English

The fourth virial coefficient for hard spheres in even dimension

Statistical Mechanics 2022-05-11 v2

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.

Cite

@article{arxiv.2109.11660,
  title  = {The fourth virial coefficient for hard spheres in even dimension},
  author = {Ignacio Urrutia},
  journal= {arXiv preprint arXiv:2109.11660},
  year   = {2022}
}

Comments

15 pages, one Figure. Two Suplemental material files

R2 v1 2026-06-24T06:16:43.877Z