Hypernetted-chain solutions for the two-dimensional classical electron gas

Abstract

The hypernetted-chain integral equation is solved numerically to yield the pair correlation function, equation of state, and free energy of a two-dimensional classical electron gas, for values of $\Gamma \equiv \frac{{\left(\pi n\right)}^{\frac{1}{2}}{e}^2}{k_{B}T}$ up to 100. The onset of short-range order in the gas is found to occur for $2.8<\mathrm{}\Gamma <2.9\mathrm{}$. In general, the results are qualitatively similar to those of the three-dimensional electron gas.