Quasi-two-dimensional imperfect Bose gas adsorbed on a surface

We study a submonolayer film adsorbed on a substrate surface as a quasi-two-dimensional (2D) imperfect Bose gas. The ground-state energy and the depletion fraction at zero temperature are calculated. It is found that the depletion is independent of the 2D density (in contrast to the 3D case), but is a monotonically increasing function of the substrate potential well depth. Qualitative conclusions are drawn about implications for superfluidity in the case of He on a weak-binding substrate.