Surface Resonances in Backward-Angle Heavy-Ion Scattering

Backward-angle excitation functions (${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=180\mathrm{}°\pm 5°$) have been measured for the systems ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ for elastic and inelastic scattering to the first excited state in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Over the investigated energy range, $17\lesssim E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\lesssim 37$ MeV, the elastic and inelastic data exhibit gross structure resonances of widths between 1 and 2 MeV modulated by a finer structure for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ ($\Delta E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\lesssim 250$ keV). Shape resonances with different principal quantum numbers are suggested as an explanation of the resonances.