Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

18 Perturbation Theories for Fluids and Solids

and, in this case, the total correlation function is

h(r) = g(r) −1. (2.30)

We can write

g

(

r

)

= e

−β

(

r

)

, (2.31)

where (r) is termed potential of mean force between two particles separated a

distance r, because from Equation 2.25 it is clear that

f(r

1

) =−

∂(r)

∂r

1

=−



V

...



V

e

−βU(r

1

...r

N

)

∂U

N

∂r

1

dr

3

...dr

N



V

...



V

e

−βU(r

1

...r

N

)

dr

3

...dr

N

(2.32)

is the mean force acting on a particle at position r

1

given that there is another particle

at position r

2

, with r =|r

2

−r

1

|, averaged over the positions of the remaining N −2

particles.

The physical meaning of the RDF is easily understood if we take into account

that the number