A remark on the Percus-Yevick approximation in higher dimensions

The five dimensional Ornstein-Zernike equation is Wiener-Hopf factorized following Baxter [1]. This formalism is then applied to five dimensional hard hyperspheres to yield an analytic result in the Percus-Yevick (PY) closure approximation. In addition, the scaled particle result for that system is also derived. The first few virial coefficients are also calculated. Apparently, the PY virial and compressibility pressures bracket the true result. Perturbative treatments for potentials with attractive tails are briefly discussed.