IReS, Strasbourg

Tetrahedral and other exotic symmetries in nuclei

A new approach to the exotic nuclear symmetries is presented. It is based on a genuine theory of symmetry considerations (point groups, their irreducible representations) rather than on the traditional comparing the ratios of frequencies of the deformed harmonic oscillator. Group theory considerations give a strong provilege to the tetrahedral and octahedral symmetries that are characterized by 48 and 96 symmetry elements, respectively, and lead both to four-fold degeneracies in the single-nucleonic spectra.

Microscopic calculations confirm the existence of the strong shell-effects related to those symmetries and predict a possibility of existence of the of the corresponding stable equilibrium deformations. The nuclear ranges are discussed where those effects can be detectable through experiments.

A new approach to the collective rotation of the quantum objects that obey to the tetrahedral and/or octahedral symmetries is presented and discussed.