Dilute resonating gases and the third virial coefficient

We study dilute gases with short range interactions and large two-body scattering lengths. At temperatures between the condensation temperature and the scale set by therange of the potential there is a high degree of universality. The first two terms in the expansion of thermodynamic functions in powers of the fugacity $z$, which measures the diluteness of the system, are determined by the scattering length only. The term proportional to $z^3$ depends only on one new parameter describing the three-body physics. We compute the third term of the expansion and show that, for many values of this new parameter, the $z^3$ term may be the dominant one.