The inference of interatomic forces from structural data on liquids

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Abstract
The measured structure factor S(k) of a monatomic fluid in principle determines uniquely the pair interatomic forces. In practice great difficulties are encountered in implementing this program because of the weak dependence of S(k) on the detailed shape of the pair interaction, particularly at high densities. Here this issue is discussed from the theoretical point of view: is present day liquidstate theory good enough to solve the problem? I find that no present day liquid state theory of S(k) has the required accuracy for general use for this purpose. However, good results are obtained when a good liquid-state theory (specifically the modified hyperetted-chain equation) for the radial distribution function is coupled with simulation of model systems in an iterative predictor-corrector method. In a real system many-body forces are present and it is shown how one can obtain the true two-body interaction starting from the effective one, if the form of the three-body interaction can be considered as known. In a quantum liquid like 4He. S(k) does not directly give information on the interaction but some evidence is presented that from the S(k) of two similar quantum fluids one can infer the difference of the pair interactions.