Spectroscopic criteria for identification of nuclear tetrahedral and octahedral symmetries: Illustration on a rare earth nucleus

Abstract

We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a Rare Earth nucleus 152 Sm. We use realistic nuclear mean-field theory calculations with the phenomenological macroscopic-microscopic method, the Gogny-Hartree-Fock-Bogoliubov approach and the general point-group theory considerations to guide the experimental identification method as illustrated on published experimental data. Following group-theory the examined symmetries imply the existence of exotic rotational bands on whose properties the spectroscopic identification criteria are based. These bands may contain simultaneously states of even and odd spins, of both parities and parity doublets at well defined spins. In the exact-symmetry limit those bands involve no E2-transitions. We show that coexistence of tetrahedral and octahedral deformations is essential when calculating the corresponding energy minima and surrounding barriers and that it has a characteristic impact on the rotational bands. The symmetries in question imply the existence of long-lived shape-isomers and, possibly, new waiting point nuclei -impacting the nucleosynthesis processes in astrophysics -and an existence of 16-fold degenerate particle-hole excitations. Specifically designed experiments which aim at strengthening the identification arguments are briefly discussed.

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

“…We illustrated the theory predictions on the example of a heavy nucleus 226 Th which, after the first discovery of the presence of both these symmetries in nature in Ref. [10], could become a favourable next experimental test-case.…”

“…The discussed symmetry properties have been used in Ref. [10] to identify the combination of octahedral and tetrahedral symmetries using existing experimental data on 152 Sm nucleus. Fig.…”

“…States are identified without necessity of detecting their decay but rather via identification of their mass/excitation energy. Mapping or searching in unknown regions always requires measurement methods that are: (i) nonscanning, thus cover the whole region of interest in a single measurement, (ii) highly sensitive, to detect also the rarest events, (iii) large dynamic range ( 10), to detected also weakly populated states, (iv) fast, to measure short-lived states and (v) high resolving power, to be able to unambiguously identify and measure also close-lying states, Ref. [17].…”

“…To our knowledge, the first example of identification of such structures in sub-atomic physics has been presented in Ref. [10].…”

“…We proceed to presenting the summary-description of the methods needed to help the identification of the new cases after the first discovery of Ref. [10].…”