Approximate particle number projection for finite range density dependent forces

The 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 ${}_{}{}^{164}{}_{}{}^{}\mathrm{Er}$ and ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$. 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, especially at high spins. © 1996 The American Physical Society.