Isovector nuclear matter properties and neutron skin thickness

Correlations among several nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. A linear correlation between the neutron skin thickness and the pressure of the neutron matter is given in terms of the ratio between the neutron and nuclear matter densities. We also discovered that the correlations between the isovector properties and the incompressibility $K$ show a singularity at the critical incompressibility $K_{c}=306$ MeV. We show that the neutron skin thickness gives crucial information about not only the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of the Skyrme interaction.