Interionic correlations in plasmas: Thomas-Fermi hypernetted-chain density-functional theory

Abstract

A simplified version of the density-functional theory of Dharma-wardana and Perrot is introduced in which the Kohn-Sham-Schr\"odinger equation for the electrons is replaced by the Thomas-Fermi (TF) statistical approximation, while interionic correlations are still treated classically in the hypernetted-chain (HNC) approximation. The nonlinear TF and HNC equations are coupled by a defining relation for the effective ion-ion interaction potential. The resulting TF HNC theory smoothly interpolates between the Debye-H\"uckel and confined-atom TF theories. It is easily solved in the strong-coupling regime, while for weak and intermediate couplings it agrees well with solutions of the more elaborate density-functional theories for both ion distributions and effective potentials. We have found that the computer code solving our model does not converge in certain areas of \ensuremath{\rho}-T space, but at present we can only speculate as to the significance, if any, of this fact.