usual mean-field theory [@Ketterson-Song-99] for a sufficiently general interaction potential (at least, when only pairing correlations are taken into account). In particular, in the limit of very weak attraction (BCS limit), the argument of section \[SEC-central potentials leading to exotic pairing\] applies. Thus we expect that, for the type of interaction that we are interested in, represented in Fig. \[FIG-two\_plots\] (b), pairing with $ l=2 $ will be preferred to $ l=0 $ for a range of values of the density, $ n=k_{F}^{3}/3\pi ^{2} $, such that $ k_{F}r_{0}\sim 3 $. In the extreme case in which the attraction takes place only exactly at $ r=r_{0} $ one expects the densities at which the preferred value $ l_{max} $ of the angular momentum quantum number changes to be given by $$\label{phase transition wc}
j_{0}\left( k_{F}r_{0}\right) ^{2}=j_{2}\left( k_{F}r_{0}\right) ^{2}$$ This result, which is degenerate in the quantum number $ m $, is exact for the DSM (\[delta-shell potential\]), and it gives the boundaries of a *quantum phase transition* in which the ground state changes the rotational symmetry.

On the other hand in the dilute, strong coupling limit (BE limit), there is no longer a well-defined Fermi surface and the approximation (\[angle 