Symmetry energy at subnuclear densities and nuclei in a neutron-star crust

We examine how the properties of inhomogeneous nuclear matter at subnuclear densities depend on the density dependence of the symmetry energy. We focus on a parameter that characterizes the density dependence of the symmetry energy S(n) at about nuclear density n0. It is the density symmetry coefficient L = 3n0(dS/dn)n=n0 . From the saturation properties of stable nuclei, we find that the usual symmetry energy coefficient S0 = S(n0) has a strong correlation with L (S0 ≈ 28+ 0.075L MeV). Thus, we have essentially only one uncertain parameter L. Using a macroscopic nuclear model we calculate the sizes and shapes of nuclei in neutron star matter at zero temperature for different assumptions about the density dependence of the symmetry energy. We find that for smaller symmetry energy at subnuclear densities, corresponding to larger density symmetry coefficient L, the charge number of nuclei is smaller, and the critical density at which matter with nuclei or bubbles becomes uniform is lower. The value of the key parameter L could be constrained from global neutron-excess dependencies of radii and masses in nuclear chart. Hence, systematic measurements of radii and masses of neutron-rich nuclei could help reveal the structure of matter around the inner boundary of a neutron-star crust.