Background: The properties of nuclei located in the region “south” of ${}^{208}\mathrm{Pb}$ are important for understanding the $r$-process nucleosynthesis. While some isomeric states and their spectroscopic properties have been investigated experimentally in neutron-rich Pb, Tl, and Hg isotopes recently, a large portion of the area still remains unreachable.

The $\beta$ decay of ${}^{207}\mathrm{Hg}$ into the single-proton-hole nucleus ${}^{207}\mathrm{Tl}$ has been studied through $\gamma$-ray spectroscopy at the ISOLDE Decay Station (IDS) with the aim of identifying states resulting from coupling of the $\pi s_{1/2}^{-1}$, $\pi d_{3/2}^{-1}$, and $\pi h_{11/2}^{-1}$ shell model orbitals to the collective octupole vibration. Twenty-two states were observed lying between 2.6 and 4.0 MeV, eleven of which were observed for the first time, and 78 new transitions were placed. Two octupole states ($s_{1/2}$-coupled) are identified and three more states ($d_{3/2}$-coupled) are tentatively assigned using spin-parity inferences, while further $h_{11/2}$-coupled states may also have been observed for the first time. Comparisons are made with state-of-the-art large-scale shell model calculations and previous observations made in this region, and systematic underestimation of the energy of the octupole vibrational states is noted. We suggest that in order to resolve the difference in predicted energies for collective and noncollective $t=1$ states ($t$ is the number of nucleons breaking the ${}^{208}\mathrm{Pb}$ core), the effect of $t=2$ mixing may be reduced for octupole-coupled states. The inclusion of mixing with $t=0,2,3$ excitations is necessary to replicate all $t=1$ state energies accurately.

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 − ⊗ 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, Pb 208 remains a puzzle for our understanding of nuclear structure.

The $\beta$ decay of ${}^{208}\mathrm{Hg}$ into the one-proton hole, one neutron-particle ${{}_{81}{}^{208}\mathrm{Tl}}_{127}$ nucleus was investigated at CERN-ISOLDE. Shell-model calculations describe well the level scheme deduced, validating the proton-neutron interactions used, with implications for the whole of the $N>126$, $Z<82$ quadrant of neutron-rich nuclei. While both negative and positive parity states with spin 0 and 1 are expected within the $Q_{\beta }$ window, only three negative parity states are populated directly in the $\beta$ decay. The data provide a unique test of the competition between allowed Gamow-Teller and Fermi, and first-forbidden $\beta$ decays, essential for the understanding of the nucleosynthesis of heavy nuclei in the rapid neutron capture process. Furthermore, the observation of the parity changing $0^{+}\to 0^{-}\beta$ decay where the daughter state is core excited is unique, and can provide information on mesonic corrections of effective operators.

The nuclear two-photon or double-gamma ($2\gamma$) decay is a second-order electromagnetic process whereby a nucleus in an excited state emits two gamma rays simultaneously. To be able to directly measure the $2\gamma$ decay rate in the low-energy regime below the electron-positron pair-creation threshold, we combined the isochronous mode of a storage ring with Schottky resonant cavities. The newly developed technique can be applied to isomers with excitation energies down to $\sim 100\mathrm{keV}$ and half-lives as short as $\sim 10\mathrm{ms}$. The half-life for the $2\gamma$ decay of the first-excited $0^{+}$ state in bare ${}^{72}\mathrm{Ge}$ ions was determined to be 23.9(6) ms, which strongly deviates from expectations.