On radii of neutron distributions in nuclei

We consider the analyses of the differences between rms radii (Δ = r_n - r_p) of neutron and proton distributions in a wide variety of nuclei. We note that apart from its own intrinsic interest, the quantity Δ is of importance for isotope shifts, core polarization contributions to the Coulomb energy differences of mirror pairs (Nolen-Schiffer anomaly) and the renormalization of the effective interaction. For example, if Δ were very small in ⁴⁸Ca then the Nolen-Schiffer anomaly could be explained by a core polarization mechanism. We consider critically the various methods of determining Δ and conclude that at present probably the most reliable method is high energy (≈ 1 GeV) proton-nucleus scattering. The different theoretical analyses based upon, e.g., the multiple diffraction theory (where Glauber amplitude is the leading term) or the optical potential (KMT) formalisms appear to be converging to essentially the same answer when analyzing the same data. High energy α-particles and medium energy pions can also become useful sources of information if higher order optical potentials are treated with care. We find that Δ is rather large in ⁴⁸Ca, i.e. there is a neutron skin, so that the Nolen-Schiffer anomaly cannot be explained by a core polarization mechanism. The results of high energy proton-nucleus scattering are in excellent agreement with current density dependent Hartree-Fock calculations.