Spectroscopy of ${}^{99}\mathrm{Cd}$ and ${}^{101}\mathrm{In}$ from $\beta$ decays of ${}^{99}\mathrm{In}$ and ${}^{101}\mathrm{Sn}$

We report on new $\gamma$-ray spectroscopy results from $\beta$ decays of ${}^{99}\mathrm{In}$ and ${}^{101}\mathrm{Sn}$. 30 new $\gamma$ rays were observed following the $\beta$ decay of ${}^{99}\mathrm{In}$, and inconsistencies in the literature with respect to the $\gamma$ rays following the $\beta$ decay of ${}^{101}\mathrm{Sn}$ were addressed with two confirmed cases and two new transitions. The experimental $\gamma$-ray energies, intensities, and coincidence relationships are discussed with shell model calculations, where theoretical $\beta$-decay branching ratios from the parent nuclei and $\gamma$-ray cascades of excited states from the daughter nuclei were combined to generate hypothetical $\beta \gamma$ spectra and $\beta \gamma \gamma$ coincidence matrices. The most intense $\beta$-delayed $\gamma$-ray branches in both ${}^{99}\mathrm{Cd}$ and ${}^{101}\mathrm{In}$ were well reproduced with this approach, and several $\gamma$ rays were assigned to new excited states based on their good agreement with shell model predictions.

Figure 1

Segrè chart of nuclides around the doubly magic nucleus ${}^{100}\mathrm{Sn}$. Different colors indicate the available experimental information for each nucleus. The amount of knowledge on excited state(s) varies widely among the different nuclei.

Figure 2

Background-subtracted $\gamma$-ray spectra of $\beta$-decay events correlated between 0 and 5 s after ${}^{99}\mathrm{In}$ implantation. The peaks labeled in black correspond to the previously observed $\gamma$ rays in ${}^{99}\mathrm{Cd}$ [8] and other background contaminants as labeled. New transitions from this decay spectroscopy experiment are labeled in blue. See the text for the tentative assignment of the 481-keV $\gamma$ ray in ${}^{99}\mathrm{Cd}$. The full amplitudes of the 441-keV $\gamma$-ray line and the 511-keV electron-positron annihilation peak are shown in the inset.

Figure 3

$\gamma \gamma$ coincidence projections of some of the transitions shown in Fig. 2, with gates as indicated in each histogram. The black and blue color schemes on the energy labels are the same as in Fig. 2, and those with red labels indicate the absence of coincidences with the most intense $\gamma$ rays in ${}^{99}\mathrm{Cd}$. The peaks which are marked with energies in parentheses are tentative coincidences. The transitions marked with asterisks are Compton peaks from random background $\gamma$ rays originating from much more abundant nuclei, such as ${}^{97}\mathrm{Pd}$.

Figure 4

Level schemes of ${}^{99}\mathrm{Cd}$ from the $\beta \gamma$ spectroscopy of ${}^{99}\mathrm{In}$. The half-life of ${}^{99}\mathrm{In}$ was determined in a previous work (Park 2019 [23]). The energies of the states and the transitions are in keV. The states which are linked by black arrows were previously assigned in Ref. [8]. New $\gamma$ rays which were placed in the level scheme of ${}^{99}\mathrm{Cd}$ are drawn as blue arrows. For the SM results, only the most relevant states for comparison with the proposed experimental level scheme are shown.

Figure 5

Background-subtracted $\gamma$-ray spectrum of $\beta$-decay events correlated between 0 and 3 s after ${}^{101}\mathrm{Sn}$ implantation. $\gamma$-ray energies labeled in black were reported in Ref. [16], and are also observed in this experiment. The energy labels in red accompanied by arrows correspond to the previously reported $\gamma$ rays [11, 16] which were not observed in this work. New transitions assigned to ${}^{101}\mathrm{In}$ are marked with blue labels. The inset shows the raw intensity of the 511-keV annihilation peak.

Figure 6

Experimental (black) and theoretical (blue and red) $\beta$-delayed $\gamma$-ray intensities in ${}^{99}\mathrm{Cd}$. The initial-final spin labels are taken from SM calculations, and the dashed lines and ellipses help guide the reader the matching transitions where tentative spins were previously assigned [8, 9].

Figure 7

Calculated partial half-lives of electromagnetic decay (points) and proton emission (lines and color bands) modes of predicted excited states in ${}^{101}\mathrm{In}$ as a function of excitation energy. The proton emission half-life curves with $l=2$ and $l=4$ were derived based on Ref. [32] and $S_p=1710\left(200\right)\mathrm{keV}$ [30], where the colored bands correspond to the $1\sigma$ variations in $S_p$. The points are derived from SM calculations.

Figure 8

Intensity distributions of $\beta$-delayed proton emission branches as a function of the excitation energy in ${}^{101}\mathrm{In}$. SM-A and SM-B refer to the assumed ground-state spins of ${}^{101}\mathrm{Sn}$ being $5/2^{+}$ or $7/2^{+}$, respectively. The experimental $E_{\beta p}$ spectrum adopted from Ref. [23] was shifted by the proton separation energy of ${}^{101}\mathrm{In}$ [30] and corrected for $\beta$-particle energy summing effects as discussed in Ref. [36]. See the text for details.

Figure 9

Experimental (black) and theoretical (blue and red) $\beta$-delayed $\gamma$-ray intensities in ${}^{101}\mathrm{In}$. The discriptions of SM-A and SM-B are the same as in Fig. 8. The black points with arrows correspond to $2\sigma$ upper limits on the intensities of the $\gamma$ rays which were previously reported but not observed in this work. The black dashed curve at $E_{\gamma }<1000\mathrm{keV}$ illustrates a $2\sigma$ upper limit on $\gamma$-ray intensities derived from statistical fluctuations in the energy spectrum displayed in Fig. 5. The initial-final spin labels are taken from SM calculations. For the sets with $l=2$ proton emission, the downward arrows in the legend indicate the results obtained with reduced $b_{\beta p}$ values after raising the extrapolated $S_p$ value by $1\sigma$ and adopting the $1\sigma$-reduced $b_{\beta }$ values for proton-emitting states.

Figure 10

Level schemes of ${}^{101}\mathrm{In}$ from the $\beta \gamma$ spectroscopy of ${}^{101}\mathrm{Sn}$. The half-life of ${}^{101}\mathrm{Sn}$ was determined in a previous work (Park 2019 [23]). The transitions and the level energies are in keV. The theoretical excitation energy of the 7/$2^{+}$ state in ${}^{101}\mathrm{Sn}$ is within $\approx 100\mathrm{keV}$ of the 5/$2^{+}$ state. In ${}^{101}\mathrm{In}$, the excited states above the label “FE EXP” were previously assigned in a fusion-evaporation experiment [8] and not populated in this experiment. For the SM results, only the states which are most relevant for the comparison are presented. The SM states without $J^{\pi }$ labels have the same values as the adjacent experimental states. The assignment of the 2116- and 2157-keV $\gamma$ rays observed in this work is very tentative, as indicated with blue dashed lines. See the text for discussion.