Quantum Phase Transitions in Finite Nuclei

In the last years evidence for quantum phase transitions (QPT) in the equilibrium shapes of atomic nuclei has been extensively discussed. These QPT occur as a function of the number of nucleons. Their extreme and surprising rapidity as a function of nucleon number will be discussed in terms of the interactions among the valence nucleons, their dependence on the nuclear orbits, and on shell structure. Extrordinarily simple models (called critical point symmetries) that describe nuclei at critical points of these QPT will be described, along with comparisons of their predictions with extensive data. Predictions of exotic nuclei where new examples of such QPT may be found will be motivated by a simple counting scheme.