The Lebowitz and Percus mean spherical approximation (MSA) (1966) (Ref. 1) closure is given by

The Blum and Hoye mean spherical approximation (MSA) (1978-1980) (Refs 2 and 3) closure is given by

and

where
and
are the total and the direct correlation functions for two spherical
molecules of i and j species,
is the diameter of 'i species of molecule.
Duh and Haymet (Eq. 9 Ref. 4) write the MSA approximation as

where
and
comes from the WCA division of the Lennard-Jones potential.
By introducing the definition (Eq. 10 Ref. 4)

one can arrive at (Eq. 11 in Ref. 4)

The Percus Yevick approximation may be recovered from the above equation by setting
.
References
- [PR_1966_144_000251]
- [JSP_1978_19_0317_nolotengoSpringer]
- [JSP_1980_22_0661_nolotengoSpringer]
- [JCP_1995_103_02625]