The Kirkwood instability in a mean field context

Abstract

We demonstrate for systems with pair potentials of the form V(r)=γdφ(γr) that the Kirkwood instability analysis of the first equation in the BBGKY hierarchy is correct in the limit γ→0. The cancellation of singular behavior, which occurs for models with short range potentials when higher order equations in the BBGKY hierarchy are considered, does not occur in this mean field (γ→0) limit.