Volume integrals and mean square radii of optical potentials by inversion

Within Glauber's eikonal approximation, the volume integrals and mean square radii of the real and imaginary parts of the optical potential are expressed as integrals of the parametrized phase shifts which can directly be obtained from comparison with scattering experiments. Evaluating these quantities using McIntyre-Wang-Becker s-matrix parametrizations for 12C - 12C scattering shows that they are comparable with the corresponding quantities for the phenomenological Woods-Saxon potentials that fit the same data. Non-eikonal corrections are evaluated and found to be relatively small even at energies as low as 8 MeV / nucleon