Noncondensation of a⁴He submonolayer film

A⁴He film may be modeled only approximately as a two-dimensional (2D) system. This paper calculates the energy shift due to motion in the third dimension, the z direction perpendicular to the surface. Special attention is paid to the question of whether the ground-state solution of this quasi-2D problem is a liquid (as is that of the 2D problem) or a gas. The z motion has substantial effects in the case of weak-binding surfaces, for which numerical results are obtained. An assessment is made of the various approaches used: perturbation theory and variational, adiabatic, and effective potential methods.