The nucleus is a strongly correlated system. In fact, the naive picture of the independent particle model and the magic numbers holds by very little even for its pillars, the famous doubly magic nuclei. Shape coexistence in nuclei is ubiquitous and occurs because the quadrupole-quadrupole correlations are highly favored by the nuclear spherical mean fied. At the very neutron rich side, they can even make some semi-magic nuclei deformed in their ground states, leading to the so called Islands of Inversion.
I will visit these islands and describe them within the Spherical Shell Model with (large scale) Configuration Mixing, guided by symmetry considerations, the SU(3) heuristics which we have dubbed SPQR. The tour will finish at doubly magic 78Ni and the fifth Island of Inversion.