Collective excitations in nuclei

The properties of the nucleus cannot be reduced to the properties of its constituents: it is a complex system. The fact that many properties of the nucleus are consequences of the existence of mean-field potential is a manifestation of this complexity. In particular, the nucleons can thus self-organize in collective motions such as giant resonances. Therefore the study of this collective motions is a very good tool to understand the properties of the nucleus itself. The purpose of this article is to stress some aspects of these collective vibrations. We have studied how an ensemble of fermions as the nucleus can self-organize in collective vibrations which are behaving like a gas of bosons in weak interaction. Understanding of these phenomena remains one of the important subjects of actuality in the context of quantal systems in strong interaction. In particular, the study of the states with one or two vibration quanta provides a direct information on the structure of nuclei close to their ground states. Moreover, some collective states appear to be very robust against the onset of chaos. This is the case of the hot giant dipole built on top of a hot nucleus which seems to survive up to rather high temperatures. Their sudden disappearance is still a subject of controversy. It may be that the mean-field and the associated collective states are playing a crucial role also in catastrophic processes such as the phase-transitions. Indeed, when the system is diluted the collective vibrations may become unstable and it seems that these unstable modes provide a natural explanation to the self organization of the system in drops. Finally, considering the diversity of the different structures of exotic nuclei one may expect new vibration types. All these studies are showing the diversity of the collective motions of strongly correlated quantum systems such as the nucleus but many open questions remain to be solved. (authors)