A NEW GEOMETRICALLY BASED INTEGRAL-EQUATION HIERARCHY FOR HARD-SPHERESYSTEMS .1. BASIC THEORY AND THERMODYNAMIC RESULTS

A new hierarchy of integral equations for the background correlation f unctions of hard spheres is derived using geometrical and physical arg uments. The theory is distinct from, but has links with, other theorie s and results, including scaled-particle theory, zero-separation theor ems, and the Born-Green-Yvon hierarchy. Three closure approximations f or the hierarchy are proposed and their results examined for the equat ion of state. The zeroth-order approximation leads to a simple algebra ic equation for the compressibility factor as a function of density an d gives exact second and third virial coefficients. The first-order ap proximation also gives an exact fourth virial coefficient, and the sec ond-order approximation gives an exact fifth virial coefficient. The s econd-order approximation yields compressibility factors much more acc urate than any other available first-principles theory. Furthermore, a t the highest fluid densities it is essentially as accurate as the Car nahan-Starling equation of state, and at medium densities it is more a ccurate.