Deformation ofsd-shell nuclei derived from inelastic scattering of 50 MeV α particles

Differential cross sections for elastic and inelastic α scattering on ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}$, and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ have been measured at 50 MeV. The data have been analyzed in the coupled-channel approach considering the model of a symmetric rotor together with the double-folding model for the optical potential. As an alternative also a Woods-Saxon parametrization for the radial shape of the real part of the optical potential has been considered. Both parametrizations yield similar results for the quadrupole and hexadecapole moments. These isoscalar multipole moments are consistent with those obtained from electromagnetic probes and with the predictions of microscopic shell-model calculations. Large deformations are needed to describe the enhancement of the elastic-scattering cross section at backward angles for ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}$.