Three-Body Quantum Correction to the Free Energy of a Simple Liquid and the Role of Pair and Triplet Potentials in Isotopic Distillation

Abstract

The lowest-order quantum correction to the partition function and free energy of a simple dense fluid is generalized to take account of many-body forces. The three-body quantum correction is calculated using the triple-dipole potential for the nonadditive interaction, assuming the superposition approximation for the triplet correlation function, and taking the pair correlation functions from x ray and neutron diffraction experiments. In the case of liquid Ar near the triple point, the three-body correction is small enough to be neglected in connection with isotopic distillation experiments. These experiments provide values for 〈 ∇2U 〉, where U is the total interaction energy of the molecules in the liquid, and the results can be used in conjunction with experimental radial distribution functions to test empirical pair potentials u(r) for the Ar—Ar interaction. Several forms of u(r) are investigated and the Barker—Pompe, Kingston, and (exp-6) potentials are found to give the best results for 〈 ∇2U〉. The values of 〈 ∇2U 〉 test the repulsive region of the potential and are much less sensitive to the form of u(r) than is the vapor pressure of the liquid near the triple point. The vapor-pressure and isotopic-distillation tests are compared.