Revised $B(E2; 2^{+}_{1} \rightarrow 0^{+}_{1})$ value in the semi-magic nucleus $^{210}$Pb

TL;DR

This study precisely measured the $B(E2)$ value for the first excited state in $^{210}$Pb using gamma-ray spectroscopy, confirming shell-model predictions and enhancing understanding of semi-magic nuclei.

Contribution

The paper provides a more precise $B(E2)$ measurement for $^{210}$Pb's $2^+_1$ state and compares it with shell-model calculations, supporting a consistent nuclear structure description.

Findings

The new $B(E2)$ value is consistent with previous data but more precise.

Shell-model calculations agree well with the experimental data.

The results support the shell-model's applicability to semi-magic nuclei.

Abstract

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)$$\downarrow$ value of ${119\;^{+\;9}_{-\;8}\;\hspace{-0pt}\,\text{e}^2\text{fm}^4}$ is consistent with previously reported measurements, but with significantly improved precision. The available experimental data for the $2^+_1$-$4^+_1$-$6^+_1$-$8^+_1$ multiplet are compared with shell-model calculations based on the well-established Kuo-Herling interaction. The new $B(E2)$$\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.