  A toy model is defined and solved perturbatively with the aim of examining
some claimed "resonant" enhancements of certain reaction rates that enter
popular models of leptogenesis. We find: a) that such enhancements are absent;
and b) that the perturbative solution, as done correctly using finite-
temperature field theory, is well defined without the "resumming" procedures
found in the literature. The pathologies that led to the perceived need for
these procedures are an artifact of uncritical use of weighted vacuum cross-
sections in the determination of rates, without adequate attention to the
effects of the medium upon the single particle states within it.
