2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192365The Lipkin-Nogami method is generalized to deal with finite range density dependent forces. New expressions are derived and realistic calculations with the Gogny force are performed for the nuclei $^{164}$Er and $^{168}$Er. The sharp phase transition predicted by the mean field approximation is washed out by the Lipkin-Nogami approach; a much better agreement with the experimental data is reached with the new approach than with the Hartree-Fock_Bogoliubov one, specially at high spins.5 pages, RevTeX 3.0, 3 postscript figures included using uufiles. Submitted to Phys. Rev. LettNuclear Theorytext