Collective Excitations in ${\mathrm{Pb}}^{207}$, ${\mathrm{Pb}}^{208}$, and ${\mathrm{Bi}}^{209}$

The nuclei ${\mathrm{Pb}}^{207}$, ${\mathrm{Pb}}^{208}$, and ${\mathrm{Bi}}^{209}$ are investigated by inelastic scattering of 42-MeV $\alpha$ particles. The previously noted similarity in the excitation of these three nuclei is studied in detail. The excitation of collective levels is strongly favored in this experiment. The measured angular distributions show equally strong octupole levels in the three nuclei, at 2.6-MeV excitation. Levels in ${\mathrm{Pb}}^{207}$ and ${\mathrm{Pb}}^{208}$ around 3.2 MeV are found with the same strength as the known $5^{-}$ level at 3.198 MeV in ${\mathrm{Pb}}^{208}$. The previously reported level at 4.3 MeV in ${\mathrm{Pb}}^{208}$ is shown to consist of two levels at 4.12 and 4.40 MeV and their angular distributions favor a $2^{+}$ assignment. These levels are also found in ${\mathrm{Pb}}^{207}$ with the same intensity as in ${\mathrm{Pb}}^{208}$. The conclusion is drawn that the excitations in these three nuclei are due to the collective excitations of the ${\mathrm{Pb}}^{208}$ core and that the coupling to the ${\mathrm{Pb}}^{208}$ core of a single proton or a single neutron hole is very weak. Collective parameters are extracted using the Austern-Blair model which is shown to give good agreement with the measured angular distributions. The Coulomb-excitation contribution to the inelastic scattering is demonstrated by extending the angular-distribution measurements to small angles.