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arXiv · 2109.11660

The fourth virial coefficient for hard spheres in even dimension

Ignacio Urrutia
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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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Ignacio Urrutia. 2021-09-23. The fourth virial coefficient for hard spheres in even dimension. https://doi.org/10.1007/s10955-022-02913-7

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