$0_{\mathrm{gs}}^{+}\to 2_1^{+}$ Transition Strengths in ${}^{106}\mathrm{Sn}$ and ${}^{108}\mathrm{Sn}$

The reduced transition probabilities, $B(E2;0_{\mathrm{gs}}^{+}\to 2_1^{+})$, have been measured in the radioactive isotopes ${}^{108,106}\mathrm{Sn}$ using subbarrier Coulomb excitation at the REX-ISOLDE facility at CERN. Deexcitation $\gamma$ rays were detected by the highly segmented MINIBALL Ge-detector array. The results, $B(E2;0_{\mathrm{gs}}^{+}\to 2_1^{+})=0.222(19)e^2{b}^2$ for ${}^{108}\mathrm{Sn}$ and $B(E2;0_{\mathrm{gs}}^{+}\to 2_1^{+})=0.195(39)e^2{b}^2$ for ${}^{106}\mathrm{Sn}$ were determined relative to a stable ${}^{58}\mathrm{Ni}$ target. The resulting $B(E2)$ values are $\sim 30\%$ larger than shell-model predictions and deviate from the generalized seniority model. This experimental result may point towards a weakening of the $N=Z=50$ shell closure.

Figure 1

Energy and angle of the scattered beam and target particles as detected by the DSSSD. The kinematic cuts used to distinguish between ejectiles and recoils have been applied to the data. The corresponding plot for the ${}^{106}\mathrm{Sn}$ case is similar.

Figure 2

$2\mathrm{p}+1\mathrm{p}$ Doppler corrected $\gamma$-ray spectra from the ${}^{108}\mathrm{Sn}$ and ${}^{106}\mathrm{Sn}$ experiments. The peak indicated by ▪ comes from two closely located ${}^{108}\mathrm{In}$ decay $\gamma$ rays that merge due to Doppler correction. The $\gamma$ ray marked with ● is the deexcitation from the $8^{+}$ state at 1118 keV to the $7^{+}$ ground state in ${}^{106}\mathrm{In}$ [24]. Similarly the $\gamma$ ray marked with ○ is the deexcitation from the $9^{+}$ state at 1307 keV to the ground state in the same nucleus.

Figure 3

Left panel: Experimental and theoretical $B(E2)$ values. The dashed curve represents the result from a shell-model calculation using ${}^{100}\mathrm{Sn}$ as core and a $\nu (g_{7/2},d,s,h_{11/2})$ model space with a neutron effective charge $e_{\mathrm{eff}}^{\nu }=1.0e$. The solid line corresponds to using ${}^{90}\mathrm{Zr}$ as core and a $\pi (g,d,s)-\nu (g_{7/2},d,s,h_{11/2})$ model space with $e_{\mathrm{eff}}^{\nu }=0.5e$. Right panel: Enlarged version of the left panel. Only experimental results fulfilling the safe condition are shown in the two panels.

Figure 4

Theoretical $B(E2)$ values given in $e^2{b}^2$ for the even-mass Sn isotopes. The first two calculations are identical to Fig. 3. The ${}^{90}\mathrm{Zr}$ core calculation was seniority truncated and based on a monopole corrected CD-Bonn interaction [2]. The remaining calculations are based either on the N3LO interaction or a more recent CD-Bonn interaction. The number of excitations allowed in the perturbative scheme is here $5\hslash \omega$. Whether the interaction incorporated charge symmetry breaking (CSB) and charge independence breaking (CIB) is indicated in the legend.