Microscopic triaxial quadrupole-octupole collective Hamiltonian for low-energy nuclear excitations

TL;DR

The paper develops a microscopic Triaxial Quadrupole-Octupole Collective Hamiltonian (TQOCH) that unifies rotations, quadrupole-octupole vibrations, and their couplings to describe low-lying positive- and negative-parity nuclear states. Built on MDC-CDFT inputs, the 4D collective framework maps a deformation-energy surface across (beta20, beta22, beta30, beta32) and yields vibrational and rotational dynamics via a mass tensor and moments of inertia, with zero-point corrections included. Application to 152Sm shows soft behavior along quadrupole and octupole directions and reproduces many low-lying bands and transition rates, while identifying a second mode of octupole excitation and predicting a potential K^pi=4^- band; no tetrahedral minimum is found within the current model. Limitations include underestimation of moments of inertia and certain E1 strengths due to model truncations (e.g., omission of beta31), motivating extensions to include additional degrees of freedom and cross-functional checks for robustness. This work provides a direct link between microscopic deformation landscapes and spectroscopic observables, advancing the understanding of shape coexistence and octupole collectivity in nuclei.

Abstract

We present a microscopic triaxial quadrupole-octupole collective Hamiltonian (TQOCH) that unifies collective rotations, quadrupole-octupole vibrations, and their couplings to model low-lying nuclear states of both parities. The TQOCH's dynamics are governed by collective parameters derived from multidimensionally constrained covariant density functional theory. The model's validity is demonstrated through calculations of $^{152}$Sm, including its deformation energy surfaces, excitation spectra, and transition probabilities. As a predictive tool, the TQOCH probes complex nuclear phenomena like shape coexistence and phase transitions, directly connecting their microscopic origins to spectroscopic observables.

Figures (6)

• Figure 1: (Color online) Deformation energy surface (DES) of $^{152}$Sm computed using the multidimensionally constrained CDFT based on the PC-PK1 functional and a separable pairing interaction (a-e). Two-dimensional projections of the DES near the global minimum on the ($\beta_{20},\beta_{30}$), ($\beta_{20},\beta_{32}$), ($\beta_{20},\beta_{22}$), ($\beta_{30},\beta_{22}$), and ($\beta_{30},\beta_{32}$) planes. The contours join points on the surface with the same energy.
• Figure 2: (Color online) Low-energy positive- and negative-parity bands, and the corresponding $B(E2)$ values (in Weisskopf units) for intraband transitions in $^{152}$Sm. The TQOCH results (panel b) are shown in comparison with available data (panel a) NNDCGarrettAIPCP2009.
• Figure 3: (Color online) Distribution of $K$-components (projection of the angular momentum on the intrinsic z-axis) in the collective wave functions of the states $2^+_3$, $4^+_6$, $1^-_1$, $2^-_{1}$, $2^-_{2}$, and $4^-_3$.
• Figure 4: (Color online) Intrinsic electric dipole moment $D_{10}$ (in units of $eb$) of $^{152}$Sm in the $(\beta_{20}, \beta_{30})$ plane. The remaining collective degrees of freedom are fixed at the values that correspond to the global minimum.
• Figure 5: (Color online) The probability density distributions for the states $0^+_{1,2,3,4}$, $2^+_3$, and $4^+_6$ of $^{152}$Sm in the ($\beta_{20},\beta_{22}$), $(\beta_{20},\beta_{30})$, ($\beta_{30},\beta_{22}$), $(\beta_{30},\beta_{32})$ planes.