  The Richardson Hamiltonian describes superconducting correlations in a
metallic nanograin. We do a perturbative analysis of this and related
Hamiltonians, around the strong pairing limit, without having to invoke Bethe
Ansatz solvability. Rather we make use of a boson expansion method known as the
Dyson mapping. Thus we uncover a selection rule that facilitates both
time-independent and time-dependent perturbation expansions. In principle the
model we analise is realised in a very small metalic grain of a very regular
shape. The results we obtain point to subtleties sometimes neglected when
thinking of the superconducting state as a Bose-Einstein condensate. An
appendix contains a general presentation of time-independent perturbation
theory for operators with degenerate spectra, with recursive formulas for
corrections of arbitrarily high orders.
