Relativistic Hartree Research Articles

Relativistic mean field analysis of triaxial deformation for nuclei near the neutron drip line

The present study focuses on the deformation of neutron-rich nuclei near the neutron drip line. The nuclei of interest include 28O, 42Si, 58Ca, 80Ni, 100Kr, 122Ru, 152Ba, 166Sm, and 176Er. The relativistic Hartree - Bogoliubov (RHB) approach with effective density-dependent point coupling is utilized to investigate the triaxial deformation, and Skyrme - Hartree - Fock + Bardeen - Cooper - Schrieffer is used to analyze the axial deformation. The study aimed to understand the interplay between nuclear forces, particle interactions, and shell structure to gain insights into the unique behavior of neutron-rich nuclei. Despite these nuclei containing magic numbers, their shapes are still affected by the nucleons' collective behavior and energy levels. As the number of neutrons increases, the shape smoothly transitions from spherical to triaxial and then to prolate. The axial deformation analysis confirmed the results of the triaxial deformation analysis using the RHB method. An imbalance in the number of protons and neutrons can affect pairing energy, where extra neutrons can reduce overall pairing energy, and protons can disrupt the nucleon pairing due to stronger Coulomb repulsion between them.

Semiclassical Equivalence of Two White Dwarf Models as Ground States of the Relativistic Hartree–Fock and Vlasov–Poisson energies

AbstractWe are concerned with the semi-classical limit for ground states of the relativistic Hartree–Fock energies (HF) under a mass constraint, which are considered as the quantum mean-field model of white dwarfs (Lenzmann and Lewin in Duke Math J 152:257–315, 2010). In Jang and Seok (Kinet Relat Models 15:605–620, 2022), fermionic ground states of the relativistic Vlasov–Poisson energy (VP) are constructed as a classical mean-field model of white dwarfs, and are shown to be equivalent to the classical Chandrasekhar model. In this paper, we prove that as the reduced Planck constant $$\hbar $$ ħ goes to the zero, the $$\hbar $$ ħ -parameter family of the ground energies and states of (HF) converges to the fermionic ground energy and state of (VP) with the same mass constraint.

Nuclear Matter and Finite Nuclei: Recent Studies Based on Parity Doublet Model

In this review, we summarize recent studies on nuclear matter and finite nuclei based on parity doublet models. We first construct a parity doublet model (PDM), which includes the chiral invariant mass m0 of nucleons together with the mass generated by the spontaneous chiral symmetry breaking. We then study the density dependence of the symmetry energy in the PDM, which shows that the symmetry energy is larger for smaller chiral inavariant mass. Then, we investigate some finite nuclei by applying the Relativistic Continuum Hartree–Bogoliubov (RCHB) theory to the PDM. We present the root-mean-square deviation (RMSD) of the binding energies and charge radii, and show that m0=700 MeV is preferred by the nuclear properties. Finally, we modify the PDM by adding the isovector scalar meson a0(980), and show that the inclusion of the a0(980) enlarges the symmetry energy of the infinite nuclear matter.

Pseudo-Spin Symmetry and the Hints for Unstable and Superheavy Nuclei

The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the π-meson and ρ-tensor (ρ-T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta (l˜). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high-l˜ orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the ρ-T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics.

Study of Shape Evolution and Ground State Properties of Even-Even Tellurium Isotopic Mass Chain by using Relativistic Hartree Bogoliubov framework

Study of Shape Evolution and Ground State Properties of Even-Even Tellurium Isotopic Mass Chain by using Relativistic Hartree Bogoliubov framework

Neutron star core-crust transition and the crustal moment of inertia in the nonlinear relativistic Hartree approximation* *Supported in part by the National Natural Science Foundation of China (11775049, 12375112)

We investigate the effects of the σ meson mass ( ), symmetry energy, and slope of the symmetry energy on the neutron star core-crust transition density and the crustal moment of inertia ( ) in the nonlinear relativistic Hartree approach (RHA), which includes vacuum polarization. Although the core-crust transition density ( ), pressure ( ), and neutron star radius (R), which are all dependent on the symmetry energy, contribute to determining , we find that changing only the slope of symmetry energy within a reasonable range is not sufficient to reach % to achieve the large glitches of the Vela pulsar. However, since all three factors ( , , and R) increase with the increase in through scalar vacuum polarization, adjusting can easily achieve %.

Odd-even shape staggering and kink structure of charge radii of Hg isotopes by the deformed relativistic Hartree–Bogoliubov theory in continuum

We examined the shape staggering of relative charge radii in 180−186Hg isotopes, which was first measured in 1977 and recently confirmed using advanced spectroscopy techniques. To understand the nuclear structure underlying this phenomenon, we employed the deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc). Our analysis revealed that the shape staggering can be attributed to nuclear shape transition in the Hg isotopes. Specifically, we demonstrated that prolate shapes of 181,183,185Hg lead to an increase in the charge radii compared to oblate shapes of 180,182,184,186Hg isotopes. We explained the nuclear shape staggering in terms of the evolution of occupation probability (OP) of ν1i13/2, ν1h9/2, π1h9/2, and π3s1/2 states. Additionally, we clarified the kink structure of the charge radii in the Hg isotopes near N=126 magic shell does not come from the change of the OP of π1h9/2 state, but mainly by the increase of the OPs of ν1i11/2 and ν2g9/2 states.

Relativistic Hartree–Fock chiral Lagrangians with confinement, nucleon finite size and short-range effects

Relativistic Hartree–Fock chiral Lagrangians with confinement, nucleon finite size and short-range effects

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.

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation, pairing correlations and continuum in a unified way. In order to consider the triaxial deformation, the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space. In order to take the pairing correlations into account and treat the continuum properly, by using the Dirac Woods–Saxon basis, which has correct asymptotic behavior, the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved. The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented. Taking an axially deformed nucleus 24Ne and a triaxially deformed nucleus 76Ge as examples, the numerical checks are performed. A weakly bound nucleus 112Ge is taken as an example to carry out the necessary converge checks for the numerical parameters. In addition, the ground-state properties of even–even germanium isotopes are investigated. The evolutions of two-neutron separation energy, deformation, root-mean-square radii and density distribution with mass number are analyzed. The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed. It is found that the neutron drip line is extended from 114Ge to 118Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.

Effective Dynamics of Extended Fermi Gases in the High-Density Regime

We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the semiclassical scaling, and we consider a class of initial data describing zero-temperature states. In the non-relativistic case we prove that, as the density goes to infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation, for short macroscopic times. In the case of relativistic dispersion, we show convergence of the many-body evolution to the relativistic Hartree equation for all macroscopic times. With respect to previous work, the rate of convergence does not depend on the total number of particles, but only on the density: in particular, our result allows us to study the quantum dynamics of extensive many-body Fermi gases.

Quasielastic charged-current neutrino-nucleus scattering with relativistic nuclear models

Charged-current neutrino-nucleus scattering is studied in the quasielastic region with various relativistic nuclear models that include the relativistic Hartree, the nonlinear $\ensuremath{\sigma}$, the quark-meson coupling, and the chiral quark-meson coupling models. Theoretical results at several kinematics are compared with experimental data measured from MiniBooNE, T2K, MicroBooNE, and SciBooNE. While the theoretical double-differential cross sections in terms of the kinetic energy and polar angle of outgoing muon describe the T2K data well, the single-differential cross sections in terms of energy loss and the total cross sections of incident neutrino energy do not properly describe MiniBooNE, MicroBooNE, and SciBooNE data. Additionally, differences from the relativistic nuclear models are examined in detail by comparing with the experimental data. In particular, the MiniBooNE data are not consistent with MicroBooNE and SciBooNE data, where the incident neutrino energies are below 1 GeV.

Strong correlation of the neutron star core-crust transition density with the σ-meson mass via vacuum polarization

We study the neutron star core-crust transition density ρt with the inclusion of the vacuum polarization in the dielectric function in the nonlinear relativistic Hartree approach (RHAn). It is found that the strong correlation between the ρt and the scalar meson mass mσ strikingly overwhelms the uncertainty of the nuclear equation of state in the RHAn models, in contrast to the usual awareness that ρt is predominantly sensitive to the isovector nuclear potential and symmetry energy. The accurate extraction of ρt through the future gravitational wave measurements can thus provide a strong constraint on the longstanding uncertainty of mσ, which is of significance to better infer the vacuum property. As an astrophysical implication, it suggests that the correlation between ρt and mσ is very favorable to reconcile the difficulty in reproducing the large crustal moment of inertia for the pulsar glitches with the well constrained symmetry energy.

Can sub-GeV dark matter coherently scatter on the electrons in the atom?

A novel detection of sub-GeV dark matter is proposed in the paper. The electron cloud is boosted by the dark matter and emits an electron when it is dragged back by the heavy nucleus, namely the coherent scattering of the electron cloud of the atom. The survey in the x-ray diffraction shows that the atomic form factors are much more complex than the naive consideration. The results of the relativistic Hartree–Fock (RHF) method give non-trivial shapes of the atoms. The detailed calculation of the recoil of the electron cloud, the kinetics, the fiducial cross section and the corresponding calculation of detection rate are given analytically. The numerical results show that the limits of the RHF form factors are much more stringent than the recoil of a single electron, almost 4 orders stronger, and also give tight limitations compared to the Migdal effect below about several hundred MeV. The physical picture and the corresponding results are promising and need further exploration.

Microscopic study of shape variation across even–even mass chain of cadmium isotopes

The ground state shapes and properties of even–even [Formula: see text]Cd isotopes have been studied in the framework of relativistic Hartree–Bogoliubov model with two effective interactions that are density-dependent meson exchange and point coupling. The theoretical results on the binding energies, charge radii and two neutron separation energies are presented in this paper in comparison to experimental data and a reasonable agreement is found between the two. Both the interactions predict spherical to axially prolate, prolate to triaxial, triaxial to prolate and prolate to spherical transitions in cadmium isotopic mass chain. In addition, the present calculations confirm the existence of shape coexistence observed in [Formula: see text]Cd. The comparison of calculated ground state properties with the results based on PC-PK1 functional shows that PC-PK1 employed in the deformed relativistic Hartree–Bogoliubov theory in continuum has the lowest root mean square deviation for average binding energies and two neutron separation energies.

Nuclear Bubble Configuration in Heavy-Ion Collisions

We study the effects of a bubble configuration in a nucleus on heavy-ion collisions at a few tens and hundreds A MeV. We first investigate the bubble structure of 206Hg using the relativistic continuum Hartree–Bogoliubov theory and then study the 206Hg + 208Pb and 206Hg+206Hg reactions using the DaeJeon–Boltzmann–Uehling–Uhlenbeck (DJBUU) transport model. To see the role of the bubble structure, we consider the maximum density of the produced nuclear matter, directed flow of neutrons and protons, and π−/π+ ratio. We observe that the maximum density is smaller with a bubble nucleus, and the directed flow of nucleons and π−/π+ ratio may depend on the bubble structure.

Octupole shape phase transitions and critical points in neutron rich actinides

The evolution of octupole shapes and shape phase transitions in neutron rich actinides is studied within the covariant density functional framework. Octupole constrained energy surfaces, and spectroscopic observables of four isotopic chains of: Cm, Cf, Fm and No with neutron numbers 186le N le 200 are analysed using a collective quadrupole–octupole Hamiltonian (QOCH). The parameters of the Hamiltonian are determined by axially reflection-asymmetric relativistic Hartree–Bogoliubov calculations based on the energy density functional DD-PC1, and a finite-range pairing interaction. The results suggest quantum phase transitions from non-octupole to octupole deformed shapes and to octupole vibrations with increasing neutron number. ^{288}Cm is possibly close to the critical point of a simultaneous phase transition from spherical to prolate deformed and from non-octupole to stable octupole deformed configurations.

Structure and decay chain of fermium isotopes using relativistic mean-field approach

In this paper, we have analyzed the ground state structural properties of fermium-isotopes in the mass range [Formula: see text] within the relativistic mean-field with NL3[Formula: see text] and Relativistic Hartree–Bogoliubov approach with DD-ME2 parameter sets. The bulk properties, such as binding energy, root mean-square charge radius, quadruple deformation parameter, chemical potentials, two-neutron separation energy and differential two- neutron separation energy, are estimated for the above Fm- isotopic chain. All the calculated observables are compared with finite range droplet model (FRDM) predictions and experimental data wherever available. The analysis predicts the existence of shell closure in the neutron-rich region of the isotopic chain at [Formula: see text]. The decay properties such as the [Formula: see text]-decay energy and corresponding half-life for three decay chains i.e. [Formula: see text]Fm, [Formula: see text]Fm and [Formula: see text]Fm are studied. Six different empirical formulae, namely; Viola-Seaborg, Royer, modified B. Alex Brown, Parkhomenko–Sobiczewski, Universal decay law and modified universal decay law are employed to ascertain the numerical dependency of the half-life for each decay energy. A comparative study of [Formula: see text]-values and half-lives for these decay chains gives a good signature of the calculated results. The half-life calculations of three decay chains suggest that [Formula: see text]Pu, [Formula: see text]Pu, [Formula: see text]Pu are shell closure nuclei having maximum half-lives, whereas [Formula: see text]Fm, [Formula: see text]Fm and [Formula: see text]Fm are shell stabilized with lower half-lives.

Semi-bubble structure of superheavy nuclei

The nuclear structure properties of heavy and superheavy nuclei lying at the extremes of charge, especially [Formula: see text], and their density profiles have been explored using the relativistic Hartree–Bogoliubov in axial symmetry and the Skyrme–Hartree–Fock–Bogoliubov framework in transformed harmonic oscillator basis. In this study, we found that the semi-bubble (reduced central density) structure is mainly driven by Coulomb repulsion which stabilizes the nuclei either by pushing the nuclear matter in the surface region or by shape deformation. The shell effect is found maximum in spherical symmetric nuclei as the vanishing fission barrier in Liquid Drop formula indicates that the shell correction energy is responsible for the stabilization of these nuclei.

Microscopic description of even–even medium-mass tellurium isotopes within the projected shell model

The low-lying energy levels, B(E2) transition probabilities and g-factors of even–even medium-mass tellurium isotopes have been studied by employing the projected shell model (PSM) approach. The oblate ground state deformations are taken in this study that were predicted in previous relativistic Hartree Bogoliubov mean field study. The low-lying yrast and yrare states are reproduced well in these calculations. The energy and configuration of yre states are also predicted. The experimental B(E2) values and their systematics with neutron number are reproduced well in the medium-mass Te isotopes. The experimental data are available for [Formula: see text]-factors of 2[Formula: see text] states of [Formula: see text]Te isotopes which is in line with these calculations. The enhancement of g-factors at spin I = 6[Formula: see text] in all the Te isotopes considered may be attributable to the alignment of protons in [Formula: see text] subshell. Furthermore, the reduction of g-factors at spin [Formula: see text] in [Formula: see text]Te and [Formula: see text] in [Formula: see text]Te may be attributable to the alignment of neutrons in the [Formula: see text] subshell. The 8[Formula: see text] states of [Formula: see text]Te are envisaged to be of [Formula: see text] nature and in [Formula: see text]Te these states are found to be of [Formula: see text] nature.