Octupole deformation in quasiparticle states of odd-mass and odd-odd nuclei

TL;DR

The paper extends a perturbative mechanism for axial octupole deformation from even-even to odd-mass and odd-odd nuclei within a Skyrme-Hartree-Fock-BCS framework with self-consistent blocking and a $Q_{30}$ constraint. It develops a two-step, Koopmans-based formalism that decomposes the deformation-energy response into a core shift $\Delta E_0$ and a second-order single-particle correction $\Delta e$, predicting four deformation scenarios. By applying the method to selected $A\sim 150$ and $A\sim 230$ nuclei and comparing with full SHFBCS calculations, the study finds qualitative agreement and clarifies how pairing and parity-doublet couplings limit quantitative accuracy. The results highlight the relative reliability of the perturbative approach and point to avenues for improvement, including a more robust treatment of pairing and careful selection of reference cores to avoid degeneracy ambiguities.

Abstract

As a follow up of [Phys. Scr. 99 055305 (2024)], where we studied axial octupole shapes in two-quasiparticle states of even-even nuclei, we investigate this type of shapes in odd-mass and odd-odd well-deformed nuclei, using the Skyrme-Hartree-Fock-BCS approach with selfconsistent blocking and a constraint on the expectation value $Q_{30}$ of the axial octupole moment operator. To interprete the pattern of the resulting deformation energy curve as a function of $Q_{30}$, we extend the perturbative mechanism of Ref. [1]. We deduce selection rules which can predict, from the single-particle spectra at $Q_{30} = 0$, whether in a given multiquasiparticle state the deformation energy curve has a local minimum at a vanishing or a finite value of $Q_{30}$. The predictions of this perturbative mechanism are compared with actual Skyrme-Hartree-Fock-BCS calculations with a constraint on the expectation value $Q_{30}$. Overall we obtain a qualitative agreement and we show that quantitative predictions are limited by the role of pairing correlations and strong octupole coupling between quasi-degenerate members of a single-particle parity doublet.

Figures (22)

• Figure 1: Schematic representation of the four scenarios for the deformation energy curves of the studied nucleus and the even-even reference nucleus.
• Figure 2: Neutron (left panel) and proton (right panel) single-particle energies as functions of axial octupole deformation of the ^144_56Ba_88 nucleus. Labels correspond to the positive-$\Omega$ states of Kramers degenerate pairs.
• Figure 3: Same as figure \ref{['fig_Ba144_Nilsson_diagrams']} for the ^150_62Sm_88 nucleus.
• Figure 4: Same as figure \ref{['fig_Ba144_Nilsson_diagrams']} for the ^154_64Gd_90 nucleus.
• Figure 5: Same as figure \ref{['fig_Ba144_Nilsson_diagrams']} for the ^228_88Ra_140 nucleus.