Abstract:
Using the Ornstein–Zernike equation, we obtain two asymptotic equations,
one describing the exponential asymptotic behavior and the other describing
the power asymptotic behavior of the total correlation function $h(r)$. We
show that the exponential asymptotic form is applicable only on a bounded
distance interval $l<r<L$. The power asymptotic form is always applicable
for $r>L$ and reproduces the form of the interaction potential. In this case,
as the density of a rarified gas decreases, $L\to l$, the exponential
asymptotic form vanishes, and only the power asymptotic form remains.
Conversely, as the critical point is approached, $L\to\infty$, and
the applicability domain of the exponential asymptotic form increases without
bound.