  We consider the development of Cooper pairs in a self-consistent Hartree Fock
mean field for the even Sm isotopes. Results are presented at the level of a
BCS treatment, a number-projected BCS treatment and an exact treatment using
the Richardson ansatz. While projected BCS captures much of the pairing
correlation energy that is absent from BCS, it still misses a sizable
correlation energy, typically of order $1 MeV$. Furthermore, because it does
not average over the properties of the fermion pairs, the exact Richardson
solution permits a more meaningful definition of the Cooper wave function and
of the fraction of pairs that are collective.
