  It is expected that the state of an atom or molecule, initially put into an
excited state with an energy below the ionization threshold, relaxes to a
groundstate by spontaneous emission of photons which propagate to spatial
infinity. In this paper, this picture is established for a large class of
models of non-relativistic atoms and molecules coupled to the quantized
radiation field, but with the simplifying feature that an (arbitrarily tiny,
but positive) infrared cutoff is imposed on the interaction Hamiltonian.
  This result relies on a proof of asymptotic completeness for Rayleigh
scattering of light on an atom. We establish asymptotic completeness of
Rayleigh scattering for a class of model Hamiltonians with the features that
the atomic Hamiltonian has point spectrum coexisting with absolutely continuous
spectrum, and that either an infrared cutoff is imposed on the interaction
Hamiltonian or photons are treated as massive particles.
  We show that, for models of massless photons, the spectrum of the Hamiltonian
strictly below the ionization threshold is purely continuous, except for the
groundstate energy.
