The fourth virial coefficient for hard spheres in even dimension

Abstract

The fourth virial coefficient is calculated exactly for a fluid of hard spheres in even dimensions. For this purpose the complete star cluster integral is expressed as the sum of two three-folded integrals only involving spherical angular coordinates. These integrals are solved anallytically for any even dimension d and working with existing expressions for the other terms of the fourth cluster integral we obtain an expression for the fourth virial coefficient B4(d) for even d that sums a finite number of simple terms, with the number of terms increasing with d.

arXiv comment15 pages, one Figure. Two Suplemental material files

References in corpus (3)

• Analytic calculation of B4 for hard spheres in even dimensions
• Negative virial coefficients and the dominance of loose packed diagrams for D-dimensional hard spheres
• The fourth virial coefficient of a fluid of hard spheres in odd dimensions

Cited by in corpus (1)

• Geometric measures of uniaxial solids of revolution in ${\mathbb{R}}^4$ and their relation to the second virial coefficient