Excitation of ${\mathrm{Pb}}^{206}$, ${\mathrm{Pb}}^{207}$, ${\mathrm{Pb}}^{208}$, and ${\mathrm{Bi}}^{209}$ by Inelastic Electron Scattering

High-resolution measurements of the differential cross sections for inelastic scattering of 28- to 73-MeV electrons by ${\mathrm{Pb}}^{206}$, ${\mathrm{Pb}}^{207}$, ${\mathrm{Pb}}^{208}$, and ${\mathrm{Bi}}^{209}$ nuclei have been analyzed by using a distorted-wave code to extract reduced nuclear radiative transition probabilities [$B\left(\mathrm{EL}\right)\mathrm{}$'s], and transition radii. The use of an irrotational and incompressible vibrating-liquid-drop model resulted in good fits to the data. In agreement with de-Shalit's weak-coupling core-excited state model, the $B\left(\mathrm{EL}\right)\mathrm{}$'s were found to be equal for the three lead isotopes within an experimental error of about 6% for the $E2\mathrm{}$ excitations at about 4.1 MeV, and for the $E4\mathrm{}$'s at about 4.3 MeV. For all four isotopes the $B\left(E3\mathrm{}\right)\mathrm{}$'s at about 2.6 MeV were equal. Excitations of ${\mathrm{Pb}}^{208}$ at 5.25 MeV ($3^{-}$ or $4^{+}$), 5.6 MeV ($3^{-}$), and 6.2 MeV ($2^{+}$ or $0^{+}$) were observed. No strong $E2\mathrm{}$ excitation of ${\mathrm{Pb}}^{208}$ was identified between 6.2 and 18 MeV. A discussion of model and parameter dependence of the $B\left(\mathrm{EL}\right)\mathrm{}$'s and transition radii is given.