Recent astronomical observations, nuclear-reaction experiments, and microscopic calculations have placed new constraints on the nuclear equation of state (EoS) and revealed that most nuclearstructure models fail to satisfy those constraints upon extrapolation to infinite matter. A reverse procedure for imposing EoS constraints on nuclear structure has been elusive. Here we present for the first time a method to generate a microscopic energy density functional (EDF) for nuclei from a given immutable EoS. The method takes advantage of a natural Ansatz for homogeneous nuclear matter, the Kohn-Sham framework, and the Skyrme formalism. We apply it to the realistic nuclear EoS of Akmal-Pandharipande-Ravenhall and describe successfully closed-(sub)shell nuclei. In the process, we provide predictions for the neutron skin thickness of nuclei based directly on the given EoS. Crucially, bulk and static nuclear properties are found practically independent of the assumed effective mass value -a unique result in bridging EDF of finite and homogeneous systems in general.

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 ...

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The density functional theory (DFT) is based on the existence and uniqueness of a universal functional E[ρ], which determines the dependence of the total energy on single-particle density distributions. However, DFT says nothing about the form of the functional. Our strategy is to first look at what we know, from independent considerations, about the analytical density dependence of the energy of nuclear matter and then, for practical applications, to obtain an appropriate density-dependent effective interaction by reverse engineering. In a previous work on homogeneous matter, we identified the most essential terms to include in our "KIDS" functional, named after the early-stage participating institutes. We now present first results for finite nuclei, namely the energies and radii of 16,28 O, 40,60 Ca.

Background: The properties of very neutron rich nuclear systems are largely determined by the density dependence of the nuclear symmetry energy. The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore the symmetryenergy parameters such as J (value at saturation density), L (slope at saturation), Ksym (curvature at saturation) and higher-order ones independently of each other and independently of assumptions about the in-medium effective mass, as previously shown in the cases of closed-shell nuclei and neutron-star properties. Purpose: We examine the performance of EoSs with different symmetry energy parameters on properties of nuclei and observations of neutron stars and gravitational waves in an effort to constrain in particular L and Ksym or the droplet-model counterpart Kτ . Method: Assuming a standard EoS for symmetric nuclear matter, we explore several points on the hyperplane of (J, L, Ksym or Kτ ) values. For each point, the corresponding KIDS functional parameters and a pairing parameter are obtained for applications in spherical even-even nuclei. This is the first application of KIDS energy density functionals with pairing correlations in a spherical HFB computational code. The different EoSs are tested successively on the properties of closed-shell nuclei, along the Sn isotopic chain, and on astronomical observations, in a step-by-step procedure of elimination and correction. Results: A small regime of best-performing parameters is determined and correlations between symmetry-energy parameters are critically discussed. The results strongly suggest that Ksym is negative and no lower than −200 MeV, that Kτ lies between roughly −400 and −300 MeV and that L lies between 40 and 65 MeV, with L 55MeV more likely. For the selected well-performing sets, corresponding predictions for the position of the neutron drip line and the neutron skin thickness of selected nuclei are reported. The results are only weakly affected by the choice of effective mass values. Parts of the drip line can be sensitive to the symmetry energy parameters. Conclusion: Using KIDS EoSs for unpolarized homogeneous matter at zero temperature and KIDS EDFs with pairing correlations in spherical symmetry we have explored the hyperplane of symmetryenergy parameters. Using both nuclear-structure data and astronomical observations as a testing ground, a narrow regime of well-performing parameters has been determined, free of non-physical correlations and decoupled from constraints on the nucleon effective mass. The results underscore the role of Kτ and of precise astronomical observations. More-precise constraints are possible with precise fits to nuclear energies and, in the future, more-precise input from astronomical observations.

In this paper, we investigate the density dependence of the nuclear symmetry energy [Formula: see text] in the KIDS (Korea-IBS-Daegu-SKKU) framework for the nuclear equation of state (EoS) and energy-density functional (EDF). The aim is to constrain the value of the curvature parameter ([Formula: see text]) based on recent astronomical data. First, assuming a standard saturation point, we calculate bulk nuclear properties within KIDS-EDF for different values of the compression modulus of symmetric nuclear matter ([Formula: see text]) and of the leading-order symmetry energy parameters, i.e., the symmetry energy ([Formula: see text]) and slope ([Formula: see text]) at saturation density, each within a broadly accepted range, as well as [Formula: see text]. All of the above EoS parameters are varied independently of each other. The skewness parameter ([Formula: see text]) is presently kept fixed at 650[Formula: see text]MeV. For all EoS parameter sets which describe the selected nuclear data within better than [Formula: see text], we calculate the neutron star EoS and mass–radius relation and analyze the results in terms of Pearson correlation coefficients [Formula: see text]. We find that the value of [Formula: see text] is strongly correlated with the radius of both a canonical and a massive star [Formula: see text]. If we impose that all known astronomical constraints on the neutron star radii must be satisfied, we deduce [Formula: see text]. As a result, the symmetry energy as a function of the density is consistently found to have an inflection point at [Formula: see text]. We take the opportunity to report that the neutron skin thickness of [Formula: see text]Pb shows no correlation at all with the neutron star radii [Formula: see text], in contrast with studies which focus on the role of [Formula: see text] only.

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___________________________________________________________________________ AbstractThe connection from the structure and dynamics of atomic nuclei (finite nuclear system) to the nuclear equation of state (thermodynamic limit) is primarily made through nuclear energy-density functional (EDF) theory. Failure to describe both entities simultaneously within existing EDF frameworks means that we have either seriously misjudged the scope of EDF or not fully taken advantage of it. Enter the versatile KIDS Ansatz, which is based on controlled, order-by-order extensions of the nuclear EDF with respect to the Fermi momentum and allows a direct mapping from a given, immutable equation of state to a convenient Skyrme pseudopotential for applications in finite nuclei. A recent proof-of-principle study of nuclear ground-states revealed the subversive role of the effective mass. Here we summarize the formalism and previous results and present further explorations related to giant resonances. As examples we consider the electric dipole polarizability of 68 Ni and the giant monopole resonance (GMR) of heavy nuclei, particularly the fluffiness of 120 Sn. We find that the choice of the effective mass parameters and that of the compression modulus affect the centroid energy of the GMR to comparable degrees.