The radii of nucleon distribution, bulk density, and neutron skin in nuclei beyond the $\beta$-stability line are studied within the direct variational method. We evaluate the partial equation of state of finite nuclei and demonstrate that the bulk density decreases beyond the $\beta$-stability line. We show that the growth of the neutron skin in unstable nuclei does not obey the saturation condition because of the polarization effect. The value of the neutron-skin thickness $\Delta r_{np}=\sqrt{\langle r_n^2\rangle }-\sqrt{\langle r_P^2\rangle }$ is caused by the different radii (skin effect) and only slightly by the different shapes (halo effect) of neutron and proton distributions. The relative contribution of both effects depends on the competition between the symmetry energy and the spin-orbit and Coulomb interactions. The calculations of the isovector shift of the nuclear radius $\Delta r_{np}$ show its primarily linear dependence on the asymmetry parameter $X=(N-Z)/A$.

• Received 14 December 2011

DOI:https://doi.org/10.1103/PhysRevC.85.034309