Particle number projection with effective forces

The particle-number projection method is formulated for density-dependent forces and in particular for the finite-range Gogny force. Detailed formula for the projected energy and its gradient are provided. The problems arising from the neglection of any exchange term, which may lead to divergences, are thoroughly discussed and the possible inaccuracies estimated. Numerical results for the projection after variation method are shown for the nucleus 164Er and for the projection before variation approach for the nuclei 48,50Cr. We also confirm the Coulomb antipairing effect found in mean-field theories