  Background: Nuclear radius is one of the most important and basic properties
of atomic nuclei and its evolution is closely related to the saturation of the
nuclear density in the internal region but the systematics of the nuclear radii
for the neutron-rich unstable nuclei is not well known.
  Purpose: Motivated by the recent interaction cross section measurement which
indicates the 48Ca core swelling in the neutron-rich Ca isotopes, we explore
the mechanism of the enhancement of the neutron and proton radii for spherical
nuclei.
  Methods: Microscopic Hartree-Fock calculations with three sets of Skyrme-type
effective interactions are performed for the neutron-rich Ca, Ni and Sn
isotopes. The total reaction cross sections for the Ca isotopes are evaluated
with the Glauber model to compare them with the recent cross section data.
  Results: We obtain good agreement with the measured cross sections and charge
radii. The neutron and proton radii of the various "core" configurations are
extracted from the full Hartree-Fock calculation and discuss the core swelling
mechanism.
  Conclusions: The core swelling phenomena occur depending on the properties of
the occupying valence single-neutron states to minimize the energy loss that
comes from the saturation of the densities in the internal region, which
appears to be prominent in light nuclei such as Ca isotopes.
