Derivation of an equation of pair correlation function from BBGKY hierarchy

Abstract

An equation of pair correlation function has been derived from the first two members of BBGKY hierarchy in a weakly coupled inhomogeneous self gravitating system in quasi thermal equilibrium. This work may be useful to study the thermodynamic properties of the central region of a star cluster which is older than a few or more central relaxation time.

Determination of pair correlation function in a weakly correlated weakly inhomogeneous plasma

“…As derived earlier [11] for a weakly correlated dust particles, the equation of χ 12 (for the dust particles in the limit χ 12 ≪ 1) is [11]…”

“…This is the equation of the pair correlation function, which is derived from the BBGKY hierarchy. Previously, we neglected the triplet correlation function to obtain the equation of pair correlation function [8]. Therefore, we observe some additional terms in eq.…”

“…These equations are called BBGKY hierarchy. In a previous article, we have obtained an equation of pair correlation function from the first two members of BBGKY hierarchy [8]. In another article, we have solved the equations and obtained the pair correlation function of weakly coupled, weakly inhomogeneous plasma systems [9].…”

“…Using [11] the BBGKY hierarchy, the quantum binary and triplet distribution functions for a neutral many-component plasma has been determined. Previously, in a series of papers [12,13] an equation of pair correlation function was established from the first two members of BBGKY hierarchy in the weakly correlated limit and subsequently an expression of pair correlation function was derived in the weakly inhomogeneous limit. In this article we shall discuss the effect of the pair correlation function on the single particle distribution function.…”

“…Recently, parametrization of the pair correlation function and the static structure factor of the Coulomb one component plasma (OCP) has been done from the weakly coupled regime to the strongly coupled regime [10]. In a previous paper [11] an equation of pair correlation has been obtained from the first two members of BBGKY hierarchy involving the one-particle and two-particle distribution function in a weakly correlated inhomogeneous plasma system under certain approximations and the next step is to derive the pair correlation function from that equation under different physical conditions. In this Brief Communication pair correlation function is derived from the same equation for a weakly correlated inhomogeneous plasma system.…”