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The region of the nuclear landscape around the doubly-magic $^{132}$Sn is rich in nuclear structure phenomena. A relevant feature in the region is the presence of long-lived isomeric states, which may undergo both $\beta$ and $\gamma$ decay [1-3]. Spin-gap isomers arising from hindered decay routes to lower-lying levels due to a large change in nuclear spin the need for the emission of high-multipolarity $\gamma$ rays have been identified . Seniority isomers have also been found in this region [4] arising from the coupling of identical nucleons in the same nuclear shell. This coupling may lead to fully aligned states with a small energy gap for electromagnetic decays to other levels.
Another type of spin-gap isomers are those arising from fully aligned proton and neutron pairs. Examples of these isomers can be found in the nuclear chart, such as the 12$^+$ ($\nu 0f_{7/2}^{-2}\times\pi0f_{7/2}^{-2}$) $^{52}$Fe [5] and the 16$^+$ ($\nu0h_{9/2}^{-2}\times\pi0g_{9/2}^{-2}$) in $^{96}$Cd [6]. In both cases, the lower energy of the fully aligned state relative to the states with similar but lower $J^{\pi}$ states from the same multiplet result in $\beta$-decaying states. The case of $^{96}$Cd along with the spreading in energy of the yrast band in $^{92}$Pd [7] was considered to be an evidence for the dominance of a neutron-proton aligned scheme in $N=Z$ nuclei. These studies prompted a large theoretical discussion, indicating that the dominance of aligned $pn$ pairs may be a generic feature in nuclei with valence nucleons in high-$j$ orbitals. In the study provided by Y.H. Kem \textit{et al} [8], it was suggested that this dominance of $pn$ pairs is not only confined to $N=Z$ nuclei but it should be expected in other regions of the nuclear chart. In their study, it was shown how the energies of the yrast state could be explained mainly by the influence of $pn$ aligned pairs. An strong evidence of the $pn$ pair dominance in $^{128}$Cd would be the existence of a fully-aligned 18$^+$ $\beta$-decaying state based on the $\nu 0h_{11/2}^{-2} \times \pi 0g_{9/2}^{-2}$ configuration, analog to the 16$^+$ state in $^{96}$Cd. Different studies have predicted their existence [9,10], and some isomeric states have already been reported in this nucleus. A $10^+$ isomer with T$_{1/2}$ = 3.56(6) $\mu$s and 2714-keV excitation has been assigned to the two-neutron 0$h_{11/2}^{-2}$ hole configuration [11] . On the other hand, a longer-lived isomer with T$_{1/2}$ = 6.3(8) ms has also been proposed at 1572 keV above the $10^+$ isomeric level based on de-exciting transitions, and tentatively proposed as $15^-$ [9]. However, none of them correspond with the fully aligned state.
In this contribution, we present the results of a high-statistics $\beta$-decay experiment conducted at the ISOLDE facility at CERN, utilizing pure Cd beams. Strong evidence for a new $\beta$-decaying high-spin isomer in $^{128}$Cd has been found. This isomeric state is a very good candidate for the fully aligned state. A detailed discussion of the experimental evidence will be provided, alongside a comparison of the findings with state-of-the-art shell-model calculations and calculations using the Symmetry Conserving Configuration Mixing Method (SCCM) with the Gogny D1S interaction.
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