decomp of V with wc approx\]) ceases to be useful. The gap equation (\[gap eq DL\]) describes a two-body bound state with energy $ \varepsilon _{b}^{l}=2\mu  $ and wave function $ \psi _{\mathbf{k}}=\Delta _{\mathbf{k}}/2E_{\mathbf{k}} $ [@Leggett-80; @Nozieres-SchmittRink-85; @Randeria-Duan-Shieh-90] and so, evidently, the full functional form of the interaction potential $ V\left( \mathbf{r}-\mathbf{r}'\right)  $ has to be taken into account. Since $ l $ is a good quantum number for the Schrödinger equation, a well-defined angular momentum is a shared characteristic of the BCS and BE limits. On the other hand it is easy to show, using $ \mu \ll -\left| \Delta _{l,m}^{(0)}\right|  $, that in the BE limit Eq. (\[gs energy eigen V\]) becomes $$\label{sc-energy}
\frac{1}{L^{3}}\mathcal{U}_{0}=\frac{1}{2}n\varepsilon _{b}^{l}.$$ This equation has a simple interpretation: in the dilute, strong-coupling limit, the system is a BE condensate of non-overlapping pairs. Each pair has $ \hbar \mathbf{q}=0 $ and they are all in the same internal state with energy $ \varepsilon _{b}^{l} $. It follows that the energy of the system is given simply by the formation energies of the individual pairs. Since, for a central potential, the bound state with lowest energy always has $ l=0 $, one expects that *rotational symmetry is 