Shape coexistence at N=20 and N=28: Study of $02+$ states in $34Si$ and $44S$

It is well known that the nuclear shell structure changes for the most exotic nuclei. One of the consequences of this phenomenon is the modification of the "classical" magic numbers, as experimentally observed at N = 20 and N = 28. Nevertheless, the mechanisms responsible for such changes are still under discussion and more experimental information is needed to better constrain the theoretical models. In these proceedings, we report on the discovery and the experimental study by precise spectroscopy experiments of the $02+$ state in $34Si$ and $44S$⁠. The $34Si$ is located between the magic spherical $36S$ and the deformed $32Mg$⁠, member of the so-called island of inversion, whereas $44S$ is located between the magic spherical $48Ca$ and the deformed $42Si$⁠. Therefore, the structure of these nuclei, and in particular the phenomenon of shape coexistence, is of crucial importance to understand how the intruder configurations progressively dominate the ground state structure of the most exotic nuclei at both N = 20 and N = 28.