KIDS Nuclear Energy Density Functional: 1st Application in Nuclei

Abstract

We apply the KIDS (Korea: IBS-Daegu-Sungkyunkwan) nuclear energy density functional model, which is based on the Fermi momentum expansion, to the study of properties of lj-closed nuclei. The parameters of the model are determined by the nuclear properties at the saturation density and theoretical calculations on pure neutron matter. For applying the model to the study of nuclei, we rely on the Skyrme force model, where the Skyrme force parameters are determined through the KIDS energy density functional. Solving HartreeFock equations, we obtain the energies per particle and charge radii of closed magic nuclei, namely, 16 Motivated by the Brueckner theory for a realistic potential in many fermion systems and effective field theory within a dilute fermion system, the nuclear energy density functional (EDF) 1 at low density may be expanded by taking the Fermi momentum k F as the expansion parameter in homogeneous nuclear matter. This idea was investigated in Ref.[2] and the EDF called KIDS is developed. In this model, the nuclear energy density functional is written aswhere T is the kinetic energy part, the nuclear density is ρ = ρ p + ρ n and the asymmetry parameter is defined as δ = (ρ n − ρ p )/ρ, where ρ p and ρ n are the densities of protons and neutrons, respectively. The parameters of the nuclear EDF c i 's are defined asso that c i = α i for the symmetric nuclear and c i = α i + β i for the pure neutron matter. These parameters are determined by the properties of symmetric nuclear matter at the nuclear saturation density and the results of a microscopic calculation in Ref. [3]. The details on the fitting process and the results can be found in Ref. [2]. To apply the obtained EDF to the study of the properties of nuclei, we need a model for nuclear forces and we adopt the Skyrme force model and perform the Skyrme-Hartree-Fock calculations [4,5]. In our study, we write the Skyrme force as1 Although E(ρ) has the form of a function, it is, in the end, only a mapping, whose existence and uniqueness was put forth by Hohenberg and Kohn [1]. We therefore call it a functional as is common practice.

Effective density functionals beyond mean field

“…The KIDS functional was introduced for nuclear matter [300] and was recently extended to describe finite nuclei [302,303,304]. The YGLO and ELYO functionals were introduced for nuclear matter [293,298] and were extended to describe trapped neutron drops in Ref.…”

“…More recently, the effective mass was used as a criterium to adjust the KIDS functional for applications to finite nuclei [304] without altering the original EOS for matter. The EOS provided by the parametrization KIDS-ad2 of Ref.…”

“…It was found in Ref. [304] that static and bulk properties of nuclei such as masses, charge radii, and neutron skin thicknesses are not affected by the different considered values of the effective mass. For example, Fig.…”

“…The other results were calculated in Ref. [304] with parametrizations associated with an incompressibility of 240 MeV and different values of the isoscalar effective mass, denoted by µ s in the figure. Only the neutron skin thickness of the heaviest nuclei is slightly impacted by the different values of the isoscalar effective mass.…”

“…As a perspective, the authors of Ref. [304] mentioned the possibility of using in future this effectivemass-based tuning of the parameters for performing an adjustment on dynamical properties, such as collective excitations [17,185,188,353].…”