On the Radial Distribution Function in Fluids

Abstract

It is shown that if g(r) is the radial distribution function and φ(r) the pair potential, then the function F(r)=g(r) exp[φ(r)/kT]—1 has a number of properties analogous to those of the pair correlation function G(r)=g(r)—1 which are known from the Ornstein—Zernike theory. The integral of F(r) over all space is related to the fluctuations in a certain well-defined physical quantity, in the same way that the integral of G(r) is related to fluctuations in density. The integral of F(r), furthermore, is shown to be always positive, so that on the average g(r) exceeds exp[—φ(r)/kT]. Finally, it is shown that if one makes a hypothesis analogous to one which is familiar in the Ornstein—Zernike theory, then it follows that the pair correlation function G(r) cannot vanish more rapidly than the pair potential φ(r) as r→∞.