We aim to study the properties of nuclei in the south region of $^{208}$Pb systematically, 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 $^{208}$Pb. We performed large-scale shell-model calculations with a new Hamiltonian suggested in the present work. The model space is taken as the five proton 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 existing Hamiltonians, KHHE (with adjustment of its proton-proton part) and KHPE, and the monopole based universal interaction. 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. We also examine the effective charges and the quenching of the $g$ factors suitable for this region by systematic comparisons between observed and calculated electromagnetic properties. 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 isotopes around $N=126$, and provides them reasonable descriptions on nuclear properties including binding energies, excitation energies and electromagnetic properties through comprehensive and systematic studies.
Spectroscopic Amplitudes for One--Nucleon Transfer Between 1p0f--Shell Nuclei
本文计算了1 p $0\,$ f壳层下半部分核的正常低宇称态之间单核子转移的光谱振幅。用壳模型波函数进行计算，该波函数是从核哈密顿量在由1 p $_{3/2}$，1 p $_{1/2}$，$0\,$ f $_{7/2}$和$0\,$ f $_{5/2}$轨道产生的完整态集给出的空间中的对角化过程中得到的。哈密顿量包含了Richter \etal最近导出的一体和两体相互作用。给出了单核子拾取和剥离反应的求和规则。讨论了单核子拾取或剥离引起的末态激发的选择性。
How Threshold Effects in Spectroscopic Factors Influence Heavy-Ion Knockout Reactions
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所核科学理论南方中心）
