  The London ground-state energy formula as a function of number density $\rho
$ for a system of boson hard spheres of diameter $c$ at zero temperature
(corrected for the reduced mass of a pair of particles in a
``sphere-of-influence'' picture) generalized to describe fermion hard-sphere
systems with four and two intrinsic degrees of freedom such as helium-three or
neutron matter and symmetric nuclear matter, respectively, is proposed as the
crystalline energy branch for hard-sphere systems. For the fluid branch we use
the well-known, exact, low-density equation-of-state expansions for many-boson
and many-fermion systems, appropriately extrapolated to physical densities.
Here, via a double-tangent construction the crystallization and melting
densities for boson and fermion hard spheres are determined. They agree well
with variational Monte Carlo, density-functional, and Green Function Monte
Carlo calculations.
