NUCLEAR ELECTRON-CAPTURE IN A PLASMA

We consider the electron density at the position of an ion of charge Z e 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 elect ron in the vicinity of the ion, are well represented by a reduction fa ctor, exp (-Ze(2) beta kappa(D)), where beta is the inverse temperatur e and kappa(D) is the Debye wavelength. Although this factor is the di rect 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 a nd the resulting electron-capture rates. We show analytically, through a sum rule that leads to a well-defined perturbative approach, that i n the limit of Boltzmann statistics, the Salpeter factor indeed provid es the leading correction. We estimate residual effects both from Ferm i statistics and from short-range terms.