Virial coefficients and close-packing of hard spheres and disks

Using recently calculated 8th virial coefficients for hard spheres and disks, singularities in the virial expansion are reinvestigated. Using a Padé analysis, it is concluded that the singularities are associated with crystalline close-packing and not random close-packing nor with the fluid→solid phase transition. Accurate equations of state are developed for hard sphere and disk fluids. Estimates of 9th and higher virial coefficients are also given.