Statistical Mechanics of Dense Ionized Matter. I. Equilibrium Properties of the Classical One-Component Plasma

The equilibrium properties of a classical one-component plasma, in a uniform background of opposite charge, are computed for systems of various sizes by the Monte Carlo method of Metropolis et al. Following the work of Brush, Sahlin, and Teller, the periodicity of the system is accounted for by replacing the long-range Coulomb potential by an effective Ewald sum. Thermodynamic properties are computed over the whole density range of the fluid phase of the system, and their $N$ dependence is carefully investigated. A semiempirical equation of state is proposed from which all thermodynamic properties can be easily derived. Quantum corrections to these properties are calculated to first order in the Wigner expansion. Radial distribution functions, direct-correlation functions, and structure factors at various densities are tabulated. It is shown that at all densities, the direct-correlation function tends rapidly towards its Debye-H\"uckel form, in contrast to the radial distribution function. The behavior of the structure factor at small wave vectors is also shown to be in good agreement with the Debye-H\"uckel predictions at all densities.