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The Ballone-Pastore-Galli-Gazillo (BPGG) (1986) (Eq. 3.8 Ref. 1) closure relation, developed for mixtures of hard spheres, is given by

B(r)=\left[ 1+s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(r\right)

where s=15/8. It has its origins in the Martynov-Sarkisov closure (s=2). The value of s can be determined by a self-consistency condition. Notice that for s=1 the BPGG approximation reduces to the hyper-netted chain closure.


  1. P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 pp. 275-290 (1986)