Hypernetted chain solutions for the classical one-component plasma up to Γ=7000

TLDR

The authors model the bridge diagram as \(B(r)=-\lambda\Gamma/r\) with \(\lambda=0.6\,\mathrm{erf}(0.024\Gamma)\), producing distribution functions within ±0.02 of Monte‑Carlo results across the fluid regime. The HNC solutions up to \(\Gamma=7000\) agree with Monte‑Carlo data in the fluid regime, with potential‑energy errors below 0.8 % for \(20\le\Gamma\le160\) and asymptotically \(-0.8995\Gamma\); pressure and free energy show no phase transition, yet for \(\Gamma\gtrsim1500\) the pair distribution function exhibits a crystal‑like anomaly between \(2.5<r<4.0\).

Abstract

The hypernetted chain equation has been solved numerically for the classical one-component plasma in a uniform background up to Γ=7000, where Γ=(Ze)2/kTa and a is the ion-sphere radius. Numerical results are presented. The distribution functions and thermodynamical quantities obtained are in good agreement with the Monte Carlo results in the fluid region. The average potential energy Ū/NkT is in error by less than 0.8% for 20≤Γ≤160 and approaches −0.8995Γ as Γ approaches infinity. The pressure and the free energy calculated do not show any evidence of a phase transition. However, the distribution function g(r) for Γ ≳ 1500 has an unusual behavior between 2.5&amp;lt;r&amp;lt;4.0, resembling somewhat that of a hcp crystal. If we assume the sum of the bridge diagram to be of the form B(r)=−λΓ/r where λ=0.6 erf (0.024Γ), the distribution function calculated agrees to within about ±0.02 with the Monte Carlo g(r) in the whole fluid region.