21+→01+transition strengths in Sn nuclei

Abstract

The lifetime of the ${2}_{1}^{+}$ state at 1256.7 keV in $^{112}\mathrm{Sn}$ has been determined using the ($n$,${n}^{'}\ensuremath{\gamma}$) reaction. Angular distribution measurements were carried out at a neutron energy of 1.7 MeV, above the ${2}_{1}^{+}$ energy threshold and below that of the second excited level. Through the Doppler-shift attenuation method, the lifetime of the ${2}_{1}^{+}$ state is determined as ${750}_{\ensuremath{-}90}^{+125}$ fs, which gives a $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ value of ${10.9}_{\ensuremath{-}1.6}^{+1.5}$ W.u. This $E2$ strength in $^{112}\mathrm{Sn}$ also allows a redetermination of the $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ in $^{108}\mathrm{Sn}$ as 10.8(3.0) W.u. These values result in a symmetric trend around the neutron midshell in the systematics of $E2$ strengths in the even-mass tin isotopes and do not support $N=64$ or $N=66$ subshell gaps. The symmetric trend is in agreement with recent shell model predictions, where proton-core excitations were allowed in the calculations.