We consider perturbations of a model quantum system consisting of a single
bound state and continuum radiation modes. In many problems involving the i
nteraction of matter and radiation, one is interested in the effect of time
-dependent perturbations. A time-dependent perturbation will couple the bou
nd and continuum modes causing 'radiative transitions'. Using techniques of
time-dependent resonance theory, developed in earlier work on resonances i
n linear and nonlinear Hamiltonian dispersive systems, we develop the scatt
ering theory of short-lived (O(t(-1-epsilon))) spatially localized perturba
tions. For weak pertubations, we compute (to second order) the ionization p
robability, the probability of transition from the bound state to the conti
nuum states. These results can also be interpreted as a calculation, in the
paraxial approximation, of the energy loss resulting from wave propagation
in a waveguide in the presence of a localized defect.