  The analytic equation of state of nonideal Coulomb plasmas consisting of
pointlike ions immersed in a polarizable electron background (physics/9807042)
is improved, and its applicability range is considerably extended. First, the
fit of the electron screening contribution in the free energy of the Coulomb
liquid is refined at high densities where the electrons are relativistic.
Second, we calculate the screening contribution for the Coulomb solid (bcc and
fcc) and derive an analytic fitting expression. Third, we propose a simple
approximation to the internal and free energy of the liquid one-component
plasma of ions, accurate within the numerical errors of the most recent Monte
Carlo simulations. We obtain an updated value of the coupling parameter at the
solid-liquid phase transition for the one-component plasma: Gamma_m = 175.0
(+/- 0.4).
