Zero-point vibrational energy of an adsorbed film

The ground-state energy of a submonolayer⁴He film is studied, taking into account vibration perpendicular to the surface. We use an adiabatic approximation that evaluates the z motion with the surface-parallel coordinates x, y of the atoms held fixed. The coupled atoms' dynamical equations are solved using various assumptions, all of which yield a similar result. The numerical results for the zero point energy indicate that⁴He does not form a 2D liquid at zero temperature on K, Rb, or Cs surfaces; instead it is a quantum gas.