Particle correlations in the strongly coupled two-dimensional one-component plasma

The equilibrium pair-correlation function and static dielectric response function are calculated for the one-component two-dimensional plasma in the convolution (Totsuji-Ichimaru) approximation. The long-wavelength ($k\to 0$) compressibility sum rule is exactly satisfied for arbitrary values of the plasma parameter $\gamma$. For $\gamma <2\mathrm{}$ the approximation scheme accurately describes the short-range ($r\to 0$) behavior of the pair-correlation function $g\left(r\right)\mathrm{}$ while for $\gamma \ge 2$, it does not. As $\gamma \to 4$ the isothermal compressibility tends to zero as it should. The correlation energy is also calculated for this model and compared with the results for other approximation schemes and the Monte Carlo results.