Virial Equation-of-State for Hard Spheres
  Recent values for virial coefficients up to B12, when expressed in powers of density relative to maximum close packing,lead to a closed equation-of-state for the equilibrium fluid. The series obtained converges for all densities;it becomes negative and diverges to a negative pole at maximum packing. MD data for 64000 spheres in the metastable region shows the virial pressure begins to deviate at the fluid freezing density. 
Leslie V. Woodcock