Is there a dynamic effect in the screening of nuclear reactions in stellar plasmas?

Abstract

We investigate the following two questions of principle: (I) Does the ion’s kinetic energy affect its electrostatic potential energy when the ion is in statistical equilibrium with the plasma? In other words, is there a difference between a potential energy of a test particle moving in the plasma and the potential energy of a particle in statistical equilibrium with the plasma? (II) Does the effect of the plasma on the rate of the nuclear reaction depend on kinetic energy? The two issues are important for evaluating the plasma effect on nuclear reactions in astrophysical plasmas. The first effect was calculated by Carraro et al. (1988) and found to be significant. However, criticism by several authors ( Brown and Sawyer, 1997; Weneser, 1996; Gruzinov, 1997) claim that there is no such effect. We examine the relevant statistical mechanics assumptions and in the lack of a complete rigorous proof check them numerically. We find that the potential energy per particle for particles which are in statistical equilibrium is indeed independent of the potential energy of the particle at least for particles with kinetic energy up to 10 kT . The second question has to do with the kinetics of the collision between two particles in the presence of ambient plasma particles. We discuss this point and obtain the kinetic energy dependence of this interaction and relate it to the so-called ‘screening effect’. The same numerical calculation which yields the result that the potential energy does not depend on the kinetic energy yields the result that the plasma loses energy to relatively slow particles and vice versa.