Derivation of the screening effects in a plasma in statistical and thermal equilibrium

A derivation of screening effects in a moderately dense equilibrated plasma, based on the methods of finite temperature field theory, demonstrates the limits of validity of the ``weak screening`` form. Because the systematics of the theory make it possible to unambiguously separate off the leading order {ital e}{sup 3}, there can be no effects that cancel screening. The static nature of the equilibrium removes questions connected with use of time-response methods for a steady-state problem. The derived screening potential approaches the Debye-Huckel potential at large separations, but is cut off by quantum effects at short distances; the inherent violations of self-consistency in classical derivations of the Debye-Huckel potential are absent. Applied to the conditions of the Sun`s central region, screening corrections deviate only moderately from the classical, {similar_to}15%. The partial degeneracy of electrons also presents only small effects beyond those accounted for by the appropriate population factors. Given the weak role of screening, the effect of the corrections on solar neutrino fluxes is, therefore, seen to be small.