Thermodynamics of dilute gases: Application to submonolayer He films

In this paper we calculate the thermodynamic properties of submonolayer He films. We first obtain expressions for the thermodynamic properties of dilute systems of particles interacting through a short-range potential, taking into account binary interactions between the particles. These expressions are exact in the limit $n\to 0$, $n$ being the particle number density, and are valid at all temperatures. At high temperatures our expressions reduce to those obtained using the virial expansion truncated after the second term. Next we apply these expressions to He in two dimensions and compare our results with experiment and with previous calculations.