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The Lipkin-Nogami method is generalized to deal with finite range densitydependent forces. New expressions are derived and realistic calculations withthe Gogny force are performed for the nuclei $^{164}$Er and $^{168}$Er. Thesharp phase transition predicted by the mean field approximation is washed outby the Lipkin-Nogami approach; a much better agreement with the experimentaldata is reached with the new approach than with the Hartree-Fock_Bogoliubovone, specially at high spins.Comment: 5 pages, RevTeX 3.0, 3 postscript figures included using uufiles.  Submitted to Phys. Rev. Let

Approximate particle number projection for finite range density dependent forces