From Finite Nuclei to Neutron Stars: The Essential Role of High-Order Density Dependence in Effective Forces

Abstract

A unified description of finite nuclei and equation of state of neutron stars presents both a major challenge and also opportunities for understanding nuclear interactions. Inspired by the Lee–Huang–Yang formula of hard-sphere gases, we develop effective nuclear interactions with an additional high-order density dependent term. While the original Skyrme force SLy4 is widely used in studies of neutron stars, there are not satisfactory global descriptions of finite nuclei. The refitted SLy4’ force can improve descriptions of finite nuclei but slightly reduces the radius of neutron star of 1.4M ⊙ with M ⊙ being the solar mass. We find that the extended SLy4 force with a higher-order density dependence can properly describe properties of both finite nuclei and GW170817 binary neutron stars, including the mass-radius relation and the tidal deformability. This demonstrates the essential role of high-order density dependence at ultrahigh densities. Our work provides a unified and predictive model for neutron stars, as well as new insights for the future development of effective interactions.

Implications of neutron skin measurements on Skyrme equations of state*

“…The extension of Skyrme forces with an additional higher-order density dependent term is expected to provide better descriptions of finite nuclei and nuclear matter within a large range of densities [23]. The Skyrme interaction includes two-body and three-body interactions as follows [19]:…”

“…The selected nuclei are listed in our previous work [23]. The experimental binding energies are taken from [28] and the experimental charge radii are taken from [19]. In addition, the neutron skin thicknesses of Ca and Pb are included in the fitting, the experimental values of which are taken from CREX and PREX-2 [2,16].…”

“…M ⊙ Neutron skin thickness is a one-body bulk observable, and density functional theory is, in this respect, a suitable tool for descriptions of heavy nuclei. The effective Skyrme energy density functionals have been widely used in studies of neutron stars and finite nuclei [19]. For example, the SLy4 force can reasonably describe neutron stars of maximum 2.0 and tidal deformability [20] and is adopted as references in LIGO papers [21].…”

Temperature and density effects on the two-nucleon momentum correlation function from excited single nuclei

“…where ρ and ρ 0 are total nucleon density and its normal value at the ground state, i.e., 0.16 f m −3 , respectively. The above parameters α, β, and γ with an incompressibility parameter K are related to the nuclear equation of state [52][53][54][55][56][57][58].…”

Correlations between nuclear landscape boundaries and neutron-rich r-process abundances

“…Semimicroscopic and phenomenological models can be precise for known nuclei but could be less reliable for explorations. As a suitable tool, the density functional theory with high-precision effective interactions are versatile for reasonable descriptions of global finite nuclei and neutron stars, including exotic structures and dynamics of halo nuclei, and nuclear fission [8,[25][26][27][28][29][30][31][32]. Previously the properties of 39 Na and neighboring drip line nuclei have been studied [32].…”