Beta delayed neutron emission of $N=84$ $^{132}$Cd

Abstract

Using the time-of-flight technique, we measured the beta-delayed neutron emission of $^{132}$Cd. From our large-scale shell model (LSSM) calculation using the N$^3$LO interaction [Z.Y. Xu et al., Phys. Rev. Lett. 131, 022501 (2023)], we suggest the decay is dominated by the transformation of a neutron in the $g_{7/2}$ orbital, deep below the Fermi surface, into a proton in the $g_{9/2}$ orbital. We compare the beta-decay half-lives and neutron branching ratios of nuclei with $Z<50$ and $N\geq82$ obtained with our LSSM with those of leading "global" models such as Finite-Range Droplet Model (FRDM). Our calculations match known half-lives and neutron branching ratios well and suggest that current leading models overestimate the yet-to-be-measured half-lives. Our model, backed by the $^{132}$Cd decay data presented here, offers robust predictive power for nuclei of astrophysical interest such as $r$-process waiting points.

Figures (6)

• Figure 1: Gamma spectrum following the decay of $^{132}$Cd. We observe no gamma transitions in $^{132}$In and just one transition in $^{131}$In at 988 keV, populated after beta-delayed neutron emission Taprogge2014. We observe two transitions following the decay of $^{131}$In (*), and a variety of background lines corresponding to neutron scattering in Ge ($\dagger$), $^{84}$Rb contamination from a previous experiment ($\ddagger$), and the 511 keV positron annihilation line (#). The top right inset shows a schematic of the $^{132}$Cd beta-decay.
• Figure 2: Beta-delayed neutron time-of-flight spectra from the decay of $^{132}$Cd. The inset shows the neutron time-of-flight spectrum in coincidence with the 988 keV gamma line in $^{131}$In (see the inset in Fig \ref{['fig1']}). Similarly to our observation in the decay of $^{133}$In Xu2023, a large fraction of the neutron intensity concentrates in a peak at around 2 MeV. Both spectra were fitted simultaneously using a self-consistent procedure that includes all possible decay channels in $^{131}$In (see text for more details). The black transitions correspond to neutron emission populating the 1290 keV 3/2$^-$ state, the blue to the first excited state (1/2$^-$), and the red to the 9/2$^+$ ground state. The dashed line represents the background arising from the gamma-flash and uncorrelated events. Finally, the pink line corresponds to the sum of all transitions and background.
• Figure 3: Cumulative decay strength as a function of the excitation energy in $^{132}$In. We obtained the strength using the intensities from the fit of the neutron time-of-flight spectrum (Fig. \ref{['fig2']}), the total number of $^{132}$Cd decays (2.2 10$^5$), and assuming a neutron branching ratio of 100%. The large jump in strength at around 5 MeV corresponds to the most intense neutron transitions observed at 2 MeV in Fig. \ref{['fig2']}. The red line corresponds to the total decay strength calculated using the LSSM with N$^3$LO Xu2023, while the dashed red line is just the FF strength. The model reproduces very well the experimental decay strength, further supporting its consistency across $N=82,84$ nuclei with $Z<50$.
• Figure 4: Left: Decay half-lives of $N=82$ isotones (nudat2000) compared with our calculation using LSSM with N$^3$LO (red). The uncertainty bad in light red corresponds to changing the unknown Q$_{\beta}$ values by $\pm$0.5 MeV. We include calculations using FRDM-QRPA Moller2019 (dashed dark blue), D3C* Marketin2016 (dashed green), DDPC1 Ravlic2025 (dashed dark green), Ney et al. Ney2020 (dashed brown), and shell model calculations from Shimizu et al. Shimizu2021 (purple) and Zhi et al. Zhi2013 (orange). Right panel: same for $N=84$ isotones. Note that prior to our model no other LSSM calculations were available. In both cases we see that experimental values are well reproduced by models except of Ney et al. and FRDM-QRPA, the latter being the leading model used in r-process calculations Mumpower2016Mumpower2024. The "see-saw" behavior of FRDM-QRPA half-lives is driven by their treatment of pairing in their mass and Q$_{\beta}$ calculations, resulting in larger half-lives of the important even-even nuclei Mumpower2016
• Figure 5: Beta-delayed neutron branching ratios of $N=82$ to $N=85$ cadmium isotopes nudat2000, compared to the model using LSSM with N$^3$LO (red). For comparison, we show neutron branching ratios from FRDM-QRPA Moller2019 (dashed teal), DF3-CQRPA Borzov2016 (dashed dark green), and D3C* Marketin2016 (dashed green). While the LSSM with N$^3$LO calculation reproduces well all neutron branching ratios, all "global models" substantially under-predict $^{132,133}$Cd.