Outer volume integrals and mean square radii of heavy ion optical potentials

The volume integrals and root-mean-square (rms) radii of the real and imaginary parts of the ambiguous sets of optical potentials that equally fit the differential cross sections for the elastic collisions between C-12 and O-16 are evaluated when the internal region, where the optical potential is ill defined, is removed from the integrals used in their calculation. It is found that the relative dispersion of the values of these quantities around their means for each set takes the least values when the corresponding integrals are evaluated with a lower cutoff at the rms radius of the imaginary potential when the incident energy is less than 35 MeV/nucleon, and at the rms radius of the real potential at higher incident energies.