Nuclear Structure Studies in the Lead Region with Stripping Reactions

The seven single-particle neutron states in the $126<N<~184$ shell are located and identified with the ${\mathrm{Pb}}^{208}(d, p){\mathrm{Pb}}^{209}$ reaction. The missing $h_{\frac{9}{2}}$ hole state in ${\mathrm{Pb}}^{207}$ is also located and identified with ($d, t$) reactions. Nuclei with two particles and holes, such as ${\mathrm{Pb}}^{206}$, ${\mathrm{Pb}}^{208}$ (excited), ${\mathrm{Bi}}^{208}$, and ${\mathrm{Bi}}^{210}$ are studied; their level structure can be qualitatively and sometimes even semi-quantitatively understood by considering two-particle couplings using the known particle and hole states. The ground-state wave function of ${\mathrm{Pb}}^{206}$ is studied by three independent methods; all agree that it is only about 54% ${\left(p_{\frac{1}{2}}\right)}^{-2\mathrm{}}$ rather than 73% as given by shell-model calculations. The three-neutron spectra of ${\mathrm{Pb}}^{205}$ and ${\mathrm{Pb}}^{207}$ (excited) are studied, and the principal features can be understood as couplings of one particle or hole to the ground state and other low-lying states of ${\mathrm{Pb}}^{206}$. Some preliminary evidence is obtained on the $N>\mathrm{}184\mathrm{}$ shell.