Free energy of a screened ion pair

We calculate the effect of weak electrostatic screening of ions in a plasma . The original calculation by Salpeter is based on a linearization of the P oisson-Boltzmann equation for the screened electrostatic potential. This ap proximation is valid where the potential is small, but is formally invalid in the vicinity of the ions where the solutions for the potential and the a ssociated charge distribution diverge. In reality, quantum exclusion must p revent the divergence of the charge density of the screening cloud. Neverth eless, in the limit in which screening is weak, Salpeter's value for the to tal screening energy is essentially correct. Here we extend Salpeter's calc ulation to account approximately for both quantum-mechanical exclusion in t he vicinity of the ions, using what we call the Poisson-Boltzmann-Fermi-Dir ac approximation, and the polarization of the screening cloud. By matching the solution onto an expression for the two-center Poisson-Boltzmann charge distribution far from the ions we are able to construct a consistent solut ion over all space. We obtain the first-order term in the expansion of that solution, from which we calculate the free-energy associated with the scre ened ion pair. (C) 2000 American Institute of Physics. [S0022-2488(00)00301 -7].