Properties of nuclei in the inner crusts of neutron stars in the relativistic mean-field theory

We study the properties of nuclei in the inner crusts of neutron stars based on the Boguta-Bodmer nonlinear model in the relativistic mean-field theory, We carefully determine the surface diffuseness of the nuclei as the density of matter increases. The imaginary time step method is used to solve the Euler-Lagrange equation derived from the variational principle applied to the semiclassical energy density, It is shown that that with increasing density, the spherical nuclei become more neutron rich and eventually me liquid of neutrons, protons, and electrons. We find that the smaller the value of the incompressibility K, the lower the density at which the phase transition to uniform matter occurs. The relativistic extended Thomas-Fermi method is generalized to investigate nonspherical nuclei. Our results show that the spherical nucleus phase is the only equilibrium stare in the inner crusts of neutron stars.