Revised $B(E2; 2^{+}_{1} ightarrow 0^{+}_{1})$ 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.

💡 Research Summary

The paper presents a high‑precision measurement of the lifetime of the first excited 2⁺ state in the semi‑magic nucleus ²¹⁰Pb, using the recoil‑distance Doppler‑shift (RDDS) technique applied to the two‑neutron transfer reaction ²⁰⁸Pb(¹⁸O,¹⁶O)²¹⁰Pb. An 85 MeV ¹⁸O beam from a 10 MV Tandem accelerator was incident on a 0.8 mg/cm² ²⁰⁸Pb target, and a plunger device varied the target‑to‑stopper distance from 13 µm to 912 µm in eleven steps. Eleven HPGe detectors recorded γ‑rays at forward (45°) and backward (142°) angles. The key transition 2₁⁺→0₁⁺ (≈ 788 keV) was analyzed by separating the Doppler‑shifted (in‑flight) and unshifted (stopped) components.

Significant spectral contamination arose from the 2₁⁺→0₁⁺ transition of ²⁰⁶Pb and the 3₁⁺→2₁⁺ transition of ³⁶Cl, both overlapping the ²¹⁰Pb peak. The authors used particle‑gated and ungated spectra to quantify these contaminants: the known lifetime of ²⁰⁶Pb (11.8 ps) allowed an effective lifetime model for its contribution, while the ³⁶Cl line was characterized in the ungated spectra and fixed during fitting. Feeding from the 4₁⁺→2₁⁺ transition was corrected by subtracting its intensity from the unshifted component; other side‑feeding was deemed negligible.

The differential decay‑curve method (DDCM) was then applied to the distance‑dependent intensity ratios of shifted and unshifted components, yielding a distance‑by‑distance lifetime. A χ² fit to all distances gave a mean lifetime τ = 0.84 ± 0.07 ps. Converting this lifetime to a reduced transition probability using standard formulas resulted in B(E2; 2₁⁺→0₁⁺) = 119 +9/‑8 e² fm⁴. This value agrees within 1σ with the Kuo‑Herling interaction shell‑model prediction (≈ 109 e² fm⁴) and improves the precision over earlier measurements (105 ± 30 e² fm⁴).

The agreement confirms that the 2₁⁺ and 8₁⁺ states of ²¹⁰Pb can be described consistently within a single‑j (ν = 2) seniority scheme, supporting the validity of the shell‑model description for semi‑magic nuclei with two valence particles. The result also provides a reliable benchmark for effective charges and interaction parameters needed in the description of neighboring nuclei such as ²¹²Po, where previous B(E2) values showed significant discrepancies. Methodologically, the work demonstrates that the combination of RDDS and DDCM, together with careful contaminant handling, yields sub‑10 % uncertainties for picosecond‑scale lifetimes, offering a powerful tool for future high‑precision nuclear structure investigations.