Electromagnetic moments of ground and excited states calculated in heavy odd-N open-shell nuclei

TL;DR

This work demonstrates, in a no-parameter DFT framework, that electromagnetic moments of heavy open-shell odd-N nuclei can be predicted across a broad region by breaking rotational, signature, and time-reversal symmetries to align intrinsic angular momenta and then restoring angular momentum. A novel tagging method using tagged states from near $^{192}$Dy enables systematic tracking of 44 configurations (22 prolate, 22 oblate) across 22 Dy-like isotopes per element, providing a coherent picture of how single-particle structures evolve with deformation and neutron number. The results show strong agreement for electric quadrupole moments across the studied nuclei, while magnetic dipole moments exhibit more pronounced, configuration-dependent discrepancies, highlighting the sensitivity to time-odd mean fields and Coriolis-like mixing. The study furnishes extensive publicly available databases and plots, serving as a benchmark for future functional refinements and offering a pathway to unified treatment of weak- and strong-coupling regimes in heavy open-shell nuclei.

Abstract

Within nuclear DFT, we calculated spectroscopic magnetic dipole and electric quadrupole moments for various quasiparticle configurations of odd-$N$, even-$Z$, $83\leq{}N\leq125$ nuclei ranging from gadolinium to osmium. By tagging the blocked quasiparticles with single-particle states of the semi-magic dysprosium isotope, we efficiently computed 22 prolate and 22 oblate states for each of the 154 nuclei and tracked them across the entire major neutron shell. We compared this extensive set of theoretical results with experimental data for 82 states in the region. Breaking rotational, time-reversal, and signature symmetries, we aligned the intrinsic angular momenta along the axis of axial symmetry, thereby enabling full shape- and spin-self-consistent polarizations. The spectroscopic moments were then obtained by restoring rotational symmetry. We conducted a detailed analysis of the pattern of agreement and disagreement between theory and experiment in individual nuclei. For the magnetic dipole moments, agreement with the data varies and is characterized by an overall average and RMS deviation of 0.11 $μ_N$ and 0.35 $μ_N$, respectively. For the electric quadrupole moments, a good corresponding agreement of 0.16 b and 0.29 b was observed.

Figures (38)

• Figure 1: Diagram illustrating the set of odd-$N$, even-$Z$ open-shell elements and isotopes considered in this study for which (i) the calculations were performed (dots) and (ii) experimental data exist (diamonds).
• Figure 2: (Colorblind-friendly palette (Won11) online) Diagram illustrating the deformation splitting of neutron s.p. states in $^{192}$Dy, see the text for the discussion of that choice, which serves as a convenient theoretical starting point for proceeding to calculations of experimentally accessible nuclei. Calculations were carried out using constrained total axial intrinsic quadrupole moments $Q_{20}^{\text{tot}}=\pm0.4$ b, Eq. (\ref{['Qtot']}), and then extrapolated to $\pm1.6$ b for clear visualization of the splitting.
• Figure 3: Upper panels (a), (b), and (c) show the DFT spectroscopic electric quadrupole moments $Q$ (in barn). Lower panels (d), (e), and (f) show the DFT spectroscopic magnetic dipole moments $\mu$ (in $\mu_N$). Left panels (a) and (d) correspond to tag states originating from the spherical orbitals 2f$_{7/2}$ and 1h$_{9/2}$, middle panels (b) and (e) to those of 3p$_{3/2}$, 2f$_{5/2}$, and 3p$_{1/2}$, and right panels (c) and (f) to those of 1i$_{13/2}$. The figure displays all results determined for prolate tag states in dysprosium isotopes (full symbols). Note that for the $\Omega=1/2$ states, we plotted the values of $Q$ corresponding to the $I=3/2$ members of the rotational bands.
• Figure 4: Same as illustrated in Fig. \ref{['fig:Q2,mu_Dy_prol_2']}, but showing the results obtained for oblate tag states, as indicated by the open symbols.
• Figure 5: Excitation energies $E_{\text{exc}}$ of states in dysprosium isotopes calculated for the prolate tag states, upper panels (a), (b), and (c) and oblate tag states, lower panels (c), (d), and (f). Legends of symbols are shown in Figs. \ref{['fig:Q2,mu_Dy_prol_2']} and \ref{['fig:Q2,mu_Dy_obl_2']}.