Elastic scattering of 12C by 28Si

12C + 28Si elastic scattering angular distributions have been measured at twenty-three bombarding energies over a range 19 MeV < or = E/sub lab/ < or = 48 MeV. At energies below 30 MeV the angular distributions are smooth and can be reproduced with a wide variety of optical potentials; similarly, above 40 MeV the angular distributions exhibit diffraction oscillations which optical potentials can rather easily reproduce. Irregular structure is observed in the cross sections for angles larger than 500 in the bombarding energy range 30--40 MeV. No optical potential has been found to give a good account of all the data; the best potential is a surface transparent Woods-Saxon potential which has energy dependences for both real and imaginary well depths. Examination of potentials which give reasonably good fits to the 36 MeV data shows that, although these potentials agree on a real well depth at a reasonable ''strong absorption radius,'' they can have quite different Argand diagrams: even in the range of the most sensitive partial waves. A Regge analysis finds several equally good families of Regge parameters for the same choice of background potential, but larger angle data might allow this ambiguity to be lifted. A Breit-Wigner analysis gives results which are at least partially consistent with the resonance parameters reported by Ost et al. Coupled-channel calculations with a 20% reduction of real and imaginary optical model well depths give a good account of inelastic scattering to the 28Si 2+ state while leaving the elastic scattering essentially unchanged from the predictions of the unmodified one-channel optical model. In the energy range of this study the grazing partial wave is found to be the same as the most important exit channel partial wave of the 24Mg(16O,12C)28Si ground state transition