Shape transition and shape coexistence in atomic clusters and nuclei

We investigate the signature of shape transition and shape coexistence in small atomic clusters and other mesoscopic systems, such as atomic nuclei. One of the best known examples is the prolate-compact shape transition/coexistence phenomenon observed in mobility experiments on Si clusters.[1] Using a hierarchical strategy that features an extensive tight-binding-based search of the energy surface, followed by a full density functional theory investigation of the most stable structures, we recently determined the lowest-energy clusters across the range n=2 to 28.[2] The calculated properties of these clusters are in very good agreement with available measurements of dissociation energies, ionization energies and ion mobilities, providing strong evidence that these structures are the ones found in experiments. The calculations clearly exhibit a transition in the relative stability of prolate and compact clusters between n=25 and 26, coinciding exactly with the experimental behavior. The lowest energy prolate and compact structures are found almost degenerate, justifying the coexistence of shapes observed in the experiment. The binding energy per atom of the ground states vs N^-1/3 exhibits a long plateau in the transition/coexistence region, suggesting that this phenomenon may be related to a relatively small surface tension. Similar behavior was recently found in the isotope 152 of the nucleus of the element Sm, for which the ground sate, J ^π = 0⁺, is known to be very deformed, and the first excited J^π = 0⁺, is compact. A similar signature in the binding energy per atom of the Sm isotopes can be also extracted from the available experimental data.