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It is shown that the Percus–Yevick approximation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite. The results show a first-order phase transition which appears to be of the type observed numerically for the Lennard-Jones 12–6 potential.
R. J. Baxter (Sun,) studied this question.