Properties of $\gamma$-decaying isomers and isomeric ratios in the ${}^{100}\mathrm{Sn}$ region

Half-lives and energies of $\gamma$ rays emitted in the decay of isomeric states of nuclei in the vicinity of the doubly magic ${}^{100}\mathrm{Sn}$ were measured in a decay spectroscopy experiment at Rikagaku Kenkyusho (The Institute of Physical and Chemical Research) of Japan Nishina Center. The measured half-lives, some with improved precision, are consistent with literature values. Three new results include a 55-keV $E2\gamma$ ray from a new $\left(4^{+}\right)$ isomer with $T_{1/2}=0.23\left(6\right)\mu \mathrm{s}$ in ${}^{92}\mathrm{Rh}$, a 44-keV $E2\gamma$ ray from the $\left({15}^{+}\right)$ isomer in ${}^{96}\mathrm{Ag}$, and $T_{1/2}\left(6^{+}\right)=13\left(2\right)$ ns in ${}^{98}\mathrm{Cd}$. Shell-model calculations of electromagnetic transition strengths in the $(p_{1/2},g_{9/2})$ model space agree with the experimental results. In addition, experimental isomeric ratios were compared to the theoretical predictions derived with an abrasion-ablation model and the sharp cutoff model. The results agreed within a factor of 2 for most isomers. From the nonobservation of time-delayed $\gamma$ rays in ${}^{100}\mathrm{Sn}$, new constraints on the $T_{1/2}$, $\gamma$-ray energy, and internal conversion coefficients are proposed for the hypothetical isomer in ${}^{100}\mathrm{Sn}$.

Figure 1

Particle identification plots of nuclei produced in this experiment. Nuclei with isomeric $\gamma$-decay $T_{1/2}$ measurements listed in Table 1 are highlighted and labeled. The doubly magic ${}^{100}\mathrm{Sn}$ is labeled as a reference.

Figure 2

Energy-gated $\gamma$-ray time distributions and half-lives of known isomers in the ${}^{100}\mathrm{Sn}$ region, having $T_{1/2}<10\mu \mathrm{s}$. The full fit functions (solid red line) contain the signal (solid black line) and the background (dashed blue line) components.

Figure 3

Comparisons between experimental and theoretical transition strengths listed in Table 1, where the SLGM interaction, and effective charge sets (a) and (b) are described in Sec. 3a. For the calculated values labeled as “Other,” see the footnotes in Table 1.

Figure 4

$\gamma$-ray energy spectrum between 300 and 1200 ns after ${}^{92}\mathrm{Rh}$ implantation. The inset shows the time distribution of the 55.3(3)-keV $\gamma$ ray (background component as a dashed blue line) and the corresponding $T_{1/2}$.

Figure 5

Experimental and theoretical level schemes of low-energy states in ${}^{92}\mathrm{Rh}$. $\gamma$-ray transitions are labeled with their theoretical $B\left(E2\right)$ values in Weisskopf units, which were calculated with two sets of effective charges: ($e_p=1.5e,e_n=0.5e$) and ($e_p=1.72e,e_n=1.44e$), respectively.

Figure 6

$\gamma$-ray energy spectrum of ${}^{96}\mathrm{Ag}$ for $500<T_{\gamma }\left(\text{ns}\right)<6500$ after implantation. The energy gates for the $T_{1/2}$ analysis are shown as green (total) and blue (background) histogram bins. Dashed red, $\gamma$-ray coincidence projection gated by the 667-keV transition from the $\left({13}^{+}\right)$ state in ${}^{96}\mathrm{Ag}$, whose counts were multiplied by 15 for comparison. The inset shows a $\gamma$-ray time spectrum of the 44-keV peak and the deduced $T_{1/2}$ value, which is consistent with both 1.543(28) $\mu \mathrm{s}$ [47] and 1.57(2) $\mu \mathrm{s}$ measured in this work.

Figure 7

Black histogram, prompt $\gamma$-ray spectrum of ${}^{98}\mathrm{Ag}$, generated from the $\beta$-decay of ${}^{98}\mathrm{Cd}$. The counts were scaled down to 1/5 of the original values for comparison. Red histogram, time-delayed $\gamma$-ray spectrum from the same $\beta$-decay data. The inset shows a partial level scheme of ${}^{98}\mathrm{Ag}$ suggested previously in Refs. [51, 52], which agree with the results of this work.

Figure 8

Open squares, $\gamma$-ray time difference distribution of 198 keV (start) and 688/1395 keV (stop), which features only a Gaussian time jitter of the TDC; filled squares, $\gamma$-ray time difference distribution of 147 keV (start) and 198/688/1395 keV (stop), which exhibits an exponential decay component. The half-life of the $\left(6^{+}\right)$ state in ${}^{98}\mathrm{Cd}$ was determined to be 13(2) ns from the decay curve analysis.

Figure 9

Comparisons between experimental and theoretical isomeric ratios of nuclei in the ${}^{100}\mathrm{Sn}$ region. The theoretical isomeric ratios used in this plot were determined from the sharp cutoff model with $\nu =0.5$.

Figure 10

Upper limits on the half-life of a hypothetical $E2$ isomer in ${}^{100}\mathrm{Sn}$ as a function of $\gamma$-ray energy and three different isomeric ratios. The green band displays the relationship between $T_{1/2}$ and $E_{\gamma }$ for $B\left(E2\right)=0.3-2.0$ W.u. Conservative limits of $E_{\gamma }>125$ keV and $T_{1/2}<210$ ns are deduced for ${}^{100}\mathrm{Sn}$'s isomer, assuming $R=12.5\%$.