Pair Distribution Function and Two-Body Propagator

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Abstract
Starting from the ordinary definition of the pair distribution function, the following theorem is proved without the help of the cluster integral expansion and "toron" diagrams: the pair distribution function in the grand canonical ensemble can be expressed in terms of the two-body propagator corresponding to the scattering in position-reciprocal temperature space. A simple expression for the internal energy of a nonideal gas with pair interactions is obtained in terms of the pair distribution function.