  Bubble nuclei are characterized by a depletion of their central density.
Their existence is examined within three different theoretical frameworks: the
shell model as well as non-relativistic and relativistic microscopic mean-field
approaches. We propose $^{34}$Si and $^{22}$O as possible candidates for proton
and neutron bubble nuclei, respectively. In the case of $^{22}$O, we observe a
significant model dependence, thereby calling into question the bubble
structure of $^{22}$O. In contrast, an overall agreement among the models is
obtained for $^{34}$Si. Indeed, all models predict a central proton density
depletion of about 40%. This result provides strong evidence in favor of a
proton bubble in $^{34}$Si.
