Impact of octupole deformation on the nuclear electromagnetic response

TL;DR

The paper assesses how octupole deformation influences the nuclear electromagnetic response in actinides by performing self-consistent Skyrme-HFB calculations with axial symmetry (allowing parity breaking) and applying the iterative FAM-QRPA to compute $E1$, $E2$, $E3$, and $M1$ strengths across three Skyrme functionals. It compares parity-conserving and parity-breaking ground states to extract transition strengths and sum rules, finding that octupole deformation modestly affects resonance strengths but enhances low-energy $M1$ strength; isoscalar $E3$ strengths in parity-breaking solutions are significantly affected by a rotational NG mode, necessitating its removal. The study emphasizes the importance of NG-mode removal, analyzes inertia and spin-orbit contributions to low-energy strength, and suggests future work on parity restoration and angular-momentum projection to sharpen predictions and facilitate experimental tests in rare-actinide systems. Overall, the work provides a detailed, first-principles assessment of how reflection-asymmetric shapes influence collective excitations and associated sum rules in heavy nuclei, with implications for modeling nuclear response and for informing future experiments.

Abstract

Background: Properties of giant dipole resonances (GDRs), along with other nuclear resonances, provide valuable tools for refining theoretical models as they reflect collective features of nuclear matter. Among such collective phenomena is octupole deformation, whose impact on resonance features, however, is less studied. Purpose: Investigate the effect of reflection-symmetry-breaking octupole deformation on electric and magnetic transition strengths in atomic nuclei. Methods: Calculations were performed using linear response theory with the iterative finite amplitude method (FAM) to solve quasiparticle random phase approximation (QRPA)-type equations. Underlying ground-state solutions were obtained within the framework of axially symmetric Skyrme-Hartree-Fock-Bogoliubov (HFB) using three different Skyrme functionals. Results: Electric and magnetic multipole responses were calculated for octupole-deformed even-even Rn, Ra, Th, U, Pu, and Cm isotopes. Calculations were performed on top of two distinct deformed ground-state solutions: one constrained to conserve parity, and the other allowing parity breaking. Sum rules were calculated from $M1$ transition strengths and compared with the expected correlations to certain ground-state properties. Conclusions: Based on our results, the octupole deformation has only a modest effect on the transition strengths in the resonances. In turn, $M1$ transition strengths have a greater effect at lower energies (0-8 MeV), which encourages further investigation. Isoscalar $E3$ transition strength was confirmed to have a significant contribution from the rotational Nambu-Goldstone (NG) mode in the parity-breaking HFB solution, and thus, removing it was found necessary.

Figures (13)

• Figure 1: Photoabsorption cross-sections calculated from isovector (IV) electric dipole ($E1$) transition strengths for studied Th isotopes. Panels (a)--(l) show results for isotopes with mass numbers $A = 222\,\text{--}\,228$, calculated using three different Skyrme energy-density functionals, SkM*, SLy4, and UNEDF1, as indicated in each subpanel. Solid and dashed lines correspond to reflection-symmetry-conserving ($Q_3=0$) and reflection-symmetry-breaking ($Q_3\neq0$) HFB ground-state solutions, respectively. The $K=1$ mode is shown as the sum of the identical $K=\pm1$ modes.
• Figure 2: Magnetic dipole ($M1$) transition strength functions for studied U isotopes. Panels (a)--(i) show results for isotopes with mass numbers $A = 224\,\text{--}\,228$, calculated using three different Skyrme energy-density functionals, SkM*, SLy4, and UNEDF1, as indicated in each subpanel. Solid and dashed lines correspond to reflection-symmetry-conserving ($Q_3=0$) and reflection-symmetry-breaking ($Q_3\neq0$) HFB ground-state solutions, respectively. Modes with $K>0$ are shown as the sum of the corresponding identical positive and negative $K$ modes.
• Figure 3: Same as Fig. \ref{['fig:M1_U']}, but for the $K=1$ mode of the $^{224}\text{U}$ isotope only, calculated with a smaller imaginary part of the energy ($\gamma$) using two Skyrme EDFs (SkM* and SLy4), as indicated in each subpanel.
• Figure 4: Sum rules of magnetic dipole ($M1$) transitions for studied nuclei with $A=222\,\text{--}\,230$ using three different Skyrme functionals and including transitions with excitation energies between $0$ and 5MeV. Panels (a)--(c) show $m_0$ as a function of the Thouless-Valatin moment of inertia, while panels (d)--(f) show $m_0$ as a function of the square of the quadrupole deformation parameter $\beta_2$. Blue markers correspond to reflection-symmetry-conserving ($Q_3=0$) and red markers to reflection-symmetry-breaking ($Q_3\neq0$) HFB ground-state solutions. Different marker shapes indicate isotopic chains, and the straight line shows a linear fit to the $Q_3=0$ data.
• Figure 5: Energy-weighted sum rules of magnetic dipole ($M1$) transitions as a function of the total spin-orbit energy $E_\text{SO}$ for studied nuclei with $A=222\,\text{--}\,230$. Panels show results for (a) SkM*, (b) SLy4, and (c) UNEDF1 functionals, including transitions with excitation energies as indicated in the panels for each Skyrme functional. Otherwise, results are displayed using the same conventions as in Fig. \ref{['fig:M1_m0_vs_TV-MoI_beta2']}.