  The Percus-Yevick theory for monodisperse hard spheres gives very good
results for the pressure and structure factor of the system in a whole range of
densities that lie within the liquid phase. However, the equation seems to lead
to a very unacceptable result beyond that region. Namely, the Percus-Yevick
theory predicts a smooth behavior of the pressure that diverges only when the
volume fraction $\eta$ approaches unity. Thus, within the theory there seems to
be no indication for the termination of the liquid phase and the transition to
a solid or to a glass. In the present article we study the Percus-Yevick hard
sphere pair distribution function, $g_2(r)$, for various spatial dimensions. We
find that beyond a certain critical volume fraction $\eta_c$, the pair
distribution function, $g_2(r)$, which should be positive definite, becomes
negative at some distances. We also present an intriguing observation that the
critical $\eta_c$ values we find are consistent with volume fractions where
onsets of random close packing (or maximally random jammed states) are reported
in the literature for various dimensions. That observation is supported by an
intuitive argument. This work may have important implications for other systems
for which a Percus-Yevick theory exists.
