${}^{133}\mathrm{In}$: A Rosetta Stone for Decays of $r$-Process Nuclei

The $\beta$ decays from both the ground state and a long-lived isomer of ${}^{133}\mathrm{In}$ were studied at the ISOLDE Decay Station (IDS). With a hybrid detection system sensitive to $\beta$, $\gamma$, and neutron spectroscopy, the comparative partial half-lives ($\log ft$) have been measured for all their dominant $\beta$-decay channels for the first time, including a low-energy Gamow-Teller transition and several first-forbidden (FF) transitions. Uniquely for such a heavy neutron-rich nucleus, their $\beta$ decays selectively populate only a few isolated neutron unbound states in ${}^{133}\mathrm{Sn}$. Precise energy and branching-ratio measurements of those resonances allow us to benchmark $\beta$-decay theories at an unprecedented level in this region of the nuclear chart. The results show good agreement with the newly developed large-scale shell model (LSSM) calculations. The experimental findings establish an archetype for the $\beta$ decay of neutron-rich nuclei southeast of ${}^{132}\mathrm{Sn}$ and will serve as a guide for future theoretical development aiming to describe accurately the key $\beta$ decays in the rapid-neutron capture ($r$-) process.

Figure 1

Top: chart of nuclei centered on ${}^{133}\mathrm{In}$ (red star). The label $\hslash \omega$ refers to the harmonic-oscillator shells around ${}^{132}\mathrm{Sn}$. The $r$-process path is taken from Ref. [20]. Bottom: proton and neutron single-particle ($s.p.$) diagram with dominant $\beta$-decay channels in ${}^{133g}\mathrm{In}$ and ${}^{133m}\mathrm{In}$. Red and gray arrows represent GT and FF transitions, respectively.

Figure 2

Neutron TOF spectra taken in coincidence with the ${}^{133}\mathrm{In}$ $\beta$ 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 ${}^{132}\mathrm{Sn}$. On top of the background (dashed line), the spectra are fitted by the neutron response functions (magenta) consisting of 19 (blue) and 13 (red) peaks in the ground-state and isomeric decays, respectively.

Figure 3

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

Figure 4

Comparison between several global calculations and the experimental half-life (guided by dashed lines) of ${}^{133g}\mathrm{In}$. The total half-life (blue) is divided into GT (red) and FF (black) partial half-lives, with the experimental values being 260(40) and 435(60) ms, respectively. Calculations are explained in the main text.