Geometrical Study of the Pair Distribution Function in the Many-Body Problem

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Abstract
The properties of pair distribution functions which are independent of physical natures as statistics, temperature or potential were studied. We found that the inequalities (23) and (55) are always satisfied by the pair distribution function. Furthermore, the inequalities (9) and (45) are satisfied when the particles have hard-cores. These inequalities will serve as the subsidiary conditions in the variational treatments of many-body problems.