“…'(r) =exp[ -/3¢v!,(r) +sv! '(r) +bv!,(r)] , (2) where sV!, (r) = hv!, (r) -c V !, (r) and /3 = 1/ kB T. While this analysis produces a definition of the so-called " bridge" functions b v !, (r) in terms of a density expansion of highly connected bridge or "elementary" diagrams, the expansion cannot be summed and the b v !, (r) remain essentially unknown. This has given rise to a number of approximate closures, usually based on the summation of a subset of diagrams of the c V !, (r), such as the Percus-Yevick 4 (PY) and hypernetted-chain 3 (HNC) approximations.…”