  Recent self-consistent mean-field calculations predict a substantial
depletion of the proton density in the interior of 34Si. In the present study,
we investigate how correlations beyond the mean field modify this finding. The
framework of the calculation is a particle-number and angular-momentum
projected Generator Coordinate Method based on
Hartree-Fock-Bogoliubov+Lipkin-Nogami states with axial quadrupole deformation.
The parametrization SLy4 of the Skyrme energy density functional is used
together with a density-dependent pairing energy functional. For the first
time, the generator coordinate method is applied to the calculation of charge
and transition densities. The impact of pairing correlations, symmetry
restorations and shape mixing on the density profile is analyzed step by step.
All these effects significantly alter the radial density profile, and tend to
bring it closer to a Fermi-type density distribution.
