Extension of the Uhlenbeck-Ford Model with an Attraction

The Uhlenbeck-Ford model for soft repulsion, which has only a repulsive interaction, is extended by inclusion of an attraction. This extension still allows an analytical evaluation of the virial coefficients. The integrals over the graph contributions are reduced to a combinatorial problem. We have calculated the virial coefficients to order 6 in the density. A link is made between this model and more common interactions, like the 12-6 Lennard-Jones potential.