Octupole deformation in even-even Ra isotopes from covariant density functional theory with localized exchange terms in a three-dimensional lattice space
The covariant density functional theory in a three-dimensional lattice space is extended to the PCF-PK1 functional with localized exchange terms and is employed to study the nuclear shape evolution of even-even Ra isotopes. Well-developed axial octupole deformations are found for the ground states of $^{222-228}$Ra with no evidence of triaxial shapes. The energy gain of octupole deformation is employed to assess the stability of octupole deformation, with relatively larger values observed for $^{224}$Ra and $^{226}$Ra. A simplified analysis method based on the single-particle spectrum at the octupole deformation parameter $β_3=0$ is proposed to identify the key single-particle levels driving octupole deformation. It is found that the $m_z=3/2$ orbitals from $ν1j_{15/2}$ and $ν2g_{9/2}$ and the $m_z=1/2$ orbitals from $π1i_{13/2}$ and $π2f_{7/2}$, play crucial roles in the formation of octupole deformation in Ra isotopes. Furthermore, increasing the tensor coupling strength promotes octupole deformation, whereas reducing the pairing strength stabilizes it. Our results provide a microscopic understanding of octupole deformation in the Ra isotopic chain and highlight the importance of both tensor coupling and pairing correlations in reflection-asymmetric nuclear shapes.
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Tepig · 2026-07-20 11:24:19 EST
Summary
This paper applies covariant density functional theory (CDFT) with localized exchange terms in a three-dimensional lattice space to study octupole deformation in even-even Ra isotopes. The authors find well-developed axial octupole deformations in $^{222-228}$Ra, with no evidence of triaxial shapes. They propose a simplified method to identify key single-particle levels driving octupole deformation and analyze the effects of tensor coupling and pairing strength on the stability of octupole deformation.
Mathematical/empirical assessment
The paper provides a detailed analysis of the potential energy surfaces and single-particle spectra, supported by equations such as the Dirac equation and the definition of deformation parameters $\beta_2$ and $\beta_3$. The energy gain of octupole deformation is quantified via $\Delta E_{\mathrm{oct}} = E_{\mathrm{oct}} - E_{\mathrm{quad}}$, which is used to assess stability. The results are consistent with previous studies on octupole deformation in Ra isotopes, and the proposed method for identifying key orbitals is grounded in the single-particle spectrum at $\beta_3 = 0$.
Strengths
The work extends CDFT to a 3D lattice framework, enabling a more flexible description of nuclear shapes without symmetry restrictions. The inclusion of localized exchange terms and tensor couplings improves the accuracy of the model. The paper also offers a clear analysis of how tensor coupling and pairing correlations influence octupole deformation, providing insights into the microscopic mechanisms behind the observed nuclear shapes.
Concerns
The paper does not provide direct comparisons with experimental data beyond general references to prior studies. While the theoretical framework is sound, the specific impact of the 3D lattice approach on the results is not clearly isolated from other model parameters. Additionally, the role of other shape degrees of freedom, such as tetrahedral or triaxial configurations, is not explored in depth.
Final decision
Weak accept