Symmetry energy at subnuclear densities and nuclei in neutron star crusts

We examine how the properties of inhomogeneous nuclear matter at subnuclear densities depend on the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculate the size and shape of nuclei in neutron star matter at zero temperature in a way dependent on the density dependence of the symmetry energy. We find that for smaller symmetry energy at subnuclear densities, corresponding to the 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 decrease in the charge number is associated with the dependence of the surface tension on the nuclear density and the density of a sea of neutrons, whereas the decrease in the critical density can be generally understood in terms of proton clustering instability in uniform matter.