstract. We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.