coupling or for sufficiently dilute systems with strong attraction. The problem is (leaving aside the fact that the it relies on an expansion in powers of the *amplitude* of the pairing fields, while neglecting other fluctuations due exclusively to their *phase*, which are essential in two dimensions [@Loktev-Quick-Sharapov-01]) that as the density is increased interactions between the PP, which the Gaussian theory neglects, become important. Similarly, when the interaction becomes weaker the PP increase their radius and begin to overlap. Quite generally, at low densities and intermediate coupling the Gaussian theory of $ T_{c} $ must be regarded only as a convenient interpolation scheme [@Nozieres-SchmittRink-85; @Randeria-95], while it fails completely at higher densities (as is evidenced for example in the negative bosonic mass obtained for the DSM at sufficiently large values of the density and the coupling constant [@Quintanilla-Gyorffy-Annett-Wallington-02]). Such limitations (illustrated in Fig. \[FIG-validity\]) have been, at least partially, addressed [@Haussmann-93; @Haussmann-94; @Pieri-Strinati-00], however for simplicity our discussion of $ T_{c} $ below refers only to the regions of parameter space in which the standard theory [@Randeria-95] can be safely applied at that temperature. These are illustrated in Fig. \[FIG-validity\].

Let us now see what form the above standard 