The density-gradient expansion and surface properties of the one-component classical plasma

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Abstract
The surface properties of the one-component classical plasma (OCP) are re-examined by an approximate method using the density-gradient expansion truncated at second order. The coefficient of the square-gradient term is calculated via the modified hypernetted-chain (MHNC) scheme. It is found that the result is quite different from the previous ones obtained by the Baus-Hansen and mean spherical approximations. The origin of these differences and certain difficulties in the evaluation of this coefficient are discussed in some detail. The present MHNC result for the square-gradient term is used in the variational calculations for the surface density profile and the surface energy. The results of these calculations are in much better agreement than previous ones with Monte Carlo results. The authors also consider the OCP of finite size with a spherically symmetric charge background, for which Monte Carlo simulations have been performed. It is found that the surface energy appropriately defined for such systems shows appreciable size dependences especially for the OCP with small plasma parameters.