Particle Correlations in a Classical One-Component Plasma

The effect of particle correlations in a classical system of charged particles moving in a static uniform background is investigated by means of a dielectric theory developed by Singwi et al. for a completely degenerate electron gas. In this theory, the short-range correlations arising from the Coulomb interaction is taken into account through a local-field correction depending on the pair correlation function. In a first approximation (I), the pair correlation function is chosen to be time independent. The extension of allowing also the pair correlation function to adjust itself to the external field results in a screening of the Coulomb potential entering the local field. The effect of this screening has been investigated for the cases of a static random-phase-approximation (RPA) dielectric function (II) and a static fully self-consistent dielectric function (III). Numerical self-consistent calculations have been carried out for the cases I-III in order to determine the static structure factor $S\left(\overrightarrow{\mathrm{q}}\right)$. From $S\left(\overrightarrow{\mathrm{q}}\right)$ thus obtained, the Helmholtz free energy, the correlation energy, the pair correlation functions, and the isothermal compressibility have been calculated numerically, The plasma dispersion and the compressibility sum rule have also been investigated. The present method can be regarded as a rather natural extension of the RPA. Considerable improvement upon the simple Debye-Hückel (or, equivalently, classical RPA) is also found. The results of the present calculations are also compared with the results of other elaborate methods.