Self-consistent Ornstein-Zernike approximation for fluids

Accurate results for fluids at thermal equilibrium, valid both outside and inside the critical region, are difficult to obtain due to the singular nature of this region. However, for simple models like interacting hard spheres and the Ising model high accuracy has been obtained by use of SCOZA (self-consistent Ornstein-Zernike approximation). Here this approach is extended to one component fluids more generally. Outside the critical region good analytic approximations may be obtained by use of statistical mechanical results that are adjusted to experimental data and/or computer simulations. However, such approximations typically will be of mean field type in the sense that the usual singular behavior in the critical region and in the transition to it, is not present.Here the SCOZA is generalized such that approximations accurate outside the critical region are utilized as basic input in the SCOZA problem. The singular behavior is connected to correlations of increasing range that develop as the critical point is approached. These correlations contribute both to the internal energy and compressibility of the fluid, and they give another contribution to the SCOZA partial differential equation. Accurate results in the critical region are expected to be obtained by adjusting one or a few parameters.