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The density functional theory (DFT) is based on the existence and uniqueness of a universal functional $E[rho]$, 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.
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We present a minimal nuclear energy density functional (NEDF) called SeaLL1 that has the smallest number of possible phenomenological parameters to date. SeaLL1 is defined by 7 significant phenomenological parameters, each related to a specific nuclear property. It describes the nuclear masses of even-even nuclei with a mean energy error of 0.97 MeV and a standard deviation 1.46 MeV, two-neutron and two-proton separation energies with r.m.s. errors of 0.69 MeV and 0.59 MeV respectively, and the charge radii of 345 even-even nuclei with a mean error $epsilon_r=$0.022 fm and a standard deviation $sigma_r=$0.025 fm. SeaLL1 incorporates constraints on the EoS of pure neutron matter from quantum Monte Carlo calculations with chiral effective field theory two-body (NN) interactions at N3LO level and three-body (NNN) interactions at the N2LO level. Two of the seven parameters are related to the saturation density and the energy per particle of the homogeneous symmetric nuclear matter, one is related to the nuclear surface tension, two are related to the symmetry energy and its density dependence, one is related to the strength of the spin-orbit interaction, and one is the coupling constant of the pairing interaction. We identify additional phenomenological parameters that have little effect on ground-state properties, but can be used to fine-tune features such as the Thomas-Reiche-Kuhn sum rule, the excitation energy of the giant dipole and Gamow-Teller resonances, the static dipole electric polarizability, and the neutron skin thickness.
The explicit density (rho) dependence in the coupling coefficients of the non-relativistic nuclear energy-density functional (EDF) encodes effects of three-nucleon forces and dynamical correlations. The necessity for a coupling coefficient in the form of a small fractional power of rho is empirical and the power often chosen arbitrarily. Consequently, precision-oriented parameterisations risk overfitting and loss of predictive power. Observing that the Fermi momentum kF~rho^1/3 is a key variable in Fermi systems, we examine if a power hierarchy in kF can be inferred from the properties of homogeneous matter in a domain of densities which is relevant for nuclear structure and neutron stars. For later applications we want to determine an EDF that is of good quality but not overtrained. We fit polynomial and other functions of rho^1/3 to existing microscopic calculations of the energy of symmetric and pure neutron matter and analyze the fits. We select a form and parameter set which we found robust and examine the parameters naturalness and the resulting extrapolations. A statistical analysis confirms that low-order terms like rho^1/3 and rho^2/3 are the most relevant ones. It also hints at a different power hierarchy for symmetric vs. pure neutron matter, supporting the need for more than one rho^a terms in non-relativistic EDFs. The EDF we propose accommodates adopted properties of nuclear matter near saturation. Importantly, its extrapolation to dilute or asymmetric matter reproduces a range of existing microscopic results, to which it has not been fitted. It also predicts neutron-star properties consistent with observations. The coefficients display naturalness. Once determined for homogeneous matter, EDFs of the present form can be mapped onto Skyrme-type ones for use in nuclei. The statistical analysis can be extended to higher orders and for different ab initio calculations.
The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this survey we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side-by-side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry-energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.
Background: A global description of the ground-state properties of nuclei in a wide mass range in a unified manner is desirable not only for understanding exotic nuclei but for providing nuclear data for applications. Purpose: We demonstrate the KIDS functional describes the ground states appropriately with respect to the existing data and predictions for a possible application of the functional to all the nuclei by taking Nd isotopes as examples. Method: The Kohn-Sham-Bogoliubov equation is solved for the Nd isotopes with the neutron numbers ranging from 60 to 160 by employing the KIDS functionals constructed to satisfy both neutron-matter equation of state or neutron star observation and selected nuclear data. Results: Considering the nuclear deformation improves the description of the binding energies and radii. We find that the discrepancy from the experimental data is more significant for neutron-rich/deficient isotopes and this can be made isotope independent by changing the slope parameter of the symmetry energy. Conclusions: The KIDS functional is applied to the mid-shell nuclei for the first time. The onset and evolution of deformation are nicely described for the Nd isotopes. The KIDS functional is competent to a global fitting for a better description of nuclear properties in the nuclear chart.
Magnetic dipole (M1) excitations build not only a fundamental mode of nucleonic transitions, but they are also relevant for nuclear astrophysics applications. We have established a theory framework for description of M1 transitions based on the relativistic nuclear energy density functional. For this purpose the relativistic quasiparticle random phase approximation (RQRPA) is established using density dependent point coupling interaction DD-PC1, supplemented with the isovector-pseudovector interaction channel in order to study unnatural parity transitions. The introduced framework has been validated using the M1 sum rule for core-plus-two-nucleon systems, and employed in studies of the spin, orbital, isoscalar and isovector M1 transition strengths, that relate to the electromagnetic probe, in magic nuclei $^{48}$Ca and $^{208}$Pb, and open shell nuclei $^{42}$Ca and $^{50}$Ti. In these systems, the isovector spin-flip M1 transition is dominant, mainly between one or two spin-orbit partner states. It is shown that pairing correlations have a significant impact on the centroid energy and major peak position of the M1 mode. The M1 excitations could provide an additional constraint to improve nuclear energy density functionals in the future studies.
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