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

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We 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 O h -group symmetry by its tetrahedral T d -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.

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In a recent article [1] group-theory representation-methods have been combined with the realistic mean-field calculation results to elaborate new, specifically designed methods of experimental identification of the tetrahedral/octahedral symmetries in atomic nuclei. The authors demonstrated that experimental data on ¹⁵² Sm existing in the literature are fully compatible with the extremely restrictive group-theory criteria of simultaneous presence of tetrahedral and octahedral symmetries, thus identifying these symmetries in subatomic physics for the first time. We discuss theory predictions related to the systematic presence of these symmetries as well as their manifestations throughout the Periodic Table in the form of islands centred around the doublymagic tetrahedral-symmetry nuclei. The corresponding theory predictions are discussed in the context of the planned new experiments, which would employ the advanced mass-spectrometry methods [2], in view of the new experimental search criteria [1]. The addressed field of symmetry-research presents particularly promising potentialities in the domain of exotic nuclei studies. Indeed, as it can be demonstrated, in the exact tetrahedral and/or octahedral symmetry limits the corresponding nuclei emit neither E2 nor E1 radiation generating isomeric states with lifetimes which can become much longer than those of the related ground states. This is expected to open the new research strategies for the whole domain of the exotic nuclei studies throughout the Periodic Table.
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