My research interests fall in the global topic of ”many body physics”. Most of the time the many body system being the atomic nucleus, although I have made some excursions into the physics of quantum liquids with a small number of atoms. All the approaches to the structure of the nucleus that take as elementary component the nucleons (protons and neutrons) posit as starting point the existence of a self binding mean field in which the nucleons behave as independent particles. This may not be a physically sound approximation in itself, but can be a very useful mathematical scheme to derive an effective nuclear theory (ENT). The most successful ENT is the Shell Model with large scale Configuration Interaction (SM-CI). Its implementation requires a good knowledge of the ”in medium” interaction, that I have pursued using the monopole-multipole separation strategy, as well as the delineation of the minimal valence spaces that contain the relevant degrees of freedom of the problem under scrutiny. And finally the algorithms and codes to solve the associated (huge) computational problem. The Strasbourg-Madrid Shell Model collaboration has been, and continues being, instrumental to achieve these goals. Among its highlights let’s mention:
• The heuristic of the quadrupole-quadrupole interaction and its realisation in new versions of the SU(3) symmetry.
• The description of the nuclear deformation and superdeformation in a spherical basis (i.e. in the laboratory frame).
• The extension of the SM-CI calculations to regions of mass hitherto unexplored.
• The elucidation of the mechanism producing the Islands of Inversion at the neutron magic numbers N=20 and 28 for very neutron rich isotopes, and the prediction of new ones at N=40 and N=50.
Another line of work is the study of weak processes in the nucleus; standard single and double beta decays and foremost, the neutrinoless double beta decays. In the latter case we have unveiled the prominent role of the correlations in the value of the nuclear matrix elements (NME) and provided ”state of the art” values for them. A promising avenue is the study of the effect of the partial restoration of SU(4) in the NME’s.