Revised $B(E2; 2^{+}_{1} \rightarrow 0^{+}_{1})$ value in the semi-magic nucleus $^{210}$Pb
The lifetime of the $2^+_1$ state of $^{210}$Pb was measured in the $^{208}$Pb($^{18}$O, $^{16}$O)$^{210}$Pb two-neutron transfer reaction by $γ$-ray spectroscopy employing the recoil-distance Doppler-shift method. The extracted absolute $B(E2)$$\downarrow$ value of ${119\;^{+\;9}_{-\;8}\;\hspace{-0pt}\,\text{e}^2\text{fm}^4}$ is consistent with previously reported measurements, but with significantly improved precision. The available experimental data for the $2^+_1$-$4^+_1$-$6^+_1$-$8^+_1$ multiplet are compared with shell-model calculations based on the well-established Kuo-Herling interaction. The new $B(E2)$$\downarrow$ value agrees well with the shell-model prediction, providing evidence that the properties of the $2^+_1$ and $8^+_1$ states of $^{210}$Pb can be consistently described together within the nuclear shell-model framework.