Rates of thermonuclear reactions in dense plasmas

Abstract

The problem of plasma screening of thermonuclear reactions has attracted considerable scientific interest ever since Salpeter’s seminal paper, but it is still faced with controversial statements and without any definite conclusion. It is of relevant importance to thermonuclear reactions in dense astrophysical plasmas, for which charge screening can substantially affect the reaction rates. Whereas Salpeter and a number of subsequent investigations have dealt with static screening, Carraro, Schafer, and Koonin have drawn attention to the fact that plasma screening of thermonuclear reactions is an essentially dynamic effect. In addressing the issue of collective plasma effects on the thermonuclear reaction rates, the first critical overview of most of the work carried out so far is presented and the validity of the test particle approach is assessed. In contrast to previous investigations, we base our description on the kinetic equation for nonequilibrium plasmas, which accounts for the effects on the rates of thermonuclear reactions of both plasma fluctuations and screening and allows one to analyze explicitly the effects of the fluctuations on the reaction rates. Such a kinetic formulation is more general than both Salpeter’s approach and the recently developed statistical approaches and makes it possible to obtain a more comprehensive understanding of the problem. A noticeable result of the fluctuation approach is that the static screening, which affects both the interaction and the self-energy of the reacting nuclei, does not affect the reaction rates, in contrast with the results obtained so far. Instead, a reduction of the thermonuclear reaction rates is obtained as a result of the effect of plasma fluctuations related to the free self-energy of the reacting nuclei. A simple physical explanation of the slowing down of the reaction rates is given, and the relation to the dynamically screened test particle approach is discussed. Corrections to the reaction rates in the solar interior are calculated numerically. It is shown that the corrections to reactions involving 8Band 7Bemay exceed 100%. The results obtained are discussed in connection with the solar neutrino problem. The range of applicability of the approach is also discussed.