Integral equation solutions for the classical electron gas

Abstract

The hypernetted chain and Percus-Yevick approximations are used to compute the radial distribution functions and the average potential energy for a classical electron gas. The results are compared with Monte Carlo calculations. The Percus-Yevick equation gives poor results above Γ= 1.0; Γ = e 2/kTa. where a is the ion-sphere radius. The hypernetted chain equation was solved for 0.05 ≤ Γ ≤ 50. The results agree qualitatively with the Monte Carlo calculations everywhere except at very small Γ, where they agree with the Debye-Hückel approximation. Definite short-range order is predicted for Γ > 3.0, but the size of the peak in the radial distribution function is underestimated. The error in the peak size is about 9% at Γ = 50. The average potential energy is in error by less than 2% for 1 ≤ Γ ≤ 50.