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 ${\text{Γ = 1.0;\hspace{0.17em}Γ = e}}^2\mathrm{/kTa}$ , where a is the ion‐sphere radius. The hypernetted chain equation was solved for $\text{0.05 ≤ Γ ≤ 50}$ . The results agree qualitatively with the Monte Carlo calculations everywhere except at very small $\Gamma$ , where they agree with the Debye‐Hückel approximation. Definite short‐range order is predicted for $\text{Γ>3.0}$ , but the size of the peak in the radial distribution function is underestimated. The error in the peak size is about 9% at $\text{Γ = 50}$ . The average potential energy is in error by less than 2% for $\text{1 ≤ Γ ≤ 50}$ .