Critical Point Symmetries in Nuclei
  Critical Point Symmetries (CPS) appear in regions of the nuclear chart where a rapid change from one symmetry to another is observed. The first CPSs, introduced by F. Iachello, were E(5), which corresponds to the transition from vibrational [U(5)] to gamma-unstable [O(6)] behaviour, and X(5), which represents the change from vibrational [U(5)] to prolate axially deformed [SU(3)] shapes. These CPSs have been obtained as special solutions of the Bohr collective Hamiltonian. More recent special solutions of the same Hamiltonian, to be described here, include Z(5) and Z(4), which correspond to maximally triaxial shapes (the latter with ``frozen'' gamma=30 degrees), as well as X(3), which corresponds to prolate shapes with ``frozen'' gamma=0. CPSs have the advantage of providing predictions which are parameter free (up to overall scale factors) and compare well to experiment. However, their mathematical structure [with the exception of E(5)] needs to be clarified. 
Dennis Bonatsos, D. Lenis, D. Petrellis, P. A. Terziev, I. Yigitoglu