Microscopic description of triaxiality in Ru isotopes with covariant energy density functional theory

Abstract

Background: The triaxiality in nuclear low-lying states has attracted great interests for many years. Recently, the reduced transition probabilities for levels near the ground state in 110 Ru have been measured and provided strong evidences for a triaxial shape of this nucleus.Purpose: The aim of this work is to provide a microscopic study of low-lying states for the Ru isotopes with A ∼ 100 and to examine in detail the role of triaxiality, and the evolution of quadrupole shapes with the isospin and spin degrees of freedom. Method:The low-lying excitation spectra and transition probabilities of even-even Ru isotopes are described at the beyond mean-field level by solving a five-dimensional collective Hamiltonian with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1.Results: The calculated energy surfaces, low-energy spectra, intraband and interband transition rates, as well as some characteristic collective observables, such as E(4 + g.s. )/E(2 + g.s. ), E(2 + γ )/E(4 + g.s. ), B(E2; 2 + g.s. → 0 + g.s. ), and γ band staggerings are in a good agreement with the available experimental data. Conclusions:The main features of the experimental low-lying excitation spectra and electric transition rates are well reproduced, and thus strongly support the onset of triaxiality in the low-lying excited states of the Ru isotopes around 110 Ru.

Coulomb excitation of Ru102 with C12 and Garrett1, Zielińska2, Bergmaier3 et al. 2022Phys. Rev. C

“…The predicted ground-state shape is consistent with the results of recent calculations with the relativistic Hartree-Bogoliubov formalism [16] using the density-dependent ME2 [56] and PC1 [57] parametrizations that predict minima in the PES of (β 2 , γ ) = (0.25, 15 • ) and (0.25, 17 • ), respectively. Nearly identical results [17] were found using the covariant density function theory with the PC-PK1 interaction [58] that yields a minimum at (0.25, 19 • ). The calculations using a self-consistent mean-field using the Gogny-D1M interaction predict that 102 Ru possesses some γ softness but with a prolate minimum at β 2 0.2 [15].…”

“…Other calculations using relativistic Hartree-Bogoliubov formalism with density-dependent zero-and finite-range nucleon-nucleon interactions found that shape coexistence did not manifest in any Ru isotope except 104 Ru [16]. Beyond-mean-field calculations employing the five-dimensional collective Hamiltonian with parameters determined by constrained self-consistent meanfield calculations based on the relativistic energy density functional PC-PK1 predicted that 100 Ru was nearly prolate, with a global minimum in the PES at (0.22, 4 • ), and 102 Ru had a triaxial minimum at γ = 19 • and was also predicted to be rather γ soft [17]. The PESs for 104,106 Ru were somewhat similar [17].…”

“…Beyond-mean-field calculations employing the five-dimensional collective Hamiltonian with parameters determined by constrained self-consistent meanfield calculations based on the relativistic energy density functional PC-PK1 predicted that 100 Ru was nearly prolate, with a global minimum in the PES at (0.22, 4 • ), and 102 Ru had a triaxial minimum at γ = 19 • and was also predicted to be rather γ soft [17]. The PESs for 104,106 Ru were somewhat similar [17]. The Ru isotopes have also been considered in the context of lying at a critical point of a shape phase transition, with 104 Ru postulated as a candidate for E (5) symmetry [18], and 100 Ru at the critical point for the U(5)-SO(6) transition [19].…”

Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: effect of triaxial shape

“…More localized studies are more numerous than the (rare) global surveys of triaxiality. Such studies generally concentrate on regions where the BSkG1 model also predicts triaxial ground state deformation, such as the Ge and Se isotopes in the A ∼ 70 region [109][110][111][112], the Kr, Sr, Zr, Mo and Ru isotopes in the A ∼ 100 region [113][114][115][116][117][118], and the neutron-rich rare-earths around A ∼ 190 [119][120][121].…”

Band crossings in 168Ta: A particle-number conserving analysis

“…The PNC scheme has also been adopted both in non-relativistic [49,50] and relativistic mean-field models [51] and the total-Routhian-surface method with the Woods-Saxon potential [52,53]. Most recently, the shell-model-like approach, originally referred to as PNC method, based on the cranking covariant density functional theory has been developed [54]. Note that the covariant density functional theory provides a consistent description of the nuclear properties, especially the spin-orbital splitting, the pseudo-spin symmetry [55,56,57,58,59,60,61,62,63,64] and the spin symmetry in the anti-nucleon spectrum [65,66], and is reliable for the description of nuclei far away from the β-stability line [67,68], etc.…”