Probing the Evolution of the Shell Structures in Exotic Nuclei

Magic numbers are a key feature in finite Fermion systems since they are strongly related to the underlying mean field. The size of the shell gaps and their evolution far from stability can be linked to the shape and symmetry of the nuclear mean field. Moreover the study of nuclei with large neutron/proton ratio allow to probe the density dependence of the effective interaction. Changes of the nuclear density and size in nuclei with increasing N/Z ratios are expected to lead to different nuclear symmetries and excitations. In this contribution I will discuss some selected examples which show the big potential of stable beams and of binary reactions for the study of the properties of the neutron-rich nuclear many body systems.