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(Top) Chart of nuclei centered on $^{133}$In (red star). The label $\hbar\omega$ refers to the harmonic-oscillator shells around $^{132}$Sn. The $r$-process path is taken from Ref.\ \cite{skynet}. (Bottom) Proton and neutron single-particle ($\ssp$) diagram with dominant $\beta$-decay channels in $^{133g}$In and $^{133m}$In. Red and gray arrows represent GT and FF transitions respectively.

Neutron TOF spectra taken in coincidence with the $^{133}$In $\beta$ decays, with (a) corresponding to the pure ground-state decay and (b) to an admixture of ground-state (40\%) and isomeric decays (60\%). The inset (c) shows the ground-state spectrum in coincidence with the 4041-keV $\gamma$ decay in $^{132}$Sn. On top of the background (dashed line), the spectra are fitted by the neutron response functions (magenta) consisting of 18 (blue) and 13 (red) peaks in the ground-state and isomeric decays, respectively.

Comparisons of excitation energy and decay strength between LSSM and experimental data. Figures (a)-(d) show the results of four individual transitions populating the $\nu$2p-1h states. Figures (e) and (f) present cumulative strength distribution up to $E_{ex}=11$ MeV for $^{133g,m}$In, respectively. The calculation only includes the results from N$^3$LO because of its better agreement in the GT strength. The theoretical FF contribution is drawn explicitly in dashed lines.

Comparison between several global calculations and the experimental half-life (guided by dashed lines) of $^{133g}$In. The total half-life (blue) is divided into GT (red) and FF (black) partial half-lives. Calculations are explained in the main text.