Lifetime measurement of the first excited $2^{+}$ state in ${}^{108}$Te

The lifetime of the first excited $2^{+}$ state in the neutron deficient nuclide ${}^{108}$Te has been measured for the first time, using a combined recoil decay tagging and recoil distance Doppler shift technique. The deduced reduced transition probability is $B(E2;0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2^{+})=0.{39}_{-0.04}^{+0.05}{e}^2{\mathrm{b}}^2$. Compared to previous experimental data on neutron deficient tellurium isotopes, the new data point constitutes a large step (six neutrons) toward the $N=50$ shell closure. In contrast to what has earlier been reported for the light tin isotopes, our result for tellurium does not show any enhanced transition probability with respect to the theoretical predictions and the tellurium systematics including the new data is successfully reproduced by state-of-the-art shell model calculations.

Figure 1

Gamma-ray energy spectra from ten JUROGAM II detectors at the angle $\theta ={134}^{\circ }$ showing the $2^{+}\to 0^{+}$ and $4^{+}\to 2^{+}$ ${}^{108}\mathrm{Te}$ transitions at 625 keV and 664 keV, respectively (dashed lines). As the target-to-degrader distance, $d$, increases, the peaks shift from the positions corresponding to the lower velocity after the degrader to the position corresponding to the higher velocity before the degrader. The spectra shown are Doppler corrected for this higher velocity.

Figure 2

Relative intensities, $Q\left(d\right)$, for the $2^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ (blue circles) and $4^{+}\to 2^{+}$ (red squares) $\gamma$-ray transitions in ${}^{108}\mathrm{Te}$. Inset: The lifetime is deduced according to Ref. [17] for three distances (185 $\mu$m, 284 $\mu$m, 378 $\mu$m) in the region where the slope of the $2^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ curve is well defined. The error bars reflect statistical uncertainties of $Q$. The uncertainty in $d$ is below 1 $\mu$m for all data points, except at 957(19) $\mu$m.

Figure 3

Upper panel: Experimental $B\left(E2\right)$ values for Te isotopes (solid circles), together with the new $B\left(E2\right)$ data point for ${}^{108}\mathrm{Te}$ (open circle). The data are compared to the shell model calculation with ${\varepsilon }_{sp}$ values according to Ref. [1] (SM${}^a$, dashed line) and with the $d_{5/2},g_{7/2}$ orbitals inverted, see text (SM${}^b$, solid line). The effective charges used were $e_{\mathrm{eff}}^{\nu }=0.8e$, $e_{\mathrm{eff}}^{\pi }=1.5e$. For the midshell (small solid squares), the model space ($g_{7/2},d,s,h_{11/2}$) was limited, allowing excitations of up to four neutrons above the Fermi level in the $h_{11/2}$ subshell. This leads to the underestimation in the model predictions visible around midshell.