Sub-Barrier Coulomb Excitation of ${}^{110}\mathrm{Sn}$ and Its Implications for the ${}^{100}\mathrm{Sn}$ Shell Closure

The first excited $2^{+}$ state of the unstable isotope ${}^{110}\mathrm{Sn}$ has been studied in safe Coulomb excitation at $2.82\mathrm{MeV}/u$ using the MINIBALL array at the REX-ISOLDE post accelerator at CERN. This is the first measurement of the reduced transition probability of this state using this method for a neutron deficient Sn isotope. The strength of the approach lies in the excellent peak-to-background ratio that is achieved. The extracted reduced transition probability, $B(E2:0^{+}\to 2^{+})=0.220\pm 0.022e^2{b}^2$, strengthens the observation of the evolution of the $B(E2)$ values of neutron deficient Sn isotopes that was observed recently in intermediate-energy Coulomb excitation of ${}^{108}\mathrm{Sn}$. It implies that the trend of these reduced transition probabilities in the even-even Sn isotopes is not symmetric with respect to the midshell mass number $A=116$ as ${}^{100}\mathrm{Sn}$ is approached.

Figure 1

Scattered beam and target particles as detected in the DSSSD. The upper branch corresponds to scattered ${}^{58}\mathrm{Ni}$ and the lower branch to ${}^{110}\mathrm{Sn}$ particles, respectively. The kinematical cuts used for the identification of beam and target particles are also indicated in the figure.

Figure 2

Single and particle-$\gamma$ coincindence $\gamma$-ray spectra before Doppler correction (top panels). Doppler-corrected $\gamma$-ray spectra for 2-particle $\gamma$-ray coincident events (central panel) and the corresponding Doppler-corrected $\gamma$-ray spectra for the sum of 2-particle and 1-particle reconstructed events for ${}^{110}\mathrm{Sn}$ and ${}^{58}\mathrm{Ni}$ (bottom panel). See text for detailed discussion.

Figure 3

Current status of measured $B(E2)$ values for the first $2^{+}$ state in even-even Sn isotopes. Note the shift in $B(E2)$ in ${}^{114}\mathrm{Sn}$ as the $g_{7/2}$ and $d_{5/2}$ orbits start to dominate the configuration. The ${\chi }^2$, taken per degree of freedom, for the deviation between the experimental values and the theoretical predications for the mass number sequences $A_1=\{114,112,110,108\}$, $A_2=\{114,112,108\}$, and $A_3=\{114,112,110\}$ is ${\chi }_1^2=1.6$, ${\chi }_2^2=1.7$, and ${\chi }_3^2=1.9$ for the ${}^{90}\mathrm{Zr}$ core. The corresponding values for the ${}^{100}\mathrm{Sn}$ core is ${\chi }_1^2=3.3$, ${\chi }_2^2=4.2$, and ${\chi }_3^2=4.4$, respectively. Consequently, due to the rather small error the current measurement is statistically a more significant test of the deviation from theory than the previous measurement of ${}^{108}\mathrm{Sn}$.