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Register a new userSymmetry energy in nuclear density functional theory
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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.
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The neutron and proton drip lines represent the limits of the nuclear landscape. While the proton drip line is measured experimentally up to rather high $Z$-values, the location of the neutron drip line for absolute majority of elements is based on theoretical predictions which involve extreme extrapolations. The first ever systematic investigation of the location of the proton and neutron drip lines in the covariant density functional theory has been performed by employing a set of the state-of-the-art parametrizations. Calculated theoretical uncertainties in the position of two-neutron drip line are compared with those obtained in non-relativistic DFT calculations. Shell effects drastically affect the shape of two-neutron drip line. In particular, model uncertainties in the definition of two-neutron drip line at $Zsim 54, N=126$ and $Zsim 82, N=184$ are very small due to the impact of spherical shell closures at N=126 and 184.
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 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.
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 soliton existence in sub-atomic many-nucleon systems is discussed. In many nucleon dynamics represented by the nuclear time-dependent density functional formalism, much attention is paid to energy and mass dependence of the soliton existence. In conclusion, the existence of nuclear soliton is clarified if the temperature of nuclear system is from 10 to 30 MeV. With respect to the mass dependence $^{4}$He and $^{16}$O are suggested to be the candidates for the self-bound states exhibiting the property of nuclear soliton.
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