The Onset of deformation in atomic nuclei and atomic clusters

It is well know that atomic nuclei and atomic clusters exhibit properties that can be related to intrinsic deformation. The physical signals of deformation are different, but one can show that for these two mesoscopic systems one can identify the sizes for which they undergo shape transitions using a simple criteria. We give examples of shape transitions in these system and we show how they can be identified experimentally looking to the binding energy per particle vs n^-1,3, where n is the number of particles. It is also know that most mesoscopic systems exhibit prolate deformations. It is interesting to understand why the emergence of prolate deformation is dominant. We present some quantum mechanisms that could explain the dominance of the prolate shapes in nuclei.