Nuclear Reaction Rates in a Plasma

The problem of determining the effects of the surrounding plasma on nuclear reaction rates in stars is formulated ab initio, using the techniques of quantum statistical mechanics. We derive a result that expresses the complete effects of Coulomb barrier penetration and of the influence of the surrounding plasma in terms of matrix elements of well defined operators. We find that possible "dynamical screening" effects that have been discussed in the literature are absent. The form of our results suggests that an approach that relies on numerical calculations of the correlation functions in a classical Coulomb gas, followed by construction of an effective two body potential and a quantum barrier penetration calculation, will miss physics that is as important as the physics that it includes.