The gas phase of continuous systems of hard spheres interacting via n-bodypotential

We show that a system of classical continuous hard spheres interacting thro ugh a general n body potential satisfying suitable integrability conditions , admits a high temperature-low activity gas phase. We find explicitly a co ndition on the activity lambda and the inverse temperature beta which ensur es that the Mayer series for the pressure is absolutely convergent uniforml y in the volume.