Homologous states and the structure of nuclei in the lead region

Abstract

The structure of both low-lying and highly excited states and electromagnetic transitions in ${}^{206}\mathrm{Pb}$ and ${}^{205}\mathrm{Tl}$ has been studied within the framework of the shell model. The calculation predicts the occurrence of states in ${}^{206}\mathrm{Pb}$ with a structure homologous to parent states in ${}^{205}\mathrm{Tl},$ a phenomenon experimentally reported in these systems via $(p\ensuremath{\rightarrow},\ensuremath{\alpha})$ reactions, in analogy with other regions of the mass table. This feature is not restricted to configurations where the two neutron holes are coupled to angular momentum zero, but also applies to higher configurations corresponding to angular momentum recoupling of the two neutron holes. The calculated results, obtained with both a modified surface delta interaction and Kuo-Herling interaction, are in good agreement with the experimental data, further supporting the ability of these interactions to describe nuclear properties in the lead region.