NUCLEAR-REACTION RATES IN A PLASMA

The problem of determining the effects of the surrounding plasma on nu clear reaction rates in stars is formulated ab initio, using the techn iques of quantum statistical mechanics. Subject to the condition that the nuclear reactions ensue only at very close approach of the fusing ions and the condition that the reaction be slow, the authors derive a result that expresses the complete effects of Coulomb barrier penetra tion and of the influence of the surrounding plasma in terms of matrix elements of well-defined operators. The corrections do not separate i nto the product of initial-state and final-state effects. When the ene rgy release in the reaction is much greater than thermal energies, the corrections reduce, as expected, to evaluation of the equilibrium pro bability of one ion's being very near to the position of another ion. We address the calculation of this probability in an approach that is based on perturbation theory in the couplings of the plasma particles to the two fusing particles, with the Coulomb force between the fusing particles treated nonperturbatively and interactions among the plasma particles treated in the one loop approximation. We recapture standar d screening effects, find a correction term that depends on the quantu m-mechanical nature of the plasma, and put an upper bound on the magni tude of the further correction terms for the case of a weakly coupled plasma. We find that possible ''dynamical screening'' effects that hav e been discussed in the literature are absent. The form of our results suggests that an approach that relies on numerical calculations of th e correlation functions in a classical Coulomb gas, followed by constr uction of an effective two-body potential and a quantum barrier penetr ation calculation, will miss physics that is as important as the physi cs that it includes.