Nuclear Electron Capture in a Plasma

We consider the electron density at the position of an ion of charge Ze in aplasma under conditions approximating those in the core of the sun. Numericalcalculations have shown that the plasma effects on the density, over and abovethe ordinary Coulomb factors that are obtained in the absence ofelectron-electron interactions, are well represented by a reduction factor,exp{- Z e^2 beta kappa_D }, where beta is the inverse temperature and kappa_Dis the Debye wave length. Although this factor is the direct analogue of theSalpeter enhancement factor for the fusion rates in stars, the elementaryconsiderations that establish it in the fusion case are not applicable to thedetermination of the electron density and the resulting electron capture rates.We show analytically, through a sum rule that leads to a well-definedperturbative approach, that in the limit of Boltzmann statistics the Salpeterfactor indeed provides the leading correction. We estimate residual effects,both from Fermi statistics and from short range terms.Comment: 20 pages, RevTe