Neutron star structure and collective excitations of finite nuclei

We study relationships between properties of collective excitations in finite nuclei and the phase transition density $n_t$ and pressure $P_t$ at the inner edge separating the liquid core and the solid crust of a neutron star. A theoretical framework that includes the thermodynamic method, relativistic nuclear energy density functionals and the quasiparticle random-phase approximation is employed in a self-consistent calculation of $(n_t,P_t)$ and collective excitations in nuclei. The covariance analysis shows that properties of charge-exchange dipole transitions, isovector giant dipole and quadrupole resonances and pygmy dipole transitions are correlated with the core-crust transition density and pressure. A set of relativistic nuclear energy density functionals, characterized by systematic variation of the density dependence of the symmetry energy of nuclear matter, is used to constrain possible values for $(n_t,P_t)$. By comparing the calculated excitation energies of giant resonances, energy weighted pygmy dipole strength, and dipole polarizability with available data, we obtain the weighted average values: $n_t = 0.0955 \pm 0.0007$ fm$^{-3}$ and $P_t = 0.59 \pm 0.05$ MeV fm$^{-3}$.