The Electrostatic Screening of Nuclear Reactions in the Sun

Abstract

We apply the method of Shaviv & Shaviv to evaluate from Ðrst principles the plasma screening correction to the rate of nuclear reactions under conditions similar to those prevailing in the present-day Sun. We calculate the screening factor for the p-p chain and the CN cycle nuclear reactions. We Ðnd the following :1. The mean Ðeld approximation la is not strictly valid under the conditions prevaila`Debye-Huckel ing in the core of the Sun. A kinetic approach should be implemented.2. The mean energy exchange between any two scattering particles and the plasma is positive for low relative kinetic energies and negative for high relative kinetic energies. The turnover in a pure hydrogen plasma occurs at about for the p-p reaction, for example, and changes E kin~rel B 2kT \ E Gamow B 6kT with the particular reaction. The net energy exchange, namely, the sum over all pairs of scattering particles in the 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 Ñuctuations and nonspherical e †ects are crucial in a †ecting the screening. We investigate the source of the Ñuctuations and their power spectrum. In view of the particular behavior of the Ñuctua-tions we derive the net e †ect of the plasma on the reaction rate for each reaction investigated here.5. The derived screening corrections, which are a function of the relative kinetic energy and depend on the environment, are averaged over the distribution of relative velocities and cross section to obtain the total screening correction. The preliminary results are obtained in two easy-to-handle limits. The p-p reaction is found to be enhanced relative to reaction in vacuum, while higher Z reactions, like the Be7 ] p reaction, are suppressed relative to the classical Salpeter theory.6. In the Appendix we show the connection between the screening and the coefficients in the FokkerPlanck equation. We use the same computer program to calculate the coefficient in the Fokker-Planck equation and Ðnd a behavior that supports the present Ðndings of the general values and behavior of the screening.

Nuclear astrophysics with radioactive beams

“…[91], higher order effects, beyond the Debye-Hückel approximation, modify the screening enhancement in solar fusion reactions by only a very small amount of about 1%. This conclusion is not in accord with results obtained by other authors [92,87].…”

“…These claims have been substantiated with molecular dynamics calculations [92]. However, it has not been pursued further and has not been verified independently.…”

“…On the proton-rich side of the nuclear chart, β-decay half-lives are an important input for nucleosynthesis models that describe the reaction flow in the rp process and the final abundances. While much data has been available on the proton-rich side of the nuclear chart, some information in key regions, as for example around the nuclei 92,94 Mo and 96,98 Ru, which are found in the solar system in unexpectedly large abundances, could only be gathered recently with technical improvements crucial for experiments on proton-rich nuclei.…”

Negentropy in Many-Body Quantum Systems

“…In addition, Dappen-Mussak [36,37] and Shaviv [50] have criticized the use of the stationary Salpeter screening. Bahacall et al [51], on the other side, have strongly supported the Salpeter approach in stars, but their arguments have also been criticized [52,53].…”

Numerical experiments in screening theory

“…Recently Bahcall et al (2002) (hereafter BBGS) have discussed the Salpeter formula for calculating the electrostatic screening of nuclear reactions in plasma and claim to have shown that it should apply to the Sun and that all claims concerning dynamic effects are wrong, including the recent results of Shaviv & Shaviv (2001) (hereafter SS01). The discussion of BBGS is based on the assumption that the mean field electrostatic potential is a good assumption ignoring the fact that in the core of the Sun this very assumption may not be justified.…”