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

We present a study of the self-consistent Ornstein\u2013Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width \u3b4. The main purpose of this investigation is to elucidate whether, in the limit \u3b4\u2009\u2192\u20090, the SCOZA predicts a finite value for the second virial coefficient at the critical temperature B 2(T c), and whether this theory can lead to an improvement of the approximate Percus\u2013Yevick solution of the sticky hard-sphere (SHS) model due to Baxter [J. Chem. Phys. 49, 2770 (1968)]. For the SW of non-vanishing \u3b4, the difficulties due to the influence of the boundary condition at high density, already encountered in an earlier investigation by Sch\uf6ll-Paschinger et al. [J. Chem. Phys. 123, 234513 (2005)], prevented us from obtaining reliable results for \u3b4\u2009