$\beta$ decay of ${}^{129}\mathrm{Cd}$ and excited states in ${}^{129}\mathrm{In}$

The $\beta$ decay of ${}^{129}\mathrm{Cd}$, produced in the relativistic fission of a ${}^{238}\mathrm{U}$ beam, was experimentally studied at the RIBF facility at the RIKEN Nishina Center. From the $\gamma$ radiation emitted after the $\beta$ decays, a level scheme of ${}^{129}\mathrm{In}$ was established comprising 31 excited states and 69 $\gamma$-ray transitions. The experimentally determined level energies are compared to state-of-the-art shell-model calculations. The half-lives of the two $\beta$-decaying states in ${}^{129}\mathrm{Cd}$ were deduced and the $\beta$ feeding to excited states in ${}^{129}\mathrm{In}$ were analyzed. It is found that, as in most cases in the $Z<50$, $N\le 82$ region, both decays are dominated by the $\nu 0g_{7/2}\to \pi 0g_{9/2}$ Gamow–Teller transition, although the contribution of first-forbidden transitions cannot be neglected.

Figure 1

Germanium add-back spectrum recorded in coincidence with the first $\beta$ decay observed in WAS3ABi within 450 ms after the implantation of a ${}^{129}\mathrm{Cd}$ ion and requiring that the implantation and the decay occurred in the same DSSSD and with a maximum position difference of 1 mm in the horizontal and vertical directions. The transitions labeled with symbols correspond to known transitions in ${}^{129}\mathrm{Sn}$ (%), populated in the $\beta$ decay of the daughter nucleus ${}^{129}\mathrm{In}$, in ${}^{128}\mathrm{In}$ (&), populated after $\beta$-delayed neutron emission from ${}^{129}\mathrm{Cd}$ or the decay of ${}^{128}\mathrm{Cd}$ (see text for details), in ${}^{131}\mathrm{Sn}$ (#) and ${}^{132}\mathrm{Sn}$ ($), through the false correlation of $\beta$ decays of ${}^{131}\mathrm{In}$ and ${}^{132}\mathrm{In}$ to the implanted ${}^{129}\mathrm{Cd}$ ions and the annihilation of positrons produced in the pair creation in the germanium detectors (@). Single-escape peaks have been marked with (SE) and peaks arising from room background with (bkg).

Figure 2

The $\gamma$-ray spectra in (a) prompt coincidence with the the 1796.5 keV transition, (b) prompt coincidence with the 2155.6 keV transition, (c) coincidence (without time condition) with the 334.1 keV transition, and (d) prompt coincidence with the 995.1 keV transition.

Figure 3

Proposed level scheme of ${}^{129}\mathrm{In}$ established based on the intensities of and the coincidence relations between $\gamma$ rays emitted following the $\beta$ decay of ${}^{129}\mathrm{Cd}$.

Figure 4

The $\gamma$-ray spectra in prompt coincidence with (a) the 542.0 keV transition, (b) the 769.2 keV transition, (c) the 1422.9 keV transition, and (d) the 1761.6 keV transition.

Figure 5

(top) Time distribution of all decays correlated to the implanted ${}^{129}\mathrm{Cd}$ ions and fit to the data with the fit function $f\left(x\right)$ (see text for details). (bottom) Comparison between fits obtained with the fit function $g\left(x\right)$, which considers two $\beta$-decaying states in ${}^{129}\mathrm{Cd}$ with half-lives of 242 and 104 ms corresponding to the literature values, and the data. “IR” refers to the relative population of the 104-ms-half-life component (see text for details).

Figure 6

Summed time distributions for the decays of the two $\beta$-decaying states in ${}^{129}\mathrm{Cd}$ in coincidence with (a) the 358.9, 995.1, 1354.2, 1796.5, and 2155.6 keV transitions, and (b) the 1422.9 and 1586.2 keV transitions in the daughter nucleus ${}^{129}\mathrm{In}$. The fit with a single-exponential decay function is shown in red. (c) The time distribution of all decays following the decay of the ms isomer in ${}^{129}\mathrm{Cd}$ (see text for details) and fit to the data with the fit function accounting for the activity of the $11/2^{-}$ state in ${}^{129}\mathrm{Cd}$, the activities of the two $\beta$-decaying states in the daughter nucleus ${}^{129}\mathrm{In}$, and a constant background.

Figure 7

Experimental and calculated energy levels in ${}^{129}\mathrm{In}$. Only the experimental states below an excitation energy of 1.5 MeV and the known isomeric $(23/2^{-})$, $17/2^{-}$, and $(29/2^{+})$ states [15, 16, 17] are included in the comparison.

Figure 8

Distribution of the GT strengths, B(GT), for the decay of the $11/2^{-}$ (top) and $3/2^{+}$ (bottom) states in ${}^{129}\mathrm{Cd}$ as obtained within the present shell-model approach. The experimental GT strengths to the $(13/2^{-})$ state at an excitation energy of 3150 keV and the $(5/2^{+})$ levels at 3184 and 3348 keV are shown as red dots with error bars.