Mean-field based approaches to pairing correlations in atomic nuclei

The evolution of the pairing correlations from closed shell to midshell nuclei is analyzed in the Sn isotopes with the Finite Range Density Dependent Gogny force. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the Lipkin-Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairing regime is also approach dependent, specially at shell closure.