Solidification ofHe4monolayer

We apply a variational method to calculate ground-state properties of a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ monolayer on a neutral substrate. A stable solid phase occurs at densities above 0.091 ${\mathrm{\AA }}^{-2\mathrm{}}$. The melting density is about 0.095 ${\mathrm{\AA }}^{-2\mathrm{}}$ and the freezing density is about 0.085 ${\mathrm{\AA }}^{-2\mathrm{}}$, which is about 5% higher than the observed freezing density. We also describe an improved method for solving the Percus-Yevick equation.