The nucleus is one of the most multi-faceted many-body systems in the universe. It exhibits a multitude of responses depending on the way one probes it. With increasing technical advancements of beams at the various accelerators and of detection syst
ems the nucleus has, over and over again, surprised us by expressing always new ways of organized structures and layers of complexity. Nuclear magnetism is one of those fascinating faces of the atomic nucleus we discuss in the present review. We shall not just limit ourselves to presenting the by now very large data set that has been obtained in the last two decades using various probes, electromagnetic and hadronic alike and that presents ample evidence for a low-lying orbital scissors mode around 3 MeV, albeit fragmented over an energy interval of the order of 1.5 MeV, and higher-lying spin-flip strength in the energy region 5 - 9 MeV in deformed nuclei, nor to the presently discovered evidence for low-lying proton-neutron isovector quadrupole excitations in spherical nuclei. To the contrary, we put the experimental evidence in the perspectives of understanding the atomic nucleus and its various structures of well-organized modes of motion and thus enlarge our discussion to more general fermion and bosonic many-body systems.
The matrix elements of the quadrupole variables and canonic conjugate momenta, emerging from collective nuclear models are calculated within a $SU(1,1)times O(5)$ basis. Using a harmonic oscillator implementation of the SU(1,1) degree of freedom, it
can be shown that the matrix elements of the quadrupole phonon creation and annihilation operators can be calculated in a pure algebraic way, making use of an intermediate state method.
