Signature of shape transition and shape coexistence in mesoscopic systems

We investigate the phenomena of shape transition and shape coexistence in mesoscopic systems, specifically in atomic clusters and atomic nuclei. We focus particularly on the well-known shape transition in silicon clusters of n atoms, Sin, near n = 25, and the Samarium isotope chain near 152Sm. In both cases, we find that the shape transition region can be identified with a plateau in the curve of binding energy per particle vs. n−1/3, where n is the number of particles. To underscore the similarity of this signature of shape evolution for diverse systems, we show that it also applies to the growth of Lennard-Jones clusters.