  We consider a simple model which is a caricature of a crystal interacting
with a radiation field. The model has two bands of continuous spectrum and the
particle can pass from the upper one to the lower by radiating a photon, the
coupling between the excited and deexcited states being of a Friedrichs type.
Under suitable regularity and analyticity assumptions we find the continued
resolvent and show that for weak enough coupling it has a curve-type
singularity in the lower halfplane which is a deformation of the upper-band
spectral cut. We then find a formula for the decay amplitude and show that for
a fixed energy it is approximately exponential at intermediate times, while the
tail has a power-like behaviour.
