Revised $B(E2;2_1^{+}\to 0_1^{+})$ 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 $\gamma$-ray spectroscopy employing the recoil-distance Doppler-shift method. The extracted absolute $B(E2)$$\downarrow$ value of $119{}_{-8}^{+9}{\text{e}}^2{\text{fm}}^4$ is consistent with previously reported measurements, but with significantly improved precision. The available experimental data for the $2_1^{+}$-$4_1^{+}$-$6_1^{+}$-$8_1^{+}$ multiplet are compared with shell-model calculations based on the well-established Kuo-Herling interaction. The new $B(E2)$$\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.