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 (3α) reaction can increase greatly over the value appropriate for helium burning stars owing to hadronically induced deexcitation of the Hoyle state. In this Letter we use a statistical model to evaluate the enhancement as a function of temperature and density. For a density of 10^{6}  g cm^{-3} enhancements can exceed a factor of 100. In high temperature or density situations, the enhanced 3α 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.