On the hard sphere bridge function

The bridge function for a simple fluid can be written as a diagrammatic expansion involving either the Mayer f-function f(r) or the total correlation function h(r). At each order, the h-bond expansion includes all f-bond diagrams to that order plus an infinite subset of higher order f-bond diagrams. Thus, taken to any order, the h-bond expansion is generally considered more accurate than the f-bond expansion. However, here we show that for hard spheres, the lowest order h-bond approximation for the bridge function is much less accurate than the corresponding f-bond approximation.