The inelastic scattering of ${}^{12}\mathrm{C}$ from ${}^{208}\mathrm{Pb}$ at an incident energy of 98 MeV exhibits a curious anomaly. While the shape of the angular distribution for populating the 4.086-MeV $2_1^{+}$ level of ${}^{208}\mathrm{Pb}$ is well reproduced by distorted wave Born approximation (DWBA) calculations, a coupling strength approximately double that of the accepted value is required. The inelastic scattering of a 270-MeV ${}^3\mathrm{He}$ beam from a ${}^{208}\mathrm{Pb}$ target exhibits similar behavior. This minor mystery has remained unsolved for the past 50 years. A solution is suggested based on the high level density of ${}^{208}\mathrm{Pb}$ in the region of 4-MeV excitation energy and the possibility that the measured $2_1^{+}$ angular distributions contain contributions from a number of unresolved levels, in particular the 4.324-MeV $4_1^{+}$. The coupling strengths for these levels, required as input for DWBA calculations, were obtained from an analysis of existing high-resolution ${}^{208}\mathrm{Pb}$($p,p^{\prime }$) scattering data, while the $2_1^{+}$ coupling strength was fixed by the adopted value of the $B\left(E2\right)$. Using these strengths a consistent description of a wide range of light-ion scattering data is obtained, in addition to the “anomalous” ${}^{12}\mathrm{C}$ and ${}^3\mathrm{He}$ data. While the individual contributions of the levels other than the $2_1^{+}$ and $4_1^{+}$ are negligible, their sum makes a significant contribution to the total angular distribution.

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• Energy levels
• Inelastic scattering reactions
• Nuclear reactions
• 190 ≤ A ≤ 219
• Collective models
• Optical, coupled-channel & distorted wave models