Abstract
Based on the previously developed pseudopotential model of the dust particles interaction, which takes into account both the finite size and screening effects, the equilibrium distribution functions are investigated in a broad range of plasma parameters. The treatment stems entirely from the renormalization theory of plasma particles interactions which leads to the so-called generalized Poisson-Boltzmann equation. In particular, an analytical expression for the static structure factor of the dust particles is proposed and its non-monotonic behavior in the hyper-netted chain approximation is found in a specified domain of plasma parameters to indicate the formation of short- or even long-range order in the system.