  We calculate the phase behavior of hard spheres with size polydispersity,
using accurate free energy expressions for the fluid and solid phases. Cloud
and shadow curves, which determine the onset of phase coexistence, are found
exactly by the moment free energy method, but we also compute the complete
phase diagram, taking full account of fractionation effects. In contrast to
earlier, simplified treatments we find no point of equal concentration between
fluid and solid or re-entrant melting at higher densities. Rather, the fluid
cloud curve continues to the largest polydispersity that we study (14%); from
the equilibrium phase behavior a terminal polydispersity can thus only be
defined for the solid, where we find it to be around 7%. At sufficiently large
polydispersity, fractionation into several solid phases can occur, consistent
with previous approximate calculations; we find in addition that coexistence of
several solids with a fluid phase is also possible.
