Half-lives of neutron-rich ${}^{128–130}\mathrm{Cd}$

The $\beta$-decay half-lives of ${}^{128–130}\mathrm{Cd}$ have been measured with the newly commissioned GRIFFIN $\gamma$-ray spectrometer at the TRIUMF-ISAC facility. The time structures of the most intense $\gamma$ rays emitted following the $\beta$ decay were used to determine the half-lives of ${}^{128}\mathrm{Cd}$ and ${}^{130}\mathrm{Cd}$ to be $T_{1/2}=246.2\left(21\right)$ ms and $T_{1/2}=126\left(4\right)$ ms, respectively. The half-lives of the $3/2^{+}$ and $11/2^{-}$ states of ${}^{129}\mathrm{Cd}$ were measured to be $T_{1/2}(3/2^{+})=157\left(8\right)$ ms and $T_{1/2}(11/2^{-})=147\left(3\right)$ ms. The half-lives of the Cd isotopes around the $N=82$ shell closure are an important ingredient in astrophysical simulations to derive the magnitude of the second $r$-process abundance peak in the $A\sim 130$ region. Our new results are compared with recent literature values and theoretical calculations.

Figure 1

Activity of the 857 keV $\gamma$-ray photopeak in ${}^{128}\mathrm{In}$. The half-life of ${}^{128}\mathrm{Cd}$ from this transition is determined to be 245.8 (21) ms. The inset shows the gate on the 857 keV $\gamma$ ray as well as the strong 831.5 keV $\gamma$ ray following the $\beta$ decay of ${}^{128}\mathrm{In}$. Note that the time represents the amount of time that has elapsed since the start of a cycle. Background data were collected for 1000 ms before the beam was turned on. The beam was turned off at 11.5 s.

Figure 2

A portion of the $\beta$-gated $\gamma$-ray energy spectrum for the ${}^{129}\mathrm{Cd}$ experiment. The strongest peaks in the spectrum are labeled. $\gamma$ rays emitted following the $\beta$ decay of ${}^{129}\mathrm{Sn}$ are labeled with * and $\gamma$ rays following the $\beta$ decay of ${}^{128}\mathrm{Sn}$ are labeled with &.

Figure 3

A portion of the ${}^{129}\mathrm{Cd}$ decay scheme (adapted from Ref. [18]) that shows the transitions relevant to the measurement of the half-life (see text for details). The $\gamma$ rays that were used in the half-life analysis are shown in red. Note that the ordering of the ground state and isomeric state in ${}^{129}\mathrm{Cd}$ is unknown; in this context “$x$” can be $<0$ keV.

Figure 4

(a) Fitted activity of the $11/2^{-}$ state using the 358.9, 1796.5, and 2155.6 keV $\gamma$ rays. (b) Fitted activity of the $3/2^{+}$ state using the 1422.9 and 1586.2 keV $\gamma$ rays. Note that the time represents the amount of time that has elapsed since the start of a cycle.

Figure 5

A portion of the $\beta$-gated $\gamma$-ray energy spectrum for the ${}^{130}\mathrm{Cd}$ experiment. The strongest peaks in the spectrum are labeled, including the doublet at 951 keV. The three strong $\gamma$ rays at 451, 1170, and 1669 keV were used for the half-life analysis. $\gamma$ rays following the $\beta$ decay of ${}^{130}\mathrm{In}$ are labeled with *.

Figure 6

Sum of the 451, 1170, and 1669 keV $\gamma$-ray time distributions. The half-life obtained from the fit is 126 (4) ms. Note that the time represents the amount of time that has elapsed since the start of a cycle.

Figure 7

Comparison between the calculated half-lives using the $\text{DF}3+\text{CQRPA}$ [34] and $\text{RHB}+\text{RQRPA}$ [35] models to the measured half-lives of ${}^{128}\mathrm{Cd},{}^{129}\mathrm{Cd}$, and ${}^{130}\mathrm{Cd}$. The measured half-lives in this work are in good agreement with Ref. [12, 18] but do not agree with the previous measurements of Refs. [11, 14, 15, 16, 31]. Some error bars are not visible in the plot because they are smaller than the data points. Ha01: [11], Lo15: [12], Fo88: [14], Ar09: [16], Ta15 [18], Kr86 [19].