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

Abstract

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.

About Competition Between Tetrahedral and Octahedral Symmetries in Atomic Nuclei

“…[4,5] that in the Rare Earth nuclei one should expect the coexistence of these two deformations, whereas in the recent Ref. [6] it has been predicted that the same should be expected for at least some Actinide nuclei. In this article we will focus on the lighter nuclei of (and around) Zirconium, in which the above property is predicted by us not to apply.…”

“…In the meantime a more rigorous interpretation has been developed in terms of the spin-, and particle-number projected Hartree-Fock-Bogolyubov approach and the group theory, by Fukuoka-Strasbourg collaboration, Refs. [10,11] and [6]. The main results are summarised below.…”

Systematic Search For Evidence of Tetrahedral and Octahedral Symmetries in Subatomic Physics: Follow-up of the First Identification Case in152Sm

“…The states which in contrast to the "traditional" spectroscopic behaviour manifest neither E2 nor E1 collective transitions, the latter usually dominating the nuclear population and/or decay schemes are expected to form isomers thanks to the tetrahedral/octahedral-symmetry hindrance properties [13]. Their lifetimes, as compared to the life-times of many other states and in particular to the life-times of the ground-states, are expected to be significantly longer.…”

“…The remaining characteristic rotor structures associated with the remaining irreducible representations A 2 , E, F 1 and F 2 of the T d -group have equally exotic structural features, cf. [10,11,13] and references therein. For odd-even nuclei the characteristic spin-parity sequences are composed of half-integer spins.…”

“…whose ensembles placed on the (E − vs. − I)-plane form parabolas, [13] and references therein. The condition that isomers form a specific smooth-looking relations of the type E isomer (I) ∝ I 2 is unprecedented in the nuclear structure physics and represents a possible focus for the newly established collaborations, cf.…”