Shell-model study on spectroscopic properties in the region “south” of Pb208

Abstract

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.Purpose: We aim to study the properties of nuclei in the region south of $^{208}\mathrm{Pb}$, including the binding and excitation energies and electromagnetic properties, in order to predict unknown properties of these nuclei, such as isomerism, utilizing a theoretical model which describes the experimentally known properties precisely. We also address whether the $N=126$ shell closure is robust or not when the proton number decreases from $^{208}\mathrm{Pb}$.Methods: We performed large-scale shell-model calculations with a new Hamiltonian suggested in the present work. The model space is taken as the 5 proton orbits within $50<Z\ensuremath{\leqslant}82$ and the 13 neutron orbits within $82<N\ensuremath{\leqslant}184$, and one-particle-one-hole excitation is allowed across the $N=126$ gap. The Hamiltonian is constructed by combining the existing Hamiltonians, KHHE (with adjustment of its proton-proton part) and KHPE, and the monopole-based universal interaction.Results: The shell-model results well reproduce the experimentally observed binding energies and spectroscopic properties, such as isomerism, core excitation, and electromagnetic properties. Some possible isomeric states in neutron-rich Pb, Tl, and Hg isotopes are predicted with transition energies and half-lives. The $N=126$ shell gap is predicted to be robust from $Z=82$ down to 72 with minor reduction. We also examine the effective charges and the quenching of the $g$ factors suitable for this region by comparisons between observed and calculated electromagnetic properties.Conclusions: A new Hamiltonian is constructed for nuclei in the region south of $^{208}\mathrm{Pb}$, mainly including Pb, Tl, Hg, Au, Pt, Ir, Os, Re, and W isotopes around $N=126$, and provides them reasonable descriptions on nuclear properties including binding energies, excitation energies, and electromagnetic properties through shell-model studies. The present Hamiltonian and discussions provide fruitful information for future measurements and theoretical investigations for nuclei in this region, especially those around the $N=126$ shell, including the recommended effective charges and $g$ factors, the predicted binding energies, isomeric states, and core-excited states.