The electrostatic screening of nuclear reactions in the Sun

We apply the method of Shaviv & Shaviv to evaluate from first principles th e plasma screening correction to the rate of nuclear reactions under condit ions similar to those prevailing in the present-day Sun. We calculate the s creening factor for the p-p chain and the CN cycle nuclear reactions. We fi nd the following : 1. The mean field approximation a la Debye-Huckel is not strictly valid und er the conditions prevailing in the core of the Sun. A kinetic approach sho uld be implemented. 2. The mean energy exchange between any two scattering particles and the pl asma is positive for low relative kinetic energies and negative for high re lative kinetic energies. The turnover in a pure hydrogen plasma occurs at a bout Ekin-rel approximate to 2kT < E-Gamow <approximate to> 6kT for the p-p reaction, for example, and changes with the particular reaction. The net e nergy exchange, namely, the sum over all pairs of scattering particles in t he system, vanishes in equilibrium. 3. The turnover from energy gain to energy loss of the scattering particles is generally below the Gamow peak. The details depend on the masses of the interacting particles relative to the mass of the particles in the ambient plasma. 4. The fluctuations and nonspherical effects are crucial in affecting the s creening. We investigate the source of the fluctuations and their power spe ctrum. In view of the particular behavior of the fluctuations we derive the net effect of the plasma on the reaction rate for each reaction investigat ed here. 5. The derived screening corrections, which are a function of the relative kinetic energy and depend on the environment, are averaged over the distrib ution of relative velocities and cross section to obtain the total screenin g correction. The preliminary results are obtained in two easy-to-handle li mits. The p-p reaction is found to be enhanced relative to reaction in vacu um, while higher Z reactions, like the Be-7 + p reaction, are suppressed re lative to the classical Salpeter theory. 6. In the Appendix we show the connection between the screening and the coe fficients in the Fokker-Planck equation. We use the same computer program t o calculate the coefficient in the Fokker-Planck equation and find a behavi or that supports the present findings of the general values and behavior of the screening.