Decay of correlations in fluids: The one-component plasma from Debye-Hückel to the asymptotic-high-density limit

The decay of structural correlations in the classical one-component plasma is analyzed by calculating the poles of the Fourier transform of the total (pairwise) correlation function $h\left(r\right)\mathrm{}$ for two integral equation theories, the soft mean spherical approximation and the hypernetted chain (HNC). We show that for all except the largest values of the plasma coupling constant $\Gamma ,$ the leading-order pole contribution provides an accurate description of $h\left(r\right)\mathrm{}$ at intermediate range, as well as the ultimate asymptotic decay. The crossover from monotonic decay at weak coupling to exponentially damped oscillatory decay at strong coupling is shown to arise from the same mechanism as that which occurs for charge correlations in binary ionic fluids. We calculate the values of $\Gamma$ at which the crossover occurs in the two theories. The role of higher-order poles and (within the HNC) other singularities in determining the intermediate range behavior of $h\left(r\right)\mathrm{}$ for strong coupling is discussed. We investigate the properties of the solutions of the integral equations in the strong coupling, $\overrightarrow{\Gamma }\infty ,$ asymptotic high-density limit (AHDL). Padé approximants are employed in order to test the validity of the scaling laws proposed for the potential energy, direct correlation function, and for the poles and their contributions to $h\left(r\right)\mathrm{}$ in the AHDL. Our numerical results provide strong support for the validity of the theoretical predictions concerning the AHDL.