Delta-function expansion of Mayer function with application to virial coefficients

The Mayer cluster integrals of a fluid with smooth, repulsive interactions are expanded in orders of a well-defined softness parameter. To first but not second order in softness, all virial coefficients are given by their hard-sphere forms with an effective diameter. A closed asymptotic expression is derived for the third virial coefficient which gives excellent results for the inverse power and exponential potentials.