A branch-point approximant for the equation of state of hard spheres

TL;DR

This paper introduces a novel equation of state for hard-sphere fluids using branch-point approximants, accurately predicting virial coefficients and convergence properties, surpassing traditional methods like Padé approximants.

Contribution

It develops a new branch-point approximant-based equation of state that improves predictions of virial coefficients and convergence behavior for hard-sphere fluids.

Findings

Accurately predicts higher virial coefficients.

Shows a smaller radius of convergence than close-packing.

Performs better than Padé [3/3] equations of state.

Abstract

Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value, and it is as accurate as the rescaled virial expansion and better than the Pad\'e [3/3] equations of state. Consequences regarding the convergence properties of the virial series and the use of similar equations of state for hard-core fluids in $d$ dimensions are also pointed out.