The fourth virial coefficient for hard spheres in even dimension
Ignacio Urrutia
TL;DR
This paper derives an exact analytical expression for the fourth virial coefficient of hard spheres in even dimensions, simplifying the calculation by expressing the cluster integral as a sum of two manageable integrals.
Contribution
It provides a novel exact formula for B4(d) in even dimensions, expanding analytical understanding of hard sphere fluids.
Findings
Exact expression for B4(d) in even dimensions
Simplified integral representation involving spherical angular coordinates
Finite sum of simple terms increasing with 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.
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