Analysis of nuclear structure in a converging power expansion scheme

Abstract

Background: In the framework of the newly developed generalized energy density functional (EDF) called KIDS, the nuclear equation of state (EoS) is expressed as an expansion in powers of the Fermi momentum or the cubic root of the density (rho(1/3)). Although an optimal number of converging terms was obtained in specific cases of fits to empirical data and pseudodata, the degree of convergence remains to be examined not only for homogeneous matter but also for finite nuclei. Furthermore, even for homogeneous matter, the convergence should be investigated with widely adopted various EoS properties at saturation. Purpose: The first goal is to validate the minimal and optimal number of EoS parameters required for the description of homogeneous nuclear matter over a wide range of densities relevant for astrophysical applications. The major goal is to examine the validity of the adopted expansion scheme for an accurate description of finite nuclei. Method: We vary the values of the high-order density derivatives of the nuclear EoS, such as the skewness of the energy of symmetric nuclear matter and the kurtosis of the symmetry energy, at saturation and examine the relative importance of each term in rho(1/3) expansion for homogeneous matter. For given sets of EoS parameters determined in this way, we define equivalent Skyrme-type functionals and examine the convergence in the description of finite nuclei focusing on the masses and charge radii of closed-shell nuclei. Results: The EoS of symmetric nuclear matter is found to be efficiently parameterized with only three parameters and the symmetry energy (or the energy of pure neutron matter) with four parameters when the EoS is expanded in the power series of the Fermi momentum. Higher-order EoS parameters do not produce any improvement, in practice, in the description of nuclear ground-state energies and charge radii, which means that they cannot be constrained by bulk properties of nuclei. Conclusions: The minimal nuclear EDF obtained in the present work is found to reasonably describe the properties of closed-shell nuclei and the mass-radius relation of neutron stars. Attempts at refining the nuclear EDF beyond the minimal formula must focus on parameters which are not active (or strongly active) in unpolarized homogeneous matter, for example, effective tensor terms and time-odd terms.