The Anderson–Goldstone–Nambu mode in finite and in infinite systems

There are many indications which testify to the fact that the atomic nucleus can be viewed as a spherical little ball, which can also become football-shaped and plate-shaped, filled of a superfluid Fermi liquid resulting from the condensation of Cooper pairs build out of pairs of nucleons coupled to angular momentum zero. While the transition between the normal and the superfluid phases is not expected to be, in the case of the atomic nucleus, sharp as in the case of systems with an infinitely large number of particles, the analogies which can be drawn between the behaviour of the N→∞ systems and of the atomic nucleus are found to be very much to the point, once the effects of fluctuations are taken into account. In this paper we concentrate our attention on the consequences broken symmetry has on the energy level spectrum of superfluid atomic nuclei, and on its similarities and differences with respect to the N→∞ system. Results from both theory and experiment emphasize the common origin and conceptual affinity of some of the basic phenomena associated with spontaneous symmetry breaking, like the existence of zero frequency modes. Because the atomic nucleus can be viewed as the paradigm of finite many-body fermion systems, these results may also be of relevance in the study of other finite quantal systems like metal clusters, fullerenes, quantum dots, etc.