
240 Perturbation Theories for Fluids and Solids
To determine y from this expression, we cannot use the Kirkwood superposition
approximation, Equation 6.63, because it is not enough accurate. From the simulation
data for g(σ, σ, x) as well as the low-density behavior, an expression for y was obtained
by Wertheim (1987) for the totally flexible case
y = 0.233633η
(
1 +1.482η
)
. (8.102)
A slightly different expression, namely,
y = 0.233633η
(
1 +0.472η
)
, (8.103)
was derived by Müller and Gubbins (1993), and Phan et al. (1993) reported a very
similar parametrization. To arrive at the result of Equation 8.103, the triplet correlation
function for the three BHS ...