Shape phase transitions and critical-point phenomena in atomic nuclei

Atomic nuclei exhibit phase transitions as a function of the number of their constituent protons and neutrons. These phase transitions are not of the usual thermodynamic type, but rather they are quantum phase transitions in the equilibrium shape and structure of the ground and low-lying states. This realization has sparked a new area of research, focusing on the concept of 'critical-point symmetries', which describe the structure of nuclei at phase-transitional points. Both macroscopic ( geometric or algebraic) and microscopic (shell-model) aspects of these phase transitions and of changes in structure with proton and neutron number in nuclei are discussed, along with an interpretation in terms of simple Landau theory. Finally, some alternative scenarios and schematic models for different classes of nuclei based on other simple potentials are briefly summarized.