Exact analytic expression for a subset of fourth virial coefficients of polydisperse hard sphere mixtures

TL;DR

This paper derives an exact analytical formula for a specific subset of the fourth virial coefficients in polydisperse hard sphere mixtures, focusing on configurations where the smallest sphere's radius is constrained relative to the others.

Contribution

It provides a novel exact expression for a particular class of fourth virial coefficients in polydisperse sphere systems, expanding theoretical understanding.

Findings

Exact analytic expression derived for the subset of coefficients.

Applicable to systems with radius constraints on the smallest sphere.

Enhances theoretical modeling of polydisperse mixtures.

Abstract

We derive an exact, analytic expression for the fourth virial coefficient of a system of polydisperse spheres under the constraint that the smallest sphere has a radius smaller than a given function of the radii of the three remaining particles.