Examination of inconsistencies between the deformed potential model and folding models for analysis of inelastic hadron scattering

It is customary to extract deformation lengths from inelastic scattering data by using a deformed optical potential. It is then assumed that this deformation length also characterizes the deformation of the underlying density distribution of the excited nucleus. This equivalence is exact for a dipole deformation, but this corresponds simply to a spurious excitation mode, namely a shift of the center of mass of the system. We show that, even when the potential is obtained by folding an effective interaction over the density distribution, the deformed potential model is not exact for other multipoles, except in the limit that the interaction has a zero range. The errors made when the interaction has a realistic finite range can be large