Recent advances in the nuclear shell model

In this presentation, we will expose some of the last developments in microscopic nuclear structure calculations for exotic nuclei. In a first part we will expose the basic ingredients of nuclear structure calculations with the nuclear shell model framework. In a second step we will expose recent study on the development of collectivity in neutron-rich nuclei around N=40, where experimental evidence suggest a rapid change from the spherical to rotational regime, in analogy to the island of inversion known at N=20. Theoretical calculations are performed within the interacting shell model framework using an enlarged model space outside 48Ca core comprising pf shell for the protons and (f5/2 p3/2 p1/2 g9/2 d5/2) orbits for neutrons. The effective interaction is based on realistic two-body matrix elements which are corrected empirically in its monopole part. We find a very good agreement between theoretical) results and available experimental data. We predict different development of deformation in various isotopic chains, with the maximum of collectivity occurring in the chromium isotopes. The shell evolution responsible for the observed shapes will be disc used in details, in parallel with the N=20 case. Finally the stability of the waiting point nucleus 78Ni and persistence of spin-orbit shell gaps will be discussed as the impact of 3N forces in medium-mass nuclei