Correlation of the neutron star crust-core properties with the slope of the symmetry energy and the lead skin thickness

The correlations of the crust-core transition density and pressure in neutron stars with the slope of the symmetry energy and the neutron skin thickness are investigated, using different families of relativistic mean-field parametrizations with constant couplings and nonlinear terms mixing the sigma-, omega-, and rho-meson fields. It is shown that the modification of the density dependence of the symmetry energy, involving the sigma or the omega meson, gives rise to different behaviors: the effect of the omega meson may also be reproduced within nonrelativistic phenomenological models, while the effect of the sigma meson is essentially relativistic. Depending on the parametrization with sigma-rho or omega-rho mixing terms, different values of the slope of the symmetry energy at saturation must be considered in order to obtain a neutron matter equation of state compatible with results from chiral effective field theory. This difference leads to different pressures at the crust-core transition density. A linear correlation between the transition density and the symmetry energy slope or the neutron skin thickness of the Pb-208 nucleus is obtained, only when the omega meson is used to describe the density dependence of the symmetry energy. A comparison ismade between the crust-core transition properties of neutron stars obtained by three different methods, the relativistic random phase approximation (RRPA), the Vlasov equation, and thermodynamical method. It is shown that the RRPA and the Vlasov methods predict similar transition densities for pne beta-equilibrium stellar matter.