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An investigation of the SCOZA for narrow square-well potentials and in the sticky limit

We present a study of the self consistent Ornstein-Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width delta. The main purpose of this investigation is to elucidate whether in the limit delta --> 0, the SCOZA predicts a finite value for the second virial coefficient at the critical temperature B2(Tc), and whether this theory can lead to an improvement of the approximate Percus-Yevick solution of the sticky hard-sphere (SHS) model due to Baxter [R. J. Baxter, J. Chem. Phys. 49, 2770 (1968)]. For SW of non vanishing delta, the difficulties due to the influence of the boundary condition at high density already encountered in an earlier investigation [E. Schoell-Paschinger, A. L. Benavides, and R. Castaneda-Priego, J. Chem. Phys. 123, 234513 (2005)] prevented us from obtaining reliable results for delta < 0.1. In the sticky limit this difficulty can be circumvented, but then the SCOZA fails to predict a liquid-vapor transition. The picture that emerges from this study is that for delta --> 0, the SCOZA does not fulfill the expected prediction of a constant B2(Tc) [M. G. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)], and that for thermodynamic consistency to be usefully exploited in this regime, one should probably go beyond the Ornstein-Zernike ansatz.