Solid-Superfluid Transition inHe4at Absolute Zero

A solid-superfluid phase transition applicable to ${\mathrm{He}}^4$ at the absolute zero of temperature is described, utilizing a cell model. Below the critical density which marks the onset of the superfluid, the system has these properties: (i) The energy for adding a particle to the system without creating excitations becomes equal to that for removing a particle; (ii) the excitation spectrum changes from quadratic to linear in momentum for low-momentum excitations; (iii) the zero-momentum state exhibits macroscopic occupation. We estimate the maximum occupation of the zero-momentum level to be about 6%. An estimate of the effective repulsive energy between a pair of ${\mathrm{He}}^4$ atoms confined within a specific volume yields about 16°K. The excitation spectra obtained from averaging on a simple cubic, a body-centered cubic, and a face-centered cubic system are compared with the experimental curve from neutron inelastic-scattering measurements on liquid helium.