Background: The explicit density dependence in the coupling coefficients entering the nonrelativistic nuclear energy-density functional (EDF) is understood to encode effects of three-nucleon forces and dynamical correlations. The necessity for the density-dependent coupling coefficients to assume the form of a preferably small fractional power of the density $\rho$ is empirical and the power is often chosen arbitrarily. Consequently, precision-oriented parametrizations risk overfitting in the regime of saturation and extrapolations in dilute or dense matter may lose predictive power.

We investigate nuclear-matter equations of state in neutron stars with kaon condensation. It is generally known that the existence of kaons in neutron star makes the equation of state soft so that the maximum mass of a neutron star is not likely to be greater than $2.0{M}_{$\bigodot${}}$, the maximum mass constrained by current observations. With existing Skyrme force model parameters, we calculate nuclear equations of state and check the possibility of kaon condensation in the core of neutron stars. The results show that, even with the kaon condensation, the nuclear equation of state satisfies both the maximum mass and the allowed ranges of mass and radius.

Recent astronomical observations, nuclear-reaction experiments, and microscopic calculations have placed new constraints on the nuclear equation of state (EoS) and revealed that most nuclear-structure models fail to satisfy those constraints upon extrapolation to infinite matter. A reverse procedure for imposing EoS constraints on nuclear structures 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 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.

The effects of nuclear isospin asymmetry on $\alpha$-decay lifetimes of heavy nuclei are investigated within various phenomenological models of the nuclear potential for the $\alpha$ particle. We consider the widely used simple square-well potential and Woods-Saxon potential and modify them by including an isospin asymmetry term. We then suggest a model for the potential of the $\alpha$ particle motivated by a microscopic phenomenological approach of the Skyrme force model, which naturally introduces the isospin-dependent form of the nuclear potential for the $\alpha$ particle. The empirical $\alpha$-decay lifetime formula of Viola and Seaborg [ J. Inorg. Nucl. Chem. 28, 741 (1966)] is also modified to include isospin asymmetry effects. The obtained $\alpha$-decay half-lives are in good agreement with the experimental data, and we find that including the nuclear isospin effects somehow improves the theoretical results for $\alpha$-decay half-lives. The implications of these results are discussed, and the predictions on the $\alpha$-decay lifetimes of superheavy elements are also presented.

Background: The properties of very neutron rich nuclear systems are largely determined by the density dependence of the nuclear symmetry energy. The Korea-IBS-Daegu-SKKU (KIDS) framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore the symmetry-energy parameters such as $J$ (value at saturation density), $L$ (slope at saturation), $K_{\mathrm{sym}}$ (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.