A contribution to the equation of state of fluids at low temperatures based on thermodynamic Green's functions

Abstract

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 100‡K, 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 100‡K 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.