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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 

Abstract The electricE1 and magneticM1 dipole responses of the$$N=Z$$ $N=Z$nucleus$$^{24}$$ ${}^{24}$Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the$$^{24}$$ ${}^{24}$Mg($$\gamma ,\gamma ^{\prime }$$ $\gamma ,{\gamma }^{\prime }$) reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one$$J^{\pi }=1^-$$ $J^{\pi }=1^{-}$, four$$J^{\pi }=1^+$$ $J^{\pi }=1^{+}$, and six$$J^{\pi }=2^+$$ $J^{\pi }=2^{+}$states in$$^{24}$$ ${}^{24}$Mg. De-excitation$$\gamma $$ $\gamma$rays were detected using the four high-purity germanium detectors of the$$\gamma $$ $\gamma$ELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total$$B(M1)\uparrow = 2.7(3)~\mu _N^2$$ $B\left(M1\right)\uparrow =2.7\left(3\right){\mu }_N^2$is observed, but this$$N=Z$$ $N=Z$nucleus exhibits only marginalE1 strength of less than$$\sum B(E1)\uparrow \le 0.61 \times 10^{-3}$$ $\sum B\left(E1\right)\uparrow \le 0.61\times {10}^{-3}$ e$$^2 \, $$ ${}^2$fm$$^2$$ ${}^2$. The$$B(\varPi 1, 1^{\pi }_i \rightarrow 2^+_1)/B(\varPi 1, 1^{\pi }_i \rightarrow 0^+_{gs})$$ $B(\Pi 1,1_i^{\pi }\to 2_1^{+})/B(\Pi 1,1_i^{\pi }\to 0_{\mathrm{gs}}^{+})$branching ratios in combination with the expected results from the Alaga rules demonstrate thatKis a good approximative quantum number for$$^{24}$$ ${}^{24}$Mg. The use of the known$$\rho ^2(E0, 0^+_2 \rightarrow 0^+_{gs})$$ ${\rho }^2(E0,0_2^{+}\to 0_{\mathrm{gs}}^{+})$strength and the measured$$B(M1, 1^+ \rightarrow 0^+_2)/B(M1, 1^+ \rightarrow 0^+_{gs})$$ $B(M1,1^{+}\to 0_2^{+})/B(M1,1^{+}\to 0_{\mathrm{gs}}^{+})$branching ratio of the 10.712 MeV$$1^+$$ $1^{+}$level allows, in a two-state mixing model, an extraction of the difference$$\varDelta \beta _2^2$$ $\Delta {\beta }_2^2$between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV$$0^+_2$$ $0_2^{+}$level. 

Gamma-ray detection following the inelastic neutron scattering reaction on isotopically enriched material was used to study the nuclear structure of 74 Ge. From these measurements, low-lying, low-spin excited states were characterized, new states and their decays were identified, level lifetimes were measured with the Doppler-shift attenuation method (DSAM), multipole mixing ratios were established, and transition probabilities were determined. New structural features in 74 Ge were identified, and the reanalysis of older 76 Ge data led to the placement of the 2 + member of the intruder band. In addition, a number of previously placed states in 74 Ge were shown not to exist. A procedure for future work, which will lead to meaningful data for constraining calculations of the neutrinoless double-beta decay matrix element, is suggested.