Elastic, inelastic, and single-nucleon transfer data are reported for ${}_{}{}^{28}{}_{}{}^{}$Si${+\mathrm{}}^{40}$Ca at $E_{\mathrm{lab}=225\mathrm{}}$ MeV. Standard optical model and distorted-wave Born approximation analyses of the elastic and inelastic scattering angular distributions have been performed resulting in good descriptions of the data. In the inelastic scattering analysis, the nuclear deformation lengths were found to be consistent with the Coulomb deformation lengths obtained from electron scattering. The data for one-nucleon transfers were analyzed using the distorted-wave Born approximation with the optical potential fitted to the elastic scattering and the spectroscopic factors taken from light-ion studies. With the exception of small shifts in angle, the distorted-wave Born approximation correctly predicts the shapes of the angular distributions and the relative intensities of transitions to different states populated in the same reaction. The magnitudes of the single-particle transfer cross sections are reproduced to within a factor of 1.5. However, the distorted-wave Born approximation fails to predict the nearly 40% difference in the magnitudes of the cross sections observed for the ${(}^{28}$Si, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Si}$) and ${(}^{28}$Si, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$) reactions, which populate mirror states.

• Received 13 November 1985

DOI:https://doi.org/10.1103/PhysRevC.33.1325