Nuclear Models
The atomic nucleus is a typical example of a many-body problem. On the one hand, the number of nucleons (protons and neutrons) that constitute the nucleus is too large to allow for exact calculations. On the other hand, the number of constituent particles is too small for the individual nuclear excitation states to be explained by statistical methods. Another problem, particular for the atomic nucleus, is that the nucleon-nucleon (n-n) interaction is not one of the fundamental forces of Nature, and is hard to put in a single closed equation. The nucleon-nucleon interaction also behaves differently between two free nucleons (bare interaction) and between two nucleons in the nuclear medium (dressed interaction).Because of the above reasons, specific nuclear many-body models have been devised of which each one sheds light on some selected aspects of nuclear structure. Only combining the viewpoints of different models, a global insight of the atomic nucleus can be gained. In this chapter, we revise the the Nuclear Shell Model as an example of the microscopic approach, and the Collective Model as an example of the geometric approach. Finally, we study the statistical properties of nuclear spectra, basing on symmetry principles, to find out whether there is quantum chaos in the atomic nucleus. All three major approaches have been rewarded with the Nobel Prize of Physics. In the text, we will stress how each approach introduces its own series of approximations to reduce the prohibitingly large number of degrees of freedom of the full many-body problem to a smaller manageable number of effective degrees of freedom.