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We aim to study the properties of nuclei in the south region of $^{208}$Pbsystematically, including the binding and excitation energies andelectromagnetic properties, in order to predict unknown properties of thesenuclei, such as isomerism, utilizing a theoretical model which describes theexperimentally known properties precisely. We also address whether the $N=126$shell closure is robust or not when the proton number decreases from$^{208}$Pb. We performed large-scale shell-model calculations with a newHamiltonian suggested in the present work. The model space is taken as the fiveproton orbits within $50<Z\leqslant82$ and the thirteen neutron orbits within$82<N\leqslant184$. And one-particle one-hole excitation is allowed across the$N=126$ gap. The Hamiltonian is constructed by combining the existingHamiltonians, KHHE (with adjustment of its proton-proton part) and KHPE, andthe monopole based universal interaction. The shell-model results wellreproduce the experimentally observed binding energies and spectroscopicproperties, such as isomerism, core excitation, and electromagnetic properties.Some possible isomeric states in neutron-rich Pb, Tl, and Hg isotopes arepredicted with transition energies and half-lives. We also examine theeffective charges and the quenching of the $g$ factors suitable for this regionby systematic comparisons between observed and calculated electromagneticproperties. A new Hamiltonian is constructed for nuclei in the south region of$^{208}$Pb, mainly including Pb, Tl, Hg, Au, Pt, Ir, Os, Re, and W isotopesaround $N=126$, and provides them reasonable descriptions on nuclear propertiesincluding binding energies, excitation energies and electromagnetic propertiesthrough comprehensive and systematic studies.

Systematic shell-model study on spectroscopic properties in the south region of $^{208}$Pb