β and γ bands in N=88 , 90, and 92 isotones investigated with a five-dimensional collective Hamiltonian based on covariant density functional theory: Vibrations, shape coexistence, and superdeforma

Abstract

A comprehensive systematic study is made for the collective β and γ bands in even-even isotopes with neutron numbers N = 88 to 92 and proton numbers Z = 62 (Sm) to 70 (Yb). Data, including excitation energies, B(E 0) and B(E 2) values, and branching ratios from previously published experiments are collated with new data presented for the first time in this study. The experimental data are compared to calculations using a five-dimensional collective Hamiltonian (5DCH) based on the covariant density functional theory (CDFT). A realistic potential in the quadrupole shape parameters V (β, γ) is determined from potential energy surfaces (PES) calculated using the CDFT. The parameters of the 5DCH are fixed and contained within the CDFT. Overall, a satisfactory agreement is found between the data and the calculations. In line with the energy staggering S(I) of the levels in the 2 γ + bands, the potential energy surfaces of the CDFT calculations indicate γ-soft shapes in the N = 88 nuclides, which become γ rigid for N = 90 and N = 92. The nature of the 0 2 + bands changes with atomic number. In the isotopes of Sm to Dy, they can be understood as β vibrations, but in the Er and Yb isotopes the 0 2 + bands have wave functions with large components in a triaxial superdeformed minimum. In the vicinity of 152 Sm, the present calculations predict a soft potential in the β direction but do not find two coexisting minima. This is reminiscent of 152 Sm exhibiting an X (5) behavior. The model also predicts that the 0 3 + bands are of two-phonon nature, having an energy twice that of the 0 2 + band. This is in contradiction with the data and implies that other excitation modes must be invoked to explain their origin.

An experimental view on shape coexistence in nuclei

“…Refs. [456,457]), the band associated with the 0 + 3 state has not been found. The pairing isomer "second vacuum" has been advocated by Sharpey-Schafer and co-workers 3 The pairing isomers are states constructed from a subset of Nilsson orbitals that are described as "oblate" (i.e.…”

“…The 0 + 3 states in the other N = 88 isotones, however, do not have candidates for band structures that would possess a significantly different moment of inertia from that of the ground-state or 0 + 2 bands in those nuclei. Recent in-beam γ-ray spectroscopy studies [440,441] have failed to report a band based on the 0 + 3 state, which would be surprising if such a band had a large moment of inertia extending to moderate-to-high spin.…”

Pairing vibrations in the interacting boson model based on density functional theory

“…For a more detailed analysis, we apply the pv-IBM theoretical framework to a study of the structure of the axially-symmetric N = 92 rare-earth isotones. For nuclei in this region of the nuclear chart, an unexpectedly large number of low-energy excited 0 + states have been observed [63,64]. From a theoretical point of view, they have been interpreted in terms of pairing vibrations [16], contributions of intruder orbitals [46], and excitations of double octupole phonons [65,66].…”

“…Thus, in the axial case, the energies of the γ band are hardly affected by the inclusion of the pairing degree of freedom. The corresponding experimental 2 + γ energies for 154 Sm, 156 Gd, and 158 Dy are: 1.440 [68], 1.154 [63], 0.946 MeV [64], respectively, whereas no γ band has been identified in 152 Nd. Therefore we note that, for a quantitative comparison with data, the theoretical framework should be extended with the γ degree of freedom (nonaxial shapes).…”

“…V but for the ρ 2 (E0; Ii → Ij) × 10 3 values. The experimental ρ 2 (E0) are from Refs [61,64,68,[70][71][72][73]…”