Thermonuclear ion-electron screening at all densities. I - Static solution

Abstract

A good two-fluid approximation to the equilibrium charge density surrounding a target nucleus in a plasma is obtained, and it is shown that the usual expression for the screening factor by which thermonuclear reactions are accelerated in the plasma over their vacuum values is valid only in the weak-screening regime. The standard treatments of this problem are briefly outlined, their inadequacies are indicated, and reasonable general expressions are derived for the equilibrium potential and charge density around the target nucleus. The resulting interaction energy is determined along with the action integral for the WKB approximation to penetrability. Reaction rates and screening factors are calculated, first analytically in the general case and then numerically for a two-carbon-atom reaction in a pure C-12 medium. The screening factor for resonant reactions is given, and inadequacies of the present treatment are discussed. The results are compared with those obtained by others for a carbon flash in a 0.8-solar-mass star, a late stage of carbon burning, and explosive carbon ignition in a supernova shock.