  We consider a slowly varying time dependent d-level atom interacting with a
photon field. Restricted to the single excitation atom-field sector, the model
is a time-dependent generalization of the Wigner-Weisskopf model describing
spontaneous emission of an atomic excitation into the radiation field. We
analyze the dynamics of the atom and of the radiation field in the adiabatic
and small coupling approximations, in various regimes. In particular, starting
with an excited atomic state, we provide a description of both the radiative
decay of the atom and of the buildup of the photon excitation in the field.
