In quantum statistical mechanics, the Green's function formalism provides an expression for the density of a fluid as a four-dimensional momentum-energy integral over the spectral function. This function can be expressed in terms of the complex self-energy of the single-particle excited states. By using the ladder diagram approximation, in a low activity limit at which Fermi-Dirac and Bose-Einstein distributions can be approximated by a Boltzmann distribution, the self-energy has been expressed in terms of the two-body scattering amplitude. Density and pressure can then be expressed in terms of the activity, the temperature, and the two-body scattering phase shifts. A complete numerical evaluation of these results has been made for the case of argon at 100K, represented by a hard-sphere plus square-well potential: results are presented for the complex self-energy, the density, and the pressure as a function of activity. The resulting equation of state is compared to experimental results represented by the Beattie-Bridgeman equation and good agreement is found for the gaseous part of the 100K isotherm. Furthermore, two simple analytic equations of state are derived from these expressions with additional (low-density) approximations, which resemble closely some of the equations obtained from the lattice gas theories.