WKB Approximation of the Quantum Radial Distribution Function Applied to Fluid Neon

Abstract

In order to determine the better of two neon intermolecular pair potentials, the expansion expression of the diagonal element D(r, r) of the normalized and symmetrized statistical density matrix given by exp(βF)〈r1,r2,···,rN|exp(−βH)S|r1,r2,···,rN〉is presented as a WKB expansion. Subsequently, the WKB approximation of the quantum radial distribution function g(r) for the pair potential is developed also by taking into account the particle exchange effect, and a new quantum effective pair potential is suggested. The theory is applied to fluid neon by using the Percus—Yevick and convoluted-hypernetted-chain integral equations. We used the Lennard-Jones 6–12 pair potential and the modified Buckingham—Corner 6-exp pair potential of neon at four temperatures. The comparison has been made between the theoretical relative-intensity curves of scattered x rays and their corresponding experimental curves, and also between the theoretical quantum radial distribution curves and their corresponding experimental curves with a theoretical estimate of the intensity at small-angle scattering. The theoretical result is in good agreement with the experimental result and is best for the modified Buckingham—Corner 6-exp pair potential.