  The evolution of the pairing correlations from closed shell to middle shell
nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn
isotopes. 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.
