Binary correlation and convergent collision integral for a plasma

The BBGKY hierarchy equations for a homogeneous plasma are used to derive an explicit expression for the time-asymptotic binary correlation function. Closure of the hierarchy equations is shown possible, mainly due to a difference in scaling behavior, as functions of impact parameter(s), between the driving terms in the second and third hierarchy equations. The final result is shown to be a uniform approximation for interparticle distances much smaller than the minimum of the mean free path and the density inhomogeneity length. The resulting expressions for the free energy and the collision integral are convergent.