Spectrum and scattering in a model “spin-boson” with at most three photons

A model of radiative decay with a fixed atom and not more than three photons is studied. A spectral analysis of the Hamiltonian is made. This is done by means of scattering theory in a pair of spaces with a specially chosen embedding. The existence of wave operators and their asymptotic completeness are proved. The constructions are based on a detailed analysis of the resolvent of the Hamiltonian.