Electron Screening and Thermonuclear Reactions

Abstract

SummaryIn the interior of stars most atoms are ionized, but the electrostatic potential of a bare nucleus induces a spherically symmetric polarization of the surrounding electrons and nuclei. The effect of this screening charge cloud on the rate of thermonuclear reactions is investigated for the case of complete ionization of all atoms.The charge distribution and potential of the screening cloud is calculated for two limiting cases where the electrostatic interaction energy between neighbouring nuclei is small or large compared with the thermal energy (weak or strong screening). The charge cloud is also investigated for intermediate strength of screening, for nuclear species which are rare and have a large charge.Under most stellar conditions the impact parameter for a thermonuclear collision is much smaller than the radius of a screening cloud. For such cases, a simple formula is given relating the increaae in the reaction rate to the potential of the screening cloud. Numerical values are presented for a few typical reactions. For conditions typical for the interior of ordinary main sequence stars the increase in the reaction rate is fairly small, usually less than a factor of two.

Electron screening and its effects on big-bang nucleosynthesis

“…This is verified by artificially increasing the screening obtained by traditional models [11]. We back our numerical results with very simple and transparent estimates.…”

“…where X i is the mass fraction of nuclei of type i, and T 6 is the dimensionless temperature in units of 10 6 K. The factor χ corrects for the effects of electron degeneracy [11].…”

GARSTEC—the Garching Stellar Evolution Code

“…The crucial reaction rate 12 C(α, γ ) 16 O is taken from (Kunz et al 2002). Screening is treated in general in the weak limit, following Salpeter's classical formula (Salpeter 1954).…”

Helioseismology and screening of nuclear reactions in the Sun

“…The study of screened nuclear reaction rates was started with the pioneering work of Salpeter [1], who discussed both the extreme cases of "weak" and "strong" screening, providing suitable expressions for the screening factors f ij = σv ij,plasma / σv ij,bare .…”