(untitled) (International Journal of Mathematics and Physics, 2013)
Starting from the previously developed pseudopotential model of dust particles interaction in the plasma, which takes into account both the finite-size and the screening effects, equilibrium distribution functionsarewell studied. Consideration is entirely based on the renormalization theory of plasma particles interaction which results in the so-called generalized Poisson-Boltzmann equation. The main idea is to apply the renormalization theory in order to treat the dust grains as a one component plasma with a specific interaction potential. The interaction potential derived in such a way does naturallyincorporate the number density of dust particles and can be utilized for further theoretical considerations. Such an approach provides quite effectivecalculation scheme for the radial distribution function of the dust particles whosenon-monotonic behavior is observed at different values of plasma parameters to prove short-range or even long-range order formation in the system. The correlation energy is investigated in a wide range of plasma parameters and the results are examined from the viewpoint of the thermodynamic stability.