Shell Model Approaches: From N = Z Towards the Neutron Drip Line

The shell model with large-scale configuration mixing (SM-CI) is the theoretical tool of choice in nuclear spectroscopy. In this chapter, we introduce its basic concepts and discuss our present understanding of the model in terms of the competition between the spherical mean field and the nuclear correlations. A key aspect we shall treat is the choice of the valence spaces and effective interactions. We shall discuss as well the main collective modes of the nucleus-superfluidity, associated with the pairing interaction and vibrations and rotations originating in the multipole-multipole terms-using simple models. The emergence of permanent quadrupole deformation and rotational bands brings us to study Elliott's model and some of its variants. These models make it possible to give a physically intuitive interpretation of the full-fledged SM-CI calculations. First, we examine the cases of shape coexistence in two paradigms of doubly magic nuclei, Ca-40 and Ni-56. We then move into the neutron-rich regime, to study the mechanisms that lead to the appearance of islands of inversion (IoI) at N = 40 and N = 50 and its relationship with the phenomenon of shape coexistence in Ni-68 and Ni-78.