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 d6 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)].

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