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The recent discovery and spectroscopic measurements of ${}^{27}\mathrm{O}$and ${}^{28}\mathrm{O}$suggests the disappearance of the $N=20$shell structure in these neutron-rich oxygen isotopes. We measured one- and two-proton removal cross sections from ${}^{27}\mathrm{F}$and ${}^{29}\mathrm{Ne}$, respectively, extracting spectroscopic factors and comparing them to shell model overlap functions coupled with eikonal reaction model calculations. The invariant mass technique was used to reconstruct the two-body ( ${}^{24}\mathrm{O}+n$) and three-body ( ${}^{24}\mathrm{O}+2n$) decay energies from knockout reactions of ${}^{27}\mathrm{F}$(106.2 MeV/u) and ${}^{29}\mathrm{Ne}$(112.8 MeV/u) beams impinging on a ${}^9\mathrm{Be}$target. The one-proton removal from ${}^{27}\mathrm{F}$strongly populated the ground state of ${}^{26}\mathrm{O}$and the extracted cross section of $3.4_{-1.5}^{+0.3}$mb agrees with eikonal model calculations that are normalized by the shell model spectroscopic factors and account for the systematic reduction factor observed for single nucleon removal reactions within the models used. For the two-proton removal reaction from ${}^{29}\mathrm{Ne}$an upper limit of 0.08 mb was extracted for populating states in ${}^{27}\mathrm{O}$decaying though the ground state of ${}^{26}\mathrm{O}$. The measured upper limit for the population of the ground state of ${}^{26}\mathrm{O}$in the two-proton removal reaction from ${}^{29}\mathrm{Ne}$indicates a significant difference in the underlying nuclear structure of ${}^{27}\mathrm{F}$and ${}^{29}\mathrm{Ne}$. Published by the American Physical Society2024 

Lead-208 is the heaviest known doubly magic nucleus and its structure is therefore of special interest. Despite this magicity, which acts to provide a strong restorative force toward sphericity, it is known to exhibit both strong octupole correlations and some of the strongest quadrupole collectivity observed in doubly magic systems. In this Letter, we employ state-of-the-art experimental equipment to conclusively demonstrate, through four Coulomb-excitation measurements, the presence of a large, negative, spectroscopic quadrupole moment for both the vibrational octupole $3_1^{-}$and quadrupole $2_1^{+}$state, indicative of a preference for prolate deformation of the states. The observed quadrupole moment is discussed in the context of the expected splitting of the $3^{-}\otimes 3^{-}$two-phonon states, due to the coupling of the quadrupole and octupole motion. These results are compared with theoretical values from three different methods, which are unable to reproduce both the sign and magnitude of this deformation. Thus, in spite of its well-studied nature, ${}^{208}\mathrm{Pb}$remains a puzzle for our understanding of nuclear structure. Published by the American Physical Society2025