Limiting cases

To facilitate the discussion of results of exactly solvable models, it is instructive to consider weak- and strong-pairing limits of (13). To this end, we introduce the explicit single-particle Hamiltonian

$$\hat{H}_0 = \hat H_{\mbox{\rm\scriptsize {sp}}}=\sum_{k=1}^\... ...eft(a^\dagger_k a_k + a_{\bar{k}}^\dagger a_{\bar{k}} \right)$$ (17)

where e_k are the single-particle energies defined in Sec. 2.