Enhancement of the Triple Alpha Rate in a Hot Dense Medium

In a sufficiently hot and dense astrophysical environment the rate of the triple-alpha (3alpha) reaction can increase greatly over the value appropriate for helium burning stars owing to hadronically induced de-excitation of the Hoyle state. In this paper we use a statistical model to evaluate the enhancement as a function of temperature and density. For a density of $10^6 gm cm^{-3}$ enhancements can exceed a factor of one-hundred. In high temperature/density situations, the enhanced 3alpha rate is a better estimate of this rate and should be used in these circumstances. We then examine the effect of these enhancements on production of $^{12}$C in the neutrino wind following a supernova explosion and in an x-ray burster.