Staggering in γ-band energies and the transition between different structural symmetries in nuclei

The experimental energy staggering in \ensuremath{\gamma} bands of rare earths and actinides exhibits three distinct patterns as a function of angular momentum that are typical of well-deformed structural benchmarks: \ensuremath{\gamma}-soft for nuclei situated between a vibrator and a deformed \ensuremath{\gamma}-soft structure, axially symmetric for those between a vibrator and a rigid rotor, and triaxial \ensuremath{\gamma}-rigid for nuclei between a vibrator and a rigid triaxial rotor. The three patterns are reproduced by appropriate special solutions of the Bohr Hamiltonian, as well as by interacting boson approximation calculations. A particular quantity called S(4), which is proportional to the displacement of the ${3}_{\ensuremath{\gamma}}^{+}$ level relative to the average of the ${2}_{\ensuremath{\gamma}}^{+}$ and ${4}_{\ensuremath{\gamma}}^{+}$ levels, can vary in magnitude and sign for different shapes and is found to give a good indication of structure and the evolution of structure. A sudden change in the \ensuremath{\gamma}-band staggering occurring between the vibrator and the axially symmetric rotor limits seems to be connected to the known presence of a first-order phase/shape transition in this region.