Abstract
The radius of the neutron distribution of a heavy nucleus is related to the equation of state for neutron matter that determines properties of nuclei and neutron stars. By systematically varying coupling constants characterizing the nuclear energy density functional and studying the resulting confidence ellipsoid, we quantify the relationships between the neutron skin and various properties of finite nuclei and infinite nuclear matter. According to the covariance analysis, the neutron skin is strongly correlated with the dipole polarizability and symmetry energy, and is very weakly correlated with the low-energy electric dipole strength. By adding the information on the neutron radius to the pool of observables determining the energy functional, we show how precise experimental determination of the neutron radius in ^{208}Pb would reduce theoretical uncertainties on the neutron matter equation of state.