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

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 $\text{Γ ≳ 1500}$ has an unusual behavior between 2.5<r<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.