Solution of the Percus–Yevick equation for hard hyperspheres in even dimensions.

We solve the Percus–Yevick equation in even dimensions by reducing it to a set of simple integrodifferential equations. This work generalizes an approach we developed previously for hard disks. We numerically obtain both the pair correlation function and the virial coefficients for a fluid of hyperspheres in dimensions d=4, 6, and 8, and find good agreement with the available exact results and Monte Carlo simulations. This paper confirms the alternating character of the virial series for d≥6 and provides the first evidence for an alternating character for d=4. Moreover, we show that this sign alternation is due to the existence of a branch point on the negative real axis. It is this branch point that determines the radius of convergence of the virial series, whose value we determine explicitly for d=4, 6, 8. Our results complement, and are consistent with, a recent study in odd dimensions [R. D. Rohrmann et al., J. Chem. Phys. 129, 014510 (2008)]. [ABSTRACT FROM AUTHOR]