Current shell-model progress in the investigation of ¹³²Sn and ²⁰⁸Pb regions

Within the shell-model (SM) framework, enormous progress is achieved in the investigation of nuclei far from stability, by the development of a new generation of effective interactions using many-body perturbation theory. In this context, I start with an introduction to the main ingredients of realistic shell model calculations, by giving an overview of the construction of the effective Hamiltonians. Special focus is devoted to the recent N3LOP and H₂O₈ effective interactions, derived from free nuclear potentials, via many-body perturbation technique, which are developed for the ¹³²Sn and ²⁰⁸Pb mass regions, respectively. Making use of these effective interactions, some selected results of nuclei from the two mass regions ¹³²Sn and ²⁰⁸Pb will be discussed, by addressing a large amount of information on energy levels and electromagnetic transitions. It is noteworthy that some of these SM results are used as references in the interpretation of several new experimental measurements, proving the reliability of the effective interactions. Finally, I demonstrate the evolution of the collectivity in the two mass regions, where significant quadrupole correlations appear in some nuclei, with the signature of nonaxial-band. (author)