On the theory of liquids

The present paper concerns the exact analytic forms of correlation functions of liquids and some of their macroscopic properties which these correlations determine. Since these functions are expressible in terms of the scattering structure factors of liquids, the macroscopic properties they define will be described in terms of the properties of the structure factors. One is then led, with some limitations, to a rigorous result on the behavior of pair potential energies of isolated stationary atoms at close separations. Part of the paper is devoted to a discussion of some of the limitations of the experimentally derived structure factors as well as the liquid correlation functions to which they give rise. It will be shown, on the basis of liquid helium data, that improvements in the empirical correlation functions as well as the various macroscopic liquid properties they define, require the knowledge of the structure factors over a far wider range of the momentum changes on scattering than obtained heretofore. The final topic concerns a detailed study of the asymptotic, large atomic separation, behavior of the correlation functions. The temperature limitations of a direct method yielding these asymptotic forms will be obtained. A new method of derivation of these forms, involving the scattering structure factors, will be described. This same method also leads to the asymptotic form of the structure factors themselves, at large values of the momentum changes on scattering. These latter asymptotic structure factors retain their validity over the whole temperature interval of existence of liquids.