Pb208(α,α)Pb208scattering near the Coulomb barrier

Differential cross sections for the elastic scattering of $\alpha$ particles by ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been measured over the laboratory energy range 16.0 to 25.5 MeV in 0.5-MeV steps and over the laboratory angle range of 30 to 170° in 5° steps. A unique real potential of 35±3 MeV is found in an optical-model analysis with ${\gamma }_0=1.22\mathrm{}$ fm in $R={\gamma }_0({A_1}^{\frac{1}{3}}+{A_2}^{\frac{1}{3}})$ and $a=0.57\mathrm{}\mathrm{fm}$. Uniqueness is expected for scattering in the vicinity of the Coulomb barrier once size parameters are fixed. No discrete ambiguities are found over the energy range investigated consistent with a square-well $R$-matrix model, but they may exist at higher energies.