Optical model description ofα+O16elastic scattering and alpha-cluster structure inNe20

${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\alpha , \alpha )$ elastic scattering angular distributions have been measured for incident energies 39.3, 49.5, and 69.5 MeV. These data, and previous measurements at 32.2, 104, and 146 MeV, have been subjected to a global optical model analysis. The deduced global potential has two energy-dependent parameters which are found to vary smoothly with energy and it is uniquely determined by the data. Backward angular distributions measured between 40 and 54 MeV are also presented and shown to be nicely reproduced by the model. The sensitivity of the cross sections to the various regions of the real potential has been investigated as a function of energy using the notch test technique. The low energy behavior of the differential cross sections can be understood in terms of the semiclassical decomposition of Brink and Takigawa. A natural extrapolation of the global potential below 30 MeV is shown to reproduce the wide bump observed in the experimental excitation functions around 20 MeV. This bump is shown to be due to an $l=8\mathrm{}$ shape resonance and is interpreted as the $J^{\pi }=8^{+}$ member of the $K^{\pi }=0_4^{+}$ rotational band of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, in contradiction with the current attribution. Other bound and quasibound states supported by the potential are discussed in the light of orthogonality condition model-type arguments and shown to be consistent with the well-known $K^{\pi }=0_1^{+} \mathrm{and} 0^{-}$ bands, and with the first three states of the $K^{\pi }=0_4^{+}$ band of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$.