An approach is proposed which includes ground-state correlations beyon
d RPA. This is achieved by using a renormalized quasiboson approximati
on with reference to the correlated ground state of the system, rather
than to the uncorrelated Hartree-Fock one, and by expressing the part
icle-particle and hole-hole pair operators in terms of the particle-ho
le ones. The set of the so-obtained nonlinear equations for the one-ph
onon energy and amplitudes are first solved within the Lipkin-Meshkov-
Glick model and the results are compared with those of previous approa
ches as well as with the exact ones. Applications to realistic nuclei,
starting from fully self-consistent HF + RPA calculations with a Skyr
me force are also presented.