Phase-Equivalent Ambiguities in an Optical Model: Coupled-Channel Analysis ofα+Mg24Scattering at 17 MeV

The existence of phase-equivalent ambiguities in the generalized optical model is investigated using a coupled-channel analysis of $\alpha +{}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at 17 MeV. When compound-nucleus contributions are included in the analysis it is found that the phase-equivalent ambiguities typical of the spherical optical potential still occur when the potential is nonspherical. The values obtained for the deformation parameter which are appropriate for the rotational states of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ are found to be relatively insensitive to the choice of a phase-equivalent potential. A simple explanation of this insensitivity has not yet been found.