Analytic descriptions for transitional nuclei near the critical point

Exact solutions of the Bohr Hamiltonian with a five-dimensional square well potential, in isolation or coupled to a fermion by the five-dimensional spin–orbit interaction, are considered as examples of a new class of dynamical symmetry or Bose–Fermi dynamical symmetry. The solutions provide baselines for experimental studies of even–even [E(5)] and odd-mass [E(5|4)] nuclei near the critical point of the spherical to deformed γ-unstable phase transition.