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Description
The long isotopic chains with $Z$ around 50 serve as good testing grounds for nuclear models studying the evolution of shell structure and interplay between pairing and quadruple correlations. The Cd isotopes have only two proton holes below the Z = 50 shell, being expected to show similar features with Sn nuclei except for the larger collectivity. The comparison of B($E2;2^+_1 \rightarrow 0^{+}_{g.s.}$) values between Sn ($\times$ 1.9) and Cd isotopic chains display quite similar trends in the neutron-deficient side. However, on the neutron-rich side, an unexpected bump is observed for Cd isotopes [see Fig. 1 in Phys. Rev. C 104, 034320 (2021) ]. Recently, large-scale-shell-model calculation performed by A. P. Zuker in Phys. Rev. C 103, 024322 (2021) suggest that the inclusion of N $ = $ 82 core excitation is essential to explain the bump of B($E2;2^+_1 \rightarrow 0^{+}_{g.s.}$) for Cd isotopes when increasing neutron number from 64. Meanwhile, the prediction power decrease quickly beyond $^{120}$Cd~(N$=72$), demanding a carefully modification of the interplay between pairing and quadruple interaction which is more sensitive to B($E2;4^+_1 \rightarrow 2^{+}_1$) values.
The experimental information on lifetime are available only with large uncertainties for the 2$^+$ states and still missing for the 4$^+$ states in Cd isotopes with N $>72$. It should be notices that, even though with a large error bar, an anomalous sharp decrease ($<$1) in the B$_{4^ +/2^+}$ ratio is also observed at $^{120}$Cd. In order to investigate the evolution of collectivity and the anomalous B$_{4^ +/2^+}$ ratio in the neutron-rich Cd isotopes, the current proposal aims at precisely measuring the lifetimes for the first 2$^+$ and 4$^+$ states in $^{120-126}$Cd. A multi-nucleon transfer reaction of a $^{124}$Sn beam at 900 MeV on a $^{198}$Pt target is proposed: the projectile-like fragments and the emitted $\gamma$ rays will be detected by PRISMA and AGATA spectrometers, respectively, and a dedicated plunger will be used for the lifetime measurements.