Integral equations and distribution functions for hyperdense plasmas and a local exchange-correlation approximation for many-electron systems

The hypernetted chain equation has been solved numerically for the classical one-component plasma up to GAMMA = 7000. Numerical results are presented. The radial distribution functions obtained agree qualitatively with the Monte Carlo results in the fluid region, but the peak of g(r) is underestimated as much as 15 percent at GAMMA = 160. Integral equations are investigated for the purpose of finding the one most suitable for a dense system of nuclei and electrons. A local exchange-correlation approximation for calculating the ground-state wavefunction and energy for a finite system of electrons is introduced. The new scheme differs from the well-known Kohn--Sham scheme in two aspects: (i) the local approximation is made to the correlation function rho2 (1,2) rho(1)rho(2) instead of the functional E/sub xc/[rho] and (ii) the one-electron equation is derived with the usual Rayleigh--Ritz variational principle instead of the variational principle of Hohenberg and Kohn