Cell Model of a Bose-Condensed Solid

A cell model of a Boson quantum system is described. The model has three phases at $T=0\mathrm{}$ K: normal crystal, Bose-condensed liquid, and Bose-condensed crystal. The excitation spectrum for the Bose-condensed crystal has two branches, a gapless vacancy wave mode and a vacancy-interstitial wave mode with a gap. It is proposed that this phase might be detected in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ near the liquid-solid transition line.