Equation of state of fully ionized electron-ion plasmas

Thermodynamic quantities of Coulomb plasmas consisting of pointlike ions immersed in a compressible, polarizable electron background are calculated for ion charges $Z=1\mathrm{}–26$ and for a wide domain of plasma parameters ranging from the Debye-Hückel limit to the crystallization point and from the region of nondegenerate to fully degenerate nonrelativistic or relativistic electrons. The calculations are based on the linear-response theory for the electron-ion interaction, including the local-field corrections in the electronic dielectric function. The thermodynamic quantities are calculated in the framework of the N-body hypernetted-chain equations and fitted by analytic expressions. We present also accurate analytic approximations for the free energy of the ideal electron gas at arbitrary degeneracy and relativity and for the excess free energy of the one-component plasma of ions derived from Monte Carlo simulations. The extension to multi-ionic mixtures is discussed within the framework of the linear mixing rule. These formulas provide a completely analytic, accurate description of the thermodynamic quantities of fully ionized electron-ion Coulomb plasmas, a useful tool for various applications from liquid state theory to dense stellar matter.