Examination of a ‘‘properly deformed folding potential’’ for the analysis of nuclear inelastic scattering and comparison with true folded potentials

A series of recent papers has introduced a ‘‘properly deformed folding potential’’ and applied it to the analysis of inelastic alpha-particle scattering from nuclei. We examine this procedure and find that it is no more appropriate for the folding model than other potential deformation prescriptions. To first order in the deformation for rotors, or exactly for harmonic vibrators, the procedure is equivalent to the uniform radial strain model of Onley et al. In common with other deformed potential models, it provides a transition potential which is not uniquely related to an underlying transition density. Transition moments extracted from measurements using deformed optical potentials are thus subject to uncontrolled uncertainty. We recommend that, instead, explicit folding be used to generate transition potentials. Although a choice of transition density has to be made, its relation to the transition potential, and hence to measurements, is then unambiguous. The octupole excitation of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ by alpha particles of 139 MeV is taken as an illustrative example.