Reference hypernetted-chain approximation

The reference-hypernetted-chain approximation (RHNC) proposed by Lado (1973) approximates the bridge function Cj j( ) by the bridge function C j (r) for the corresponding short-range potential ... 

One should perhaps mention some other closures that are discussed in the literature. One possibility is to combine the PY approximation for the hard core part of the potential and then use the HNC approximation to compute the corrections due to the attractive forces. Such an approach is called the reference hypernetted chain or RHNC approximation [48,49]. Recently, some new closures for a mixture of hard spheres have been proposed. These include one by Rogers and Young [50] (RY) and the Martynov-Sarkisov [51] (MS) closure as modified by Ballone, Pastore, Galli and Gazzillo [52] (BPGG). The RY and MS/BPGG closure relations take the forms... 

A closure similar to the RHNC is the modified hypernetted chain (MHNC), introduced by Rosenfeld and Ashcroft [67]. This approximation is based on the empirical observation that the bridge functions for a wide variety of pair potentials belong to the same family of curves. This means that the bridge functions calculated for a suitable reference fluid can be used to a good approximation for another fluid. The reference fluid is usually... 

The relation is referred to as the hypernetted-chain (HNC) approximation. Further linearizing expt(r, r ) in 1.23, one has the Percus-Yevick (PY) approximation,... 

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