Many-body correlations from integral geometry.

Abstract

In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was the morphometric approach, a synthesis of integral geometry and liquid-state theory, which has traditionally been derived from fundamental measure theory. We present the morphometric approach in a new context as a generalization of scaled-particle theory, and we derive several morphometric theories for hard spheres of fundamental and practical interest. Our central result is a new theory that is particularly suited to the treatment of many-body correlation functions in the hard-sphere liquid, which we demonstrate by numerical tests against simulation.