Random close packing of hard spheres and disks

A simple definition of random close packing of hard spheres is presented, and the consequences of this definition are explored. According to this definition, random close packing occurs at the minimum packing fraction $\ensuremath{\eta}$ for which the median nearest-neighbor radius equals the diameter of the spheres. Using the radial distribution function at more dilute concentrations to estimate median nearest-neighbor radii, lower bounds on the critical packing fraction ${\ensuremath{\eta}}_{\mathrm{RCP}}$ are obtained and the value of ${\ensuremath{\eta}}_{\mathrm{RCP}}$ is estimated by extrapolation. Random close packing is predicted to occur for ${\ensuremath{\eta}}_{\mathrm{RCP}}=0.64\ifmmode\pm\else\textpm\fi{}0.02$ in three dimensions and ${\ensuremath{\eta}}_{\mathrm{RCP}}=0.82\ifmmode\pm\else\textpm\fi{}0.02$ in two dimensions. Both of these predictions are shown to be consistent with the available experimental data.