New and comprehensive $\beta$- and $\beta p$-decay spectroscopy results in the vicinity of ${}^{100}\mathrm{Sn}$

A decay spectroscopy experiment on proton-rich nuclei in the vicinity of the doubly magic ${}^{100}\mathrm{Sn}$ was carried out at RIKEN Nishina Center. More than 20 nuclei with $43\le Z\le 50$ and $N\le 51$, produced by fragmentation reactions were investigated via analyses of $\beta$-decay, $\beta p$-decay, and subsequent $\gamma$-ray data. Owing to higher statistics, the precision on the half-lives of many of the ground states and isomers was improved. $\beta$-decay endpoint energies of 11 states in 8 nuclei were measured for the first time, and the corresponding $Q_{\text{EC}}$ and excitation energies were generally consistent with various mass models. Many $\beta$-delayed proton emission branching ratios were measured either for the first time or with higher precision compared to literature values, and some of them differed by more than $2\sigma$. Many of the large discrepancies were associated with nuclei with long-lived isomeric states, highlighting large systematic uncertainties involved in these measurements. Twenty-five new $\gamma$ rays were observed, and ten new states are proposed with unambiguous excitation energies, spins, and parities. Most of the energies of the excited states were consistent within 300 keV or 20%, whichever was greater, compared to shell model predictions in the proton/neutron $(p_{1/2},g_{9/2})$ model space assuming a ${}^{76}\mathrm{Sr}$ core. A signature of a new $(1/2^{-})$ isomer in ${}^{97}\mathrm{Cd}$ with $T_{1/2}=0.73\left(7\right)$ s was found, in good agreement with shell model predictions.

Figure 1

Particle identification plot of proton-rich radioactive nuclei produced in this experiment. ${}^{100}\mathrm{Sn}$ is marked as a reference.

Figure 2

Left: maximum energies deposited in $x$- and $y$-side DSSSD strips for decays correlated to ${}^{97}\mathrm{Cd}$ implantation events. The void where $3.5<E$ (MeV) $<6.0$ on the $x$-side strips is due to an ADC saturation of the $x$-side strip channels, resulting in overflow events appearing at $E>6$ MeV. Right: energy projections of the 2D matrix on the left. See Sec. 2e for details.

Figure 3

Theoretical energies of the states in ${}^{99}\mathrm{In}, {}^{99}\mathrm{Sn}$, and ${}^{100}\mathrm{Sn}$ from SM calculations with the SLGM interaction. The excitation energies are in MeV, and the energy gaps between different nuclei are not drawn in scale.

Figure 4

$\beta$-decay time distributions of individual nuclei studied in this work. Red solid lines represent the fit functions containing all the decay components. The solid and the dashed lines correspond to the $\beta$-decay components of the ground state (black) and the isomers (blue) of the parent and the daughter nuclei, respectively. The long dashed lines represent the decays of the $\beta$-decay daughter nuclei, and the short dashed lines represent the decays of the $\beta p$-decay daughter nuclei. $T_{1/2}$ displayed with $\gamma$ superscripts were determined from $\gamma$-gated $\beta$-decay time distributions. For the $\left(2^{+}\right)$ isomer in ${}^{96}\mathrm{Ag}$, the literature half-life of 6.9(5) s [34] was adopted in order to determine the $b_{\beta p}$ value of the isomer.

Figure 5

Same plot and description as Fig. 4, but for $\beta p$ decay events.

Figure 6

Experimental $\gamma$-ray gated positron energy distributions (first and third columns) from $\beta$ decays and matched Geant4-simulated energy histograms deduced from ${\chi }^2$ minimization (second and fourth columns). The arrows with dotted lines indicate the ${\chi }^2$ evaluation range. The vertical arrows point to the trial $Q_{\beta }$ with the minimum ${\chi }^2$, and the horizontal arrows with solid lines represent the $Q_{\beta }$ range where the endpoints correspond to ${\chi }^2={\chi }_{\text{min}}^2+1$ for determining $1\sigma$ uncertainties. For ${}^{96,97}\mathrm{Cd}$ and ${}^{98}\mathrm{In}$, the $Q_{\beta }$ of the isomeric states were also determined (round markers in blue). See Secs. 2d and 3c for details on the $Q_{\beta }$ measurement methods.

Figure 7

Experimental $Q_{\mathrm{EC}}$ of the eight nuclei presented in Table 2 compared with different mass models [59, 60, 61, 62], SM calculations (labeled as HB [15] and SLGM [12]) and extrapolations in AME2016 [58]. The $E_x$ of the three isomers are also compared. See Sec. 3c for descriptions of theoretical uncertainties.

Figure 8

WAS3ABi energy spectra of $\beta p$ emitters in the ${}^{100}\mathrm{Sn}$ region. Only the energies of the correlated pixels with the maximum $\mathrm{\Delta }E$ are plotted. For certain nuclei, $\beta p$ energy spectra with different time gates are drawn to compare the contributions from isomeric states and/or $\beta$-decay daughter nuclei. For ${}^{98}\mathrm{In}$, efficiency-corrected $\beta p$ energy distributions with two different $\gamma$-ray gates are plotted in order to investigate the double peak structure. See Sec. 3e for details.

Figure 9

$\beta$-delayed $\gamma$ ray spectrum of ${}^{88}\mathrm{Ru}$. Note the $\beta$-decay correlation time windows for both the main plot and the inset. The 146.0(5)-keV line was assigned as the $\left(1^{+}\right)\to \left(2^{+}\right)$ transition in ${}^{88}\mathrm{Tc}$. The inset shows the 741-keV $\gamma$ ray which belongs to ${}^{88}\mathrm{Mo}$, the $\beta$-decay granddaughter.

Figure 10

$\beta$-delayed $\gamma$ ray spectrum of ${}^{88}\mathrm{Tc}$ with a correlation time window of 0–20 s. The peaks labeled in black numbers except the 511-keV annihilation peak are previously known $\gamma$-ray transitions, and those with asterisks are from long-lived and abundant species such as ${}^{97}\mathrm{Pd}$. The subset of the spectrum where $E_{\gamma }>1200$ keV was scaled by a factor of 5 for visualization. The inset shows the coincident $\gamma$ ray spectrum of the 1508-keV $\gamma$ ray seen for the first time.

Figure 11

$\gamma$-ray spectrum from the $\beta$ decay (black line histogram) and $\beta p$ decay (red filled histogram) of ${}^{89}\mathrm{Ru}$. The correlation time window was 0–3 s. Parts of the spectrum were zoomed with the labeled scale factors for better visualization. All labeled $\gamma$-ray peaks except those at 179 and 741 keV are new.

Figure 12

$\gamma$-ray spectrum from the $\beta$ decay (main plot) and $\beta p$ decay (inset) of ${}^{90m}\mathrm{Rh}$. Two new transitions at 1164 and 1317 keV from the $\beta -\gamma$ spectrum were found. See Sec. 3i for their placements in the level scheme of ${}^{90}\mathrm{Ru}$.

Figure 13

Level schemes from ${}^{90}\mathrm{Rh}, {}^{88,89}\mathrm{Ru}$, and ${}^{88}\mathrm{Tc}$ decays. New $\gamma$ rays and proposed states in this work are drawn in blue. States and $\gamma$ rays which have been previously observed or predicted by SM are drawn in either black (for positive-parity states) and red (for negative-parity states). All excitation and $\gamma$-ray energy labels are in keV.

Figure 14

$\beta$-delayed $\gamma$-ray spectrum of ${}^{91}\mathrm{Rh}$ with a correlation time window of 0–3 s. The peaks labeled in black numbers except the 511-keV annihilation $\gamma$ ray are previously known $\gamma$-ray transitions. The inset shows a new $\gamma$-ray peak at 2248 keV.

Figure 15

$\beta$-delayed $\gamma$ ray spectrum of ${}^{92}\mathrm{Pd}$ with a correlation time window of 0–5 s. The new 257-keV $\gamma$ ray was assigned as the $\left(1^{+}\right)\to \left(2^{+}\right)$ transition in ${}^{92}\mathrm{Rh}$. The inset shows the $\beta$-decay $T_{1/2}$ fits with the 257-keV (blue squares) and 865-keV (black dots) $\gamma$-ray gates. See Sec. 3k for details.

Figure 16

$\beta p$-delayed $\gamma$ ray spectrum of ${}^{92}\mathrm{Pd}$ with a correlation time window of 0–10 s. The inset shows the $\beta p$ time profile of the 395-keV $\gamma$ ray belonging to ${}^{91}\mathrm{Tc}$ and the $T_{1/2}$ fit, whose result is consistent with $T_{1/2}{(}^{92}\text{Rh})=3.18\left(22\right)$ s from $\beta -\gamma$ analysis in Fig. 15.

Figure 17

$\beta$-delayed $\gamma$-ray spectrum of ${}^{93}\mathrm{Pd}$ with a correlation time window of 0–2 s. The short correlation window was chosen to improve the signal-to-background ratio. One new $\gamma$ ray was found at 1301 keV. The inset shows a possible signature of the previously identified 853-keV $\gamma$ ray and the absence of the 864-keV $\gamma$ ray.

Figure 18

$\beta p$-delayed $\gamma$ ray spectrum of ${}^{93}\mathrm{Pd}$ with a correlation time window of 0–5 s. The three labeled transitions have been reported in Ref. [80], and their intensities were used to determine experimental $b_{\beta p}$ to the excited states in ${}^{92}\mathrm{Ru}$.

Figure 19

Level schemes from ${}^{92,93}\mathrm{Pd}$ and ${}^{91}\mathrm{Rh}$ decays examined in this work. Additional descriptions are identical to the caption for Fig. 13.

Figure 20

$\gamma$-ray spectrum associated with the $\beta$ decay of ${}^{95}\mathrm{Ag}$, in a correlation time window of 0.1–10 s. The nonzero start time of the correlation window was used to suppress $\gamma$-ray background from the isomeric IC decays in ${}^{95}\mathrm{Ag}$ [82]. The inset shows the $\gamma$-gated $\beta$-decay $T_{1/2}$ of the 1571-keV $\gamma$ ray, in agreement with the half-life of ${}^{95}\mathrm{Ag}$.

Figure 21

$\gamma$-ray spectrum following the $\beta p$ decay of ${}^{95}\mathrm{Ag}$, with a decay correlation window of 0–8 s. One new $\gamma$ ray was found at 196 keV, and the two other labeled $\gamma$ rays confirmed the previous measurement [10].

Figure 22

$\gamma$-ray spectra associated with the $\beta$ decay of ${}^{96}\mathrm{Cd}$, in a correlation time window of 0–5 s. The peaks with # signs indicate $\gamma$ rays from the granddaughter nucleus ${}^{96}\mathrm{Pd}$. Black: prompt $\gamma$ ray spectrum where $|T_{\gamma }-T_{\beta }|<200$ ns. Red: delayed $\gamma$ ray spectrum where 200 ns $<T_{\gamma }-T_{\beta }<8200$ ns, scaled by a factor of 5. The peaks with blue labels are new $\gamma$ rays.

Figure 23

$\gamma$-ray spectrum following the $\beta p$ decay of ${}^{96}\mathrm{Cd}$, with a decay correlation window of 0–2.5 s. The inset shows the decay time profile of the unresolved $\gamma$-ray peak for the 681-keV $\gamma$ ray, which was fitted with two decay components to measure the contribution from the $\beta p$ decay of ${}^{96m}\mathrm{Cd}$.

Figure 24

Decay schemes of ${}^{96}\mathrm{Cd}$ and ${}^{95}\mathrm{Ag}$ decays. Three low-energy states in ${}^{94}\mathrm{Rh}$ populated by the $\beta p$ decay of ${}^{95}\mathrm{Ag}$ with energy labels $a,b$, and $c$ are proposed in this work. A new state in ${}^{95}\mathrm{Pd}$ with $E_x=1571$ keV is suggested. See Secs. 3m and 3n for details. New $\beta$-delayed $\gamma$ rays from the ground state of ${}^{96}\mathrm{Cd}$ were observed but could not be placed in the level scheme. SM calculations revealed several $1^{+}$ candidate states in ${}^{96}\mathrm{Ag}$ for these transitions.

Figure 25

$\beta$-delayed $\gamma$-ray spectrum of ${}^{97}\mathrm{Cd}$. The lines at 1245, 1417, and 1673 were newly observed in this work, while the previously known 2013- and 2909-keV transitions were identified for the first time from $\beta$ decays. The inset shows the $\gamma$-gated $\beta$-decay half-lives of the three new transitions, indicating a short $T_{1/2}$ associated with the 1245-keV transition. See Sec. 3o for details.

Figure 26

$\beta p$-delayed $\gamma$-ray spectrum of ${}^{97}\mathrm{Cd}$. The decay correlation time window was 0–20 s, and the $T_{\gamma }$ window was between $-200$ and 7500 ns. Two new $\gamma$ rays were detected at 1741 and 1927 keV. The inset shows the $T_{\gamma }$ distribution of the 1741-keV delayed $\gamma$ ray and the corresponding $T_{1/2}^{\gamma }$.

Figure 27

$E_{\gamma }$ spectrum following the $\beta$ decay of ${}^{98}\mathrm{In}$, from 0 to 5 s after implantation. The $\gamma$-ray time window was $-200<T_{\gamma }\left(\text{ns}\right)<800$ in order to observe the known $\gamma$-ray cascade from the $T_{1/2}\approx 150$ ns $\left(8^{+}\right)$ isomer in ${}^{98}\mathrm{Cd}$. The transitions labeled with # symbols belong to ${}^{98}\mathrm{Ag}$. The inset shows the high-energy part of the spectrum, centered around the 4157-keV $\gamma$ ray known to depopulate the $\left({10}^{+}\right)$ state in ${}^{98}\mathrm{Cd}$. See Sec. 3p for details.

Figure 28

$E_{\gamma }$ spectrum following the $\beta p$ decay of ${}^{98}\mathrm{In}$, with a correlation time window of 0–5 s. The transitions labeled in black (except the 511-keV annihilation peak) form a known $\gamma$-ray cascade of the seniority band in ${}^{97}\mathrm{Ag}$. Three new $\gamma$ rays at 602, 730, and 1417 keV were used to establish new excited states in ${}^{97}\mathrm{Ag}$.

Figure 29

Level schemes of ${}^{98}\mathrm{In}$ and ${}^{97}\mathrm{Cd}$ decays. Several excited states and deexcitation $\gamma$ rays were assigned in ${}^{97}\mathrm{Ag}$. A new $(1/2^{-})$ isomer in ${}^{97}\mathrm{Cd}$ is proposed. In addition to SM (SLGM), predictions of the $(1/2^{-})$ isomer in ${}^{97}\mathrm{Cd}$, labeled “GF” and “HB,” were calculated based on Refs. [11, 15].

Figure 30

Relative differences between experimental and theoretical energies of excited states in proton-rich nuclei. Only the states with unambiguous spin/parity assignments and one-to-one correspondence with SM levels are compared. The solid black markers indicate the energy discrepancies for the new states proposed in this work. The lines indicating an absolute energy difference of 300 keV for low-energy excited states are drawn also.