  The recently proposed Symmetry-Conserving Energy Density Functional approach
[G. Hupin, D. Lacroix and M. Bender, Phys. Rev. C84, 014309 (2011)] is applied
to perform Variation After Projection onto good particle number using Skyrme
interaction, including density dependent terms. We present a systematic study
of the Kr and Sn isotopic chains. This approach leads to non-zero pairing in
magic nuclei and a global enhancement of the pairing gap compared to the
original theory that breaks the particle number symmetry. The need to
consistently readjust the pairing effective interaction strength is discussed.
