From exotic mean-field symmetries to new classes of isomers in atomic nuclei

In this article, we address the occurrence and properties of exotic point-group symmetries in nuclei. We focus on the relations between the specific gap openings in the single-nucleon spectra, which represent a measure of nuclear stability studied with the help of the nuclear mean-field theory and accompanying octupole shape properties manifesting the link between the particular stability configurations (magic octupole gaps) and resulting exotic geometrical forms. We employ a realistic phenomenological realisation of the nuclear mean-field theory with the so-called universal Woods–Saxon Hamiltonian and the group representation theory to formulate the experimental identification criteria of the addressed symmetries. We use the newest parameterisations of the Hamiltonian obtained employing the inverse problem theory. To stabilise the modelling predictions, we detect and eliminate parametric correlations. Following earlier articles introducing the octupole “fourfold magic numbers” and “universal magic numbers”, N=136 and 198 , examined in the heavy and super-heavy nuclei, we generalise these concepts for the whole mass table for the octupole magic chain N=32, 40, 56, 64, 70, 90, 112, 136, 198 . They bring in the so-called high-rank tetrahedral and octahedral point groups strengthening the specific shell effects and gap openings and implying the unique hindrance factors: at the exact tetrahedral symmetry limit, the collective electric quadrupole and dipole reduced transition probabilities vanish provoking new isomerism. Under these circumstances, many rotational states which in other nuclei manifest strong decay probabilities, in the high-rank symmetry case become isomeric—forming a new class of nuclear high-rank symmetry isomers. The consequences for the future experimental studies of those isomers are discussed especially in the domain of exotic nuclei.