Nuclear Tetrahedral Symmetry

It has been recently pointed out that atomic nuclei with tetrahedral symmetry could be encountered all over the nuclear chart. The predictions are based on a very general analysis of symmetries of the nuclear mean-field and are inspired by the group-theory considerations. The implied unique 4-fold degeneracies of the single-particle levels characteristic of tetrahedral (and/or octahedral) symmetry of the fermionic mean-field are thought to favour the appearance of large gaps in the shell structure thus leading to stable potential minima with the corresponding symmetry. [This mechanism is similar to that of the stabilizing mechanism related to the (2j+1)-fold degeneracies at spherical shapes]. Calculations performed for a few candidate-nuclei in various mass regions show indeed that the tetrahedral-shape isomers are relatively low in energy. They are separated from the ground-state minimum by a significant barrier (up to a couple of MeV). In this paper, we would like to focus on the nuclei whose hypothetical tetrahedral-symmetry states can be found in the dedicated experiments; we present examples of related mean-field calculations and briefly discuss the envisaged experimental challenges.