Ground State ofHe4Monolayers Adsorbed on Inert Substrate

We investigate the properties of a system of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms at the absolute zero of temperature interacting via a Lennard-Jones potential, and constrained to motion in two dimensions by an otherwise inert substrate. Results of a semiclassical calculation indicate that the ground state is that of a self-bound liquid. It further indicates that a close-packed-solid configuration is not self-bound. A quantum-mechanical variational calculation is performed to obtain an upper bound on the energy of the system. A result of -0.61 °K per particle is obtained at a density of 0.035 ${\mathrm{\AA }}^{-2\mathrm{}}$. The relationship between this calculation and recent experiments on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ monolayers is briefly discussed.