Is There a Dynamic Effect in the Screening of Nuclear Reactions in Stellar Plasmas?

Abstract

Ensemble average is not the proper average for the screening problem. The proper average to use is the conditional time average over a single particle time history. The basic ergodic theorem is not applicable in this case. There is a dynamic effect on the potential energy of a particle. The effect is to reduce the enhancement of the reaction rate due to the screening. As a consequence we conclude that simple thermodynamic arguments cannot be used to infer the rate of the nuclear reaction. The Helmholtz free energy formalism when applied to the screening is a prescription to approximate the screening potential assuming that the screening potential does not depend on the energy of the reacting ions (among other assumptions). The effect of the plasma on the rate of the nuclear reaction must be derived from kinetic arguments. The contribution of the fluctuations does not average out to zero due to the non linearity of the screening correction as a function of the screening energy. Moreover, the fluctuation width can be estimated in the weak screening limit and is found to enhance the rates by a factor as large as the screening correction itself and hence plays an important role in various circumstances.