Cooper pairs in atomic nuclei

We describe recent efforts to study Cooper pairs in atomic nuclei. We consider a self-consistent Hartree Fock mean field for the even Sm isotopes and compare results based on three treatments of pairing correlations: a BCS treatment, a number-projected BCS treatment and an exact treatment using the Richardson ansatz. Significant differences are seen in the pairing correlation energies. Furthermore, because it does not average over the properties of the fermion pairs, the Richardson solution permits a more meaningful definition of the Cooper wave function and of the fraction of pairs that are collective. Our results confirm that only a few pairs near the Fermi surface in realistic atomic nuclei are collective.