1997/04/30 by Lowell S. Brown, R. F. Sawyer · 2 citations
Physics and Astronomy · #Atomic and Molecular Physics #Quantum and Classical Electrodynamics #Solar and Space Plasma Dynamics #astro-ph #nucl-th
paper · pdf · doi:10.1086/304828
published as Astrophys.J.489:968,1997 · 20 pages, RevTeX
arxiv created 1997/04/30 · openalex publication_date 1997/11/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
We consider the electron density at the position of an ion of charge Ze in a plasma under conditions approximating those in the core of the Sun. Numerical calculations have shown that the plasma effects on the density, over and above the ordinary Coulomb factor for a single electron in the vicinity of the ion, are well represented by a reduction factor, exp (- Ze 2 βκ D ), where β is the inverse temperature and κ D is the Debye wavelength. Although this factor is the direct analog of the Salpeter enhancement factor for the fusion rates in stars, the elementary considerations that establish it in the fusion case are not applicable to the determination of the electron density and the resulting electron-capture rates. We show analytically, through a sum rule that leads to a well-defined perturbative approach, that in the limit of Boltzmann statistics, the Salpeter factor indeed provides the leading correction. We estimate residual effects both from Fermi statistics and from short-range terms.