  We consider a physical system which is coupled indirectly to a Markovian
resevoir through an oscillator mode. This is the case, for example, in the
usual model of an atomic sample in a leaky optical cavity which is ubiquitous
in quantum optics. In the strong coupling limit the oscillator can be
eliminated entirely from the model, leaving an effective direct coupling
between the system and the resevoir. Here we provide a mathematically rigorous
treatment of this limit as a weak limit of the time evolution and observables
on a suitably chosen exponential domain in Fock space. The resulting effective
model may contain emission and absorption as well as scattering interactions.
