Covariant Density Functional Theory Research Articles

Bayesian inference of thermal effects in dense matter within the covariant density functional theory

The high temperatures reached in a proto-neutron star or during the post-merger phase of a binary neutron star coalescence lead to non-negligible thermal effects on the equation of state (EOS) of dense nuclear matter (NM). Here we study these effects within the covariant density functional theory employing the posteriors of a Bayesian inference, which encompasses a large sample of EOS models. Different densities and temperatures are considered. We find that for a number of quantities thermal effects are strongly correlated with the Dirac effective mass (m⁎) of the nucleons and/or its logarithmic derivative as a function of density. These results can be explained within the low temperature approximation though they survive beyond this limit.

Shapes and structure for the lowest states of the 42,44Ca isotopes

The shape and the associated dynamics of the 42,44Ca isotopes are investigated within the Bohr-Mottelson Model and the Covariant Density Functional Theory for the presence of the shape coexistence and mixing phenomena. The corresponding experimental energy spectrum and most of the electromagnetic transitions are well reproduced only by taking into account such phenomena. New possible developments of the models are indicated where improvements in agreement with the experimental data are needed.

A study of trends of neutron skin thickness and proton radii of mirror nuclei within the framework of covariant density functional theory

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, but its accurate measurement is quite challenging. We present predictions for neutron skins and proton radii for light to medium mass nuclei by employing Covariant Density Functional Theory (CDFT) based on density-dependent meson-exchange interaction. Using our microscopic predictions, we find a linear correlation between the neutron skin and the isospin asymmetry. The calculations are also extended to find a linear relationship between proton and neutron radii of mirror nuclei. Using the charge symmetry property of nuclear forces, a correlation between the neutron skin of neutron-rich nuclei and difference between the proton radii of the corresponding mirror pair has also been investigated. The inclusion of ISB term is found to affect the mirror difference charge radii of [Formula: see text]Ca-[Formula: see text]Ni mirror pair.

Prediction of novel effects in rotational nuclei at high speed

The study of high-speed rotating matter is a crucial research topic in physics due to the emergence of novel phenomena. In this letter, we combined cranking covariant density functional theory (CDFT) with a similarity renormalization group approach to decompose the Hamiltonian from the cranking CDFT into different Hermite components, including the non-relativistic term, the dynamical term, the spin-orbit coupling, and the Darwin term. Especially, we obtained the rotational term, the term relating to Zeeman-like effect, and the spin-rotation coupling due to consideration of rotation and spatial component of vector potential. By exploring these operators, we aim to identify novel phenomena that may occur in rotating nuclei. Signature splitting, Zeeman-like effect, and spin-rotation coupling are among the potential novelties that may arise in rotating nuclei. Additionally, we investigated the observability of these phenomena and their dependence on various factors such as nuclear deformation, rotational angular velocity, and magnetic field-like strength.

Pseudospin symmetry: Microscopic origin of the ground-state inversion in neutron-rich odd-A Cu isotopes

The role of the pseudospin symmetry in the inversion of the ground-state spin in Cu isotopes is investigated within the covariant density functional theory (CDFT). The density functional PC-PK1 gives a good agreement with the observed ground-state properties of the odd-A 69−79Cu. In particular, the inversion of the ground-state spin at A=75 is reproduced nicely, which can be explained by the level crossing between the proton pseudospin partners π2p3/2 and π1f5/2. It is found that the pseudospin symmetry plays a dominant role in the evolution of the energy splittings between the pseudospin partners. By comparing with the results of the nonrelativistic DFTs, our studies suggest that the pseudospin symmetry is essential to the shell evolution around this region.

Global properties of nuclei at finite-temperature within the covariant energy density functional theory

Global properties of nuclei at finite-temperature within the covariant energy density functional theory

Shape evolution and shape coexistence in even-even Mo isotopic chain

The phenomena of shape evolution and shape coexistence within the Molybdenum isotopic chain are investigated using the covariant density functional theory with the parameterizations DD-ME2 and DD-PC1. Furthermore, various ground state properties of this chain are investigated, including binding energy, two-neutron separation energy, charge radii, and two-neutron shell gap. A robust agreement is observed when comparing with the available experimental data. The ground state deformation of Mo isotopes evolves smoothly and correlates with the continuous and gradual changes observed in the physical properties. A noticeable phenomenon of shape coexistence can be observed in certain isotopes, marked by the simultaneous existence of both a triaxial and an oblate axial minimum. A pronounced and well-defined shell closure is prominently evident at the neutron magic number N=82.

Systematic investigation of proxy-SU(3) model in light nuclei

The proxy-SU(3) model is systematically used to obtain the ground state deformation and its evolution with neutron number for several isotopic chains ([Formula: see text]–34). These outputs are compared with the results of covariant density functional theory (CDFT) as well as the finite-range droplet macroscopic model (FRDM). Even Z results show good agreement with the CDFT results, while the odd Z results show good agreement with FRDM model results.

Electromagnetic properties of Λ hypernuclei with a beyond relativistic mean-field approach

We present a microscopic study of electromagnetic properties of the low-lying states of single-Λ hypernucleus Λ9Be using a quantum-number projected generator coordinate method (HyperGCM) based on covariant density functional theory. All the configurations are restricted to have axial symmetry, with the Λ hyperon in the lowest-energy state. The results are compared to the predictions of a simple particle-rotor model (PRM), for which analytic expressions are available. We show that the electromagnetic properties of Λ9Be from the HyperGCM calculation are close to those by the PRM. In particular, it is found that the magnetic moments and M1 transition strengths are less sensitive to the coupling strengths of the ΛN interaction than the electric quadrupole transition strengths. The latter may provide additional constraints on the ΛN interaction.

Revisiting the extraction of charge radii of 40Ca and 208Pb with muonic atom spectroscopy

The extractions of nuclear charge radii from muonic atom spectroscopy for 40Ca and 208Pb are revisited to analyze the model dependencies induced by employing a Fermi-type charge distribution. For that, the charge densities, together with the corresponding muonic transition energies, calculated by the covariant density functional theory are used as a benchmark. The root-mean-square deviation of transition energies is calculated to quantitatively investigate the sensitivities of transition energies to the details of the two-parameter Fermi distribution. It is found that the second and fourth moments of the charge distribution can be extracted accurately from the muonic atom spectroscopy without much model dependencies, whereas the obtained two-parameter Fermi distributions cannot reproduce the details of the benchmarking charge densities and, in particular, its surface-diffuseness parameter cannot be determined accurately with the present experimental uncertainties on the muonic transition energies.

Density-dependent relativistic mean field approach and its application to single-Λ hypernuclei in oxygen hyperisotopes* *Supported by the Fundamental Research Funds for the Central Universities, Lanzhou University (lzujbky-2022-sp02, lzujbky-2023-stlt01), the National Natural Science Foundation of China (11875152, 12275111), and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000)

The in-medium feature of nuclear force, which includes both nucleon-nucleon () and hyperon-nucleon () interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new effective interaction in the covariant density functional (CDF) theory, namely, DD-LZ1-, is obtained by fitting the experimental data of Λ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of the Λ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei, and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium interactions and core polarization effects.

Calculation of microscopic nuclear level densities based on covariant density functional theory

Calculation of microscopic nuclear level densities based on covariant density functional theory

Classification of pairing phase transition in the hot nucleus

The hot nucleus [Formula: see text] is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee–Yang’s theorem is applied to classify the pairing phase transition by analyzing the distribution of zeros of the partition function in the complex temperature plane. The distribution of zeros of the partition function converges with increasing particle numbers and illustrates the characteristics of the phase transition. In our calculations, we determine the first-order of the phase transition near the critical temperature. Different seniority states show the pairing phase transition from a superfluid to a normal phase, ranging from fully paired states to completely unpaired states.

Shape transition around 222Ra based on finite-temperature covariant density functional theory

The shape evolution and potential energy surfaces of even–even [Formula: see text]Ra are investigated in the [Formula: see text] plane by the covariant density functional theory. For octupole-deformed [Formula: see text]Ra, the free energy surfaces, the deformations, the pairing gaps, the excitation energy as well as the specific heat with increasing temperature are analyzed. Based on the specific heat, [Formula: see text]Ra exhibits three distinct discontinuities as the temperature rises. The first pairing transition occurs at [Formula: see text][Formula: see text]MeV, while the second one happens at [Formula: see text][Formula: see text]MeV when octupole deformation disappears, and the third one takes place at [Formula: see text][Formula: see text]MeV as quadrupole deformation approaches zero. The gaps at [Formula: see text] and [Formula: see text] in the single-particle levels are responsible for the octupole global minima. The shape transitions not only occur between even–even [Formula: see text]Ra, but also occur with increasing temperature for [Formula: see text]Ra.

Shell-model-like approach based on covariant density functional theory in 3D lattice space: Evolution of octupole shape in rotating 224Th

The evolution of the octupole shape with rotation in pear-shaped nuclei is a topic of broad interest. Based on the cranking covariant density functional theory in 3D lattice space, a shell-model-like approach is implemented to take into account the pairing correlations, and applied for the interleaved positive- and negative-parity bands in [Formula: see text]Th. The experimental [Formula: see text] relations are well reproduced. It is found that the octupole deformation of yrast states in [Formula: see text]Th rises slightly and then declines with increasing spin. After the band crossing, the octupole deformation suddenly disappears, i.e., a sharp transition from an octupole shape to a nearly spherical shape takes place at high spins. This is explained by the evolution of the coupling strength between the proton [Formula: see text] and [Formula: see text] orbitals with spin.

Octupole deformation and Ra puzzle with covariant density functional theory in three-dimensional lattice space

The anomaly of the residual proton–neutron interaction [Formula: see text] for Ra isotopes around [Formula: see text] deviating from the general trend, the so-called Ra puzzle, is investigated within the framework of covariant density functional theory in three-dimensional lattice space. The potential energy surfaces in [Formula: see text] plane for Ra isotopes are given by the constrained calculations. The average values of proton–neutron interaction [Formula: see text] extracted from the binding energies of Ra and Rn isotopes with axial, triaxial and reflection asymmetric calculations are compared with the data from AME2020 atomic mass evaluation. It is found that the octupole deformation provides a reasonable interpretation of the Ra puzzle.

Shape evolution of nuclei in the region of (A≈30) using covariant density functional theory

Shape evolution of even–even isotopes of Ne, Mg, Si, S, Ar and Ca in the vicinity of [Formula: see text] mass region of the nuclear chart is studied using covariant density functional theory. It will be studied based on finite range NN-interaction force represented by NL3∗ and DD-ME2 and zero finite range NN-interaction force represented by DD-PC1. Both [Formula: see text]Mg and [Formula: see text]Si exhibit shape coexistence and the ground state shape which is found to be both oblate and prolate. The spherical shape is obtained for the Ca isotopes, and for nuclei that have magic neutron numbers [Formula: see text] and 20. The rest of the isotopic chain has only one minimum and alternates between prolate and oblate shapes. Physical properties are calculated at the location of ground state deformation with neutron number ([Formula: see text]) and proton number ([Formula: see text]), such as the binding energy, two-neutron separation energies, proton, neutron and charge radii. In general, a smooth change in these properties is found, except near [Formula: see text] and 20 one can see a sharp change, which reflects the sudden change in the ground state deformation in the neighboring nuclei. A very good agreement is found with the available experimental data, HF and FRDM models

An improved microscopic core–quasiparticle coupling model for spectroscopy of odd-mass nuclei with octupole correlations

The microscopic core–quasiparticle coupling model for odd-A nuclei with octupole correlations is extended to include the monopole, quadrupole and octupole couplings between the core and the odd nucleon, based on the framework of covariant density functional theory. The model is tested in a study of low-lying excitation spectra for the odd-A nucleus [Formula: see text]Ra. Theoretical results, e.g., the parity doublets, interband [Formula: see text] and intraband [Formula: see text], are in very good agreement with the available data. In particular, the description of signature splitting in the ground-state band has been improved. This method provides a very useful tool for a systematic study of low-energy spectra in odd-mass actinides with octupole correlations.

Systematic study of elastic proton-nucleus scattering using relativistic impulse approximation based on covariant density functional theory

Systematic study of elastic proton-nucleus scattering using relativistic impulse approximation based on covariant density functional theory

Spherical, Axial, and Triaxial Symmetries in the Study of Halo Nuclei with Covariant Density Functional Theory

The halo phenomenon in exotic nuclei has long been an important frontier in nuclear physics research since its discovery in 1985. In parallel with the experimental progress in exploring halo nuclei, the covariant density functional theory has become one of the most successful tools for the microscopic study of halo nuclei. Based on spherical symmetry, the relativistic continuum Hartree–Bogoliubov theory describes the first halo nucleus 11Li self-consistently and predicts the giant halo phenomenon. Based on axial symmetry, the deformed relativistic Hartree–Bogoliubov theory in continuum has predicted axially deformed halo nuclei 42,44Mg and the shape decoupling effects therein. Based on triaxial symmetry, recently the triaxial relativistic Hartree–Bogoliubov theory in continuum has been developed and applied to explore halos in triaxially deformed nuclei. The theoretical frameworks of these models are presented, with the efficacy of exploiting symmetries highlighted. Selected applications to spherical, axially deformed, and triaxially deformed halo nuclei are introduced.