High-rank Symmetries in Nuclei: Challenges for Prediction Capacities of the Nuclear Mean-field Theories

International audienceWe report on the recent progress in the application of the group-theory criteria combined with the nuclear mean-field theory methods in the context of the experimental verification of the presence of the tetrahedral and octahedral (sometimes referred to as high-rank) symmetries in sub-atomic physics. In this article, we focus on the possible coexistence of the two classes of shapes representing the two symmetries in nuclei simultaneously as well as we discuss the possible spontaneous breaking of the octahedral Oh-group symmetry by its tetrahedral Td-subgroup symmetry partner. Experimental methods which are envisaged for the identification of the discussed symmetries, the former based on the mass spectrometry and isomer detection techniques are briefly discussed