  Long-range correlations, which are partially responsible for the observed
fragmentation and depletion of low-lying single-particle strength, are studied
in the Green's function formalism. The self-energy is expanded up to second
order in the residual interaction. We compare two methods of implementing
self-consistency in the solution of the Dyson equation beyond Hartree-Fock, for
the case of the 16O nucleus. It is found that the energy-bin method and the
BAGEL method lead to globally equivalent results. In both methods the final
single-particle strength functions are characterized by exponential tails at
energies far from the Fermi level.
