Kirkwood Phase Transition for Boson and Fermion Hard-Sphere Systems

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.