ABSTRACT
The thermodynamic and structural properties of the HS system play an essential role in some integral equation perturbation theories, as addressed in Chapter 4, as well as in other kinds of perturbation theories that will be addressed in Chapter 6. For this reason, in this chapter, after describing the different phases of the HS system, we present a number of theories for the radial distribution function and the EOS of the HS fluid and solid. Concerning the fluid, we will start with the derivation of the scaled particle theory (SPT) which, although does not provide a way to obtain the radial distribution function, the EOS arising from this theory is related to that resulting from other theories and, moreover, its extension to hard-body molecular fluids and mixtures is the basis of certain perturbation theories for molecular fluids andmixtures. Concerning the radial distribution function, we will restrict ourselves to those theories leading to analytical expressions. This includes not only the PY theory, but also other less-known theories such as the rational function approximation (RFA) and the FMSA. The latter two theories, apart from being analytical and reasonably simple to use, are very accurate and free from empirical corrections. We will end this chapter describing simple theories for the EOS and the angle-averaged radial distribution function of the solid.
