  We study the excited states of the pairing Hamiltonian providing an expansion
for their energy in the strong coupling limit. To assess the role of the
pairing interaction we apply the formalism to the case of a heavy atomic
nucleus. We show that only a few statistical moments of the level distribution
are sufficient to yield an accurate estimate of the energy for not too small
values of the coupling $G$ and we give the analytic expressions of the first
four terms of the series. Further, we discuss the convergence radius $G_{\rm
sing}$ of the expansion showing that it strongly depends upon the details of
the level distribution. Furthermore $G_{\rm sing}$ is not related to the
critical values of the coupling $G_{\rm crit}$, which characterize the physics
of the pairing Hamiltonian, since it can exist even in the absence of these
critical points.
