Shell-Model Structure ofBi208

The level structure of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Bi}$ has been investigated using both stripping and pickup reactions. The ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}({}_{}{}^3{}_{}{}^{}\mathrm{He},d)$ and ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}(\alpha ,t)$ reactions permit the identification of a series of doublets arising from the coupling of a proton in the $h_{\frac{9}{2}}$, $f_{\frac{7}{2}}$, $i_{\frac{13}{2}}$, $f_{\frac{5}{2}}$, and $p_{\frac{3}{2}}$ single-particle states with a neutron hole in the $p_{\frac{1}{2}}$ shell. The ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}\mathrm{}(d,t)\mathrm{}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )$ reactions populate the multiplets arising from coupling of a neutron hole in the $p_{\frac{1}{2}}$, $f_{\frac{5}{2}}$, $p_{\frac{3}{2}}$, $i_{\frac{13}{2}}$, $f_{\frac{7}{2}}$, and $h_{\frac{9}{2}}$ states with a proton in the $h_{\frac{9}{2}}$ shell. A detailed analysis shows that the total strength in each multiplet is close to that for the corresponding single-particle or single-hole transition on ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. In addition to the strong transitions leading to states of these multiplets, some relatively weak transitions are observed which provide a measure of the mixing of different configurations. The structure and purity of the particle-hole multiplets below about 3-MeV excitation is in good agreement with shell-model calculations.