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 (ρ 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 ρ 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 3 parameters and the symmetry energy (or the energy of pure neutron matter) with 4 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. * Electronic address: gil@knu.ac.kr † Electronic address: ymkim715@gmail.com ‡ Electronic address: hch@daegu.ac.kr § Electronic address: ppapakon@ibs.re.kr ¶ Electronic address: yohphy@knu.ac.kr the fits, a robust parameter set was chosen as a baseline for further explorations, comprising three terms for isospin-symmetric nuclear matter (SNM) and four for pure neutron matter (PNM). The naturalness of the expansion was confirmed and extrapolations to extreme density regimes, were found to be satisfactory [4]. In particular, the extrapolated results agreed with ab initio calculations for dilute neutron matter, a regime to which the model had not been fitted at all, and reproduced a realistic mass-radius ...

Self-consistent methods for structure and production of heavy and superheavy nuclei

“…The multidimensionallyconstrained CEDF and CEDF on 3D lattices have recently been introduced to describe nuclear reactions (i.e., fission) and strongly deformed exotic states [138][139][140][141][142][143]. The EDFplus-HFB approaches describe quite successfully nuclear binding energies, nuclear shapes and sizes of beta-stable and beta-unstable nuclei; see e.g., [77,78,112,115,125,127,129,[136][137][138][144][145][146][147][148][149][150][151][152][153][154][155][156][157][158][159][160][161]. Thus, the Mic-Mac approaches have reached a high accuracy in reproducing nuclear masses, at least in the known mass region.…”

“…In Refs. [158,159], a new method was suggested to construct the EDF for nuclei from a given immutable equation of state (EoS). The method takes advantage of a natural ansatz for homogeneous nuclear matter, the Kohn-Sham framework, and the Skyrme formalism.…”

“…The EDF is systematically expanded in powers of the Fermi momentum or cubic root of the density. The binding energies and the sizes of the closed-(sub)shell nuclei were successfully described [158,159]. A simple and manageable method [177] was developed for deriving coupling constants of model EDF directly from ab initio calculations performed for finite fermion systems.…”

Bayesian inference of finite-nuclei observables based on the KIDS model

“…Although up to four terms have been found optimal for a wide range of densities, the expansion can be extended to accommodate any set of EOS parameters [53] so that they can be varied independently of each other. Any set of EOS parameters characterizing, typically, the saturation point and the density dependence of the symmetry energy, is readily transposed to a nuclear EDF for finite nuclei in the highly convenient form of an extended Skyrme functional, with the additional freedom of choosing the values for the effective mass and other interaction parameters which are not active in homogeneous nuclear matter [53,54]. Studies of symmetry-energy parameters based on astronomical observations and bulk nuclear properties were publicized recently [55,56], and a pilot study of the neutron-skin thickness was also conducted [57].…”

“…The isoscalar nucleon effective mass m s = 0.82m, with m being the bare nucleon mass, is fitted to reproduce both the excitation energies of isoscalar giant quadruple resonance in 208 Pb and 120 Sn, to be shown later. G S = 132 MeVfm 5 , G V = 5 MeVfm 5 , and m v = 0.7m are chosen as the default values as those in the MSL0 model [51], while the default values of other EOS parameters are taken to be those from the KIDS-P4 parameterization that reproduces the APR EOS rather well [54]. In the present study using the Bayesian analysis, we only vary the quantities, to which the experimental observables are most sensitive after doing the sensitivity analysis, within their prior ranges, while other quantities are fixed at their default values, as shown in Table I.…”