Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

Inhomogeneous Systems 291

Let us now consider an homogeneous fluid and fix a particle, the test particle,at

position r = 0. The interaction potential between this particle and the rest of the fluid

may be considered as an external potential that renders the fluid inhomogeneous.

In this case, V (r) = u(r), the intermolecular potential of the homogeneous fluid,

ρ

0

=ρ, the bulk density of the fluid, ρ(r) =ρg(r), the RDF of the homogeneous fluid

(Lebowitz and Percus 1963b), ρ(r) =ρ(r)h(r), because far from the influence of the

test particle (r →∞) the fluid is homogeneous with density ρ and lim

r→∞

g(r) =1,

and C (r, r



;

[

ρ

]

) =c

(2)

(r), the (two-particle) ...