The smooth cut-off Hierarchical Reference Theory of fluids

Understand

We provide a comprehensive presentation of the Hierarchical Reference Theory (HRT) in the smooth cut-off formulation.

• A simple and self-consistent derivation of the hierarchy of differential equations is supplemented by a comparison with the known sharp cut-off HRT.
• Then, the theory is applied to a hard core Yukawa fluid (HCYF): a closure, based on a mean spherical approximation ansatz, is studied in detail and its intriguing relationship to the self consistent Ornstein-Zernike approximation is discussed.
• The asymptotic properties, close to the critical point are investigated and compared to the renormalization group results both above and below the critical temperature.