Pathologies in the sticky limit of hard- sphere-Yukawa models for colloidal fluids. A possible correction

A known ‘sticky hard sphere’ model, starting from a hard sphere Yukawa potential and taking the limit of infinite amplitude and vanishing range with their product remaining constant, is shown to be ill-defined. This is because its Hamiltonian (which we call SHS2) leads to an exact second virial coefficient which diverges, unlike that of Baxter's original model (SHS1). This deficiency has never been observed so far, since the linearization implicit in the ‘mean spherical approximation’ (MSA), within which the model is analytically solvable, partly masks such a pathology. To overcome this drawback and retain some useful features of SHS2, we propose both a new model (SHS3) and a new closure (‘modified MSA’), whose combination yields an analytical solution formally identical with the SHS2-MSA solution. This mapping allows the recovery of many results derived from SHS2, after a re-interpretation within a correct framework. Possible developments are indicated.