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 ...

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.

We investigate the constraints on the mass and radius of neutron stars by considering the tidal deformability in the merge of neutron star binaries. In order to extract the most reliable range of uncertainty from theory, we employ models based upon the Skyrme force and density functional theory and select models that are consistent with empirical data of finite nuclei, measured properties of nuclear matter around the saturation density, and observation of the maximum mass of neutron stars. From the selected models, we calculate the Love number k 2 , dimensionless tidal deformability Λ, and mass-weighted deformabilityΛ in the binary system. We find that all the models considered in this work giveΛ less than 800 which is the upper limit obtained from the measurement of GW170817. However, the model dependence of tidal deformability is manifest such that our results on the tidal deformability exhibit critical sensitivity to the size of neutron stars.

We present a targeted search for continuous gravitational waves (GWs) from 236 pulsars using data from the third observing run of LIGO and Virgo (O3) combined with data from the second observing run (O2). Searches were for emission from the l = m = 2 mass quadrupole mode with a frequency at only twice the pulsar rotation frequency (single harmonic) and the l = 2, m = 1, 2 modes with a frequency of both once and twice the rotation frequency (dual harmonic). No evidence of GWs was found, so we present 95% credible upper limits on the strain amplitudes h 0 for the single-harmonic search along with limits on the pulsars’ mass quadrupole moments Q 22 and ellipticities ε. Of the pulsars studied, 23 have strain amplitudes that are lower than the limits calculated from their electromagnetically measured spin-down rates. These pulsars include the millisecond pulsars J0437−4715 and J0711−6830, which have spin-down ratios of 0.87 and 0.57, respectively. For nine pulsars, their spin-down limits have been surpassed for the first time. For the Crab and Vela pulsars, our limits are factors of ∼100 and ∼20 more constraining than their spin-down limits, respectively. For the dual-harmonic searches, new limits are placed on the strain amplitudes C 21 and C 22. For 23 pulsars, we also present limits on the emission amplitude assuming dipole radiation as predicted by Brans-Dicke theory.

We use an event-by-event hydrodynamical description of the heavy-ion collision process with Glauber initial conditions to calculate the thermal emission of photons. The photon rates in the hadronic phase follow from a spectral function approach and a density expansion, while in the partonic phase they follow from the AMY perturbative rates. The calculated photon elliptic flows are lower than those reported recently by both the ALICE and PHENIX collaborations.