Neutron star structure and collective excitations of finite nuclei

A method is introduced that establishes relations 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. 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: $n_t=0.0955\pm 0.0007$ ${\mathrm{fm}}^{-3}$ and $P_t=0.59\pm 0.05$ MeV ${\mathrm{fm}}^{-3}$. This approach crucially depends on experimental results for collective excitations in nuclei and, therefore, accurate measurements are necessary to further constrain the structure of the crust of neutron stars.

Figure 1

Pearson product-moment correlation coefficients between the neutron star crust liquid-to-solid transition density $n_t$ (shaded bars - thin lines), and various observables of collective excitations for ${}^{208}\mathrm{Pb}$ and nuclear matter properties. The corresponding correlation coefficients for the pressure $P_t$ are displayed by thick (red) bars.

Figure 2

Constraints of the symmetry energy at saturation $J$ and the slope parameter $L$, obtained from a comparison of RNEDF results and data on AGDR [35] and IVGQR [32] excitation energies $\left({}^{208}\mathrm{Pb}\right)$, the dipole polarizability ${\alpha }_D$ of ${}^{208}\mathrm{Pb}$ [33], and the PDR energy-weighted strength $({}^{68}\mathrm{Ni}$ [34], ${}^{130,132}\mathrm{Sn}$ [30]).

Figure 3

The liquid-to-solid transition pressure $P_t$ for neutron-rich matter as a function of the transition density $n_t$ calculated using the RNEDF and experimental data for AGDR [31] and IVGQR [32] excitation energies $\left({}^{208}\mathrm{Pb}\right)$, the dipole polarizability ${\alpha }_D$ $\left({}^{208}\mathrm{Pb}\right)$ [33], and the PDR energy-weighted strength $\left({}^{68}\mathrm{Ni}\right)$ [34]. Previous results shown for comparison include MDI [5, 35] and DBHF + Bonn B interactions [36], and the RNEDF calculation [4].