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.

Nuclear level density is important for evaluating nuclear reaction processes, but its microscopic investigation is not frequently performed. The present work applies a recently developed shell-model-based method to estimate the level density of fission products ${}^{133–137}\mathrm{Xe}$ and ${}^{135–138}\mathrm{Ba}$. The monopole-based universal interaction, $V_{\text{MU}}$, and the M3Y type spin-orbit interaction are combined to construct the shell-model Hamiltonian. The model space is truncated based on the binding energy of each configuration, estimated from the monopole interaction. The calculated level densities of ${}^{133–137}\mathrm{Xe}$ and ${}^{135–138}\mathrm{Ba}$ are in good agreement with available experimental data. The effects of spin-orbit and tensor forces on the nuclear level density and the shell effects in the spin distribution are discussed.

Isomer spectroscopy of heavy neutron-rich nuclei beyond the $N=126$ closed shell has been performed for the first time at the Radioactive Isotope Beam Factory of the RIKEN Nishina Center. New millisecond isomers have been identified at low excitation energies, 985.3(19) keV in ${}^{213}\mathrm{Tl}$ and 874(5) keV in ${}^{215}\mathrm{Tl}$. The measured half-lives of 1.34(5) ms in ${}^{213}\mathrm{Tl}$ and 3.0(3) ms in ${}^{215}\mathrm{Tl}$ suggest spins and parities $11/2^{-}$ with the single proton-hole configuration $\pi h_{11/2}$ as leading component. They are populated via $E1$ transitions by the decay of higher-lying isomeric states with proposed spin and parity $17/2^{+}$, interpreted as arising from a single $\pi s_{1/2}$ proton hole coupled to the $8^{+}$ seniority isomer in the ${}^{A+1}\mathrm{Pb}$ cores. The lowering of the $11/2^{-}$ states is ascribed to an increase of the $\pi h_{11/2}$ proton effective single-particle energy as the second $\nu g_{9/2}$ orbital is filled by neutrons, owing to a significant reduction of the proton-neutron monopole interaction between the $\pi h_{11/2}$ and $\nu g_{9/2}$ orbitals. The new $ms$ isomers provide the first experimental observation of shell evolution in the almost unexplored $N>126$ nuclear region below doubly magic ${}^{208}\mathrm{Pb}$.

The isomeric structure and properties in proton-rich nuclides are crucial for determining the path of the rapid proton capture process ($rp$-process). For example, bound nuclei inside the dripline can have unbound isomeric states and change the $rp$-process pathway. The configuration interaction shell model is used to investigate nuclei around the $Z=N$ line at the southwest region of ${}^{100}\mathrm{Sn}$. The excitation mechanism of $1/2_1^{-}$ isomers is identified as dominated by exciting one nucleon in the $1p_{1/2}$ orbit to the $0g_{9/2}$ orbit. The study explores the decay properties of both the ground and isomeric states. Remarkably, competitive ${\beta }^{+}$ decay and proton emission are predicted in the unbound $1/2_1^{-}$ isomer of ${}^{97}\mathrm{Sn}$, suggesting potential influences on the $rp$-process pathway.

Delayed γ-ray spectroscopy was performed for evaporation residues produced in the ^{58}Ni+^{96}Ru reaction. A new isomer in _{ 70}^{150}Yb (Z=70, N=80) with a half-life of 0.62(5) μs was identified at an excitation energy of 2872(2) keV. Its spin-parity is assigned as (10^{+}) and a decay scheme is proposed based on a strong analogy with that of the isotonic _{ 68}^{148}Er. Previously, the 10^{+} isomers were observed in the N=80 even-Z isotones from the neutron-rich _{ 46}^{126}Pd to the neutron-deficient _{ 68}^{148}Er. For the first time, by combining experimental data and comprehensive large-scale shell-model calculations, we clearly identify the configurations of these isomers and demonstrate that they all exhibit seniority structures. These findings firmly establish a configuration change in the 10^{+} isomeric chain, from a pair of maximally aligned 1h_{11/2} neutrons (holes) to a pair of maximally aligned 1h_{11/2} protons around the Z=64 subshell closure. This transition serves as a unique isomeric relay underpinning the persistence of the isomeric chain.