  We investigate the effects of plasma interactions on resonance-enhanced
fusion rates in stars. Starting from basic principles we derive an expression
for the fusion rate that can serve as a basis for discussion of approximation
schemes. The present state-of-the-art correction algorithms, based on the
classical correlation function for the fusing particles and the classical
energy shift for the resonant state, do not follow from this result, even as an
approximation. The results of expanding in a perturbation solution for the case
of a weakly coupled plasma are somewhat enlightening. But at this point we are
at a loss as to how to do meaningful calculations in systems with even moderate
plasma coupling strength. Examples where this can matter are: the effect of a
possible low energy $^{12}$ C +$^{12}$ C resonance on X-ray bursts from
accreting neutron stars or on supernova 1A simulations; and the calculation of
the triple $\alpha$ rate in some of the more strongly coupled regions in which
the process enters, such as accretion onto a neutron star.
