Shell Model in the Lead Region

The structure of the low-lying states in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{210}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{210}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Tl}$, ${}_{}{}^{206}{}_{}{}^{}\mathrm{Tl}$, and ${}_{}{}^{206}{}_{}{}^{}\mathrm{Hg}$ has been calculated using a conventional shell-model approach with a central Gaussian-shaped interaction plus $P_2$ and $P_3$ multipole interactions where the $P_2$ and $P_3$ strengths were varied for each nucleus. The results are compared with the experimental data and other calculations. The agreements between the experimental energies and spectroscopic factors and the calculations are in general good. The agreements between the experimental and calculated $E2\mathrm{}$ and $M1\mathrm{}$ rates in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ are also fairly good.