Radiative decay and electromagnetic moments in $^{229}$Th determined within nuclear DFT

Abstract

Using the nuclear DFT approach with symmetry breaking and restoration, we investigate the electromagnetic properties of the ground and isomeric states in $^{229}$Th. We determine the magnetic dipole transition strength B(M1:$3/2^+_1\rightarrow 5/2^+_1)$ between these two states and discuss the effects of parity breaking, configuration mixing, and time-odd core polarization. We also determine the corresponding spectroscopic magnetic dipole and electric quadrupole moments. Because the octupole deformability of the Skyrme functionals used here is not described in sufficient detail, we analyze the results using a set of Skyrme functionals, with regression aligned with the measured octupole moments of neighboring even-even nuclei. Without parameter adjustment, the results compare favorably with the experimental data but also indicate the need to systematically adjust the octupole degrees of freedom in future functional parametrizations.

Figures (6)

• Figure 1: B(M1) values with respect to the intrinsic octupole moments $Q^3_0$ of $^{226}$Ra (left panels) and $^{230}$Th (right panels), determined for functionals reduced to the time-even mean fields (TE, upper panels) and with complete time-even and time-odd mean fields (TE+TO, lower panels). The numbers in parentheses indicate the number of successfully mixed wave functions for the two configurations, namely $(5/2^+,3/2^+)$. Vertical and horizontal stripes labelled Expt. are the experimental values of $Q^3_0$ and B(M1), respectively. Thick lines and shaded bands denote the regression results and their uncertainties, respectively (Dob18a). Arrows denote shifted points outside the scale of the figure.
• Figure 2: Same as in Fig. \ref{['Corr1a']} but for the B(M1) values calculated between converged individual (not mixed) blocked self-consistent states [631]3/2 and [633]5/2.
• Figure 3: Same as in Fig. \ref{['Corr2a']} but for the B(M1) values calculated between parity-conserving states.
• Figure 4: Summary results obtained in this Letter, compared with the experimental data PhysRevLett.132.182501(Bee25)Yamaguchi2024. The shown values are: B(M1) (a), magnetic dipole moments of the 5/2$^+$ (b) and 3/2$^+$ (c) states, and electric quadrupole moments of the 5/2$^+$ (d) and 3/2$^+$ (e) states. Circles and diamonds correspond to the regression aligned with the measured octupole moments of $^{226}$Ra and $^{230}$Th, respectively.
• Figure 5: Same as Fig. \ref{['Corr1a']} but for magnetic dipole moments.