Neutron stars and supernova explosions in the framework of Landau's theory
A general formula of the symmetry energy for many-body interaction is proposed and the commonly used two-body interaction symmetry energy is recovered. Within Landau's theory (Lt), we generalize two equations of state (EoS) CCS$\delta$3 and CCS$\delta$5 to asymmetric nuclear matter. We assume that the density and density difference between protons and neutrons divided by their sum are order parameters. We use different EoS to study neutron stars by solving the TOV equations. We demonstrate that different EoS give different mass and radius relation for neutron stars even when they have exactly the same ground state (gs) properties ($E/A$, $\rho_0$, $K$, $S$, $L$ and $K_{sym}$). Furthermore, for one EoS we change $K_{sym}$ and fix all the other gs parameters. We find that for some $K_{sym}$ the EoS becomes unstable at high density even for neutron matter. This suggests that a neutron star (NS) can exist below and above the instability region but in different states: a quark gluon plasma (QGP) at high density and baryonic matter at low density. If the star's central density is in the instability region, then we associate these conditions to the occurrence of Supernovae (SN).