Relativistic Mean-field Approximation Research Articles

Kink of the nuclear charge radius isotope shift and overlaps of the neutron and proton orbitals in lead

Within the relativistic mean field approximation, we analyse the kink effect (KE) in the evolution of the charge radius isotope shift of lead isotopes as a function of the neutron number N. We show that if the interactions between neutron and proton states responsible for the KE are assumed to be proportional either to the overlaps of their corresponding wave functions or to those of their corresponding probability density distributions, it is not possible, by themselves, to explain the KE. However, we find that the small component of the single-particle Dirac spinors plays a relevant role in the kink formation. By considering the contribution of the N−126 valence neutrons to the proton central potential, we can explain the generation of the KE and why neutrons in the 1i11/2 orbital are more kinky than when they are in the 2g9/2 orbital.

Insights into Neutron Star Equation of State by Machine Learning

Due to its powerful capability and high efficiency in big data analysis, machine learning has been applied in various fields. We construct a neural network platform to constrain the behaviors of the equation of state of nuclear matter with respect to the properties of nuclear matter at saturation density and the properties of neutron stars. It is found that the neural network is able to give reasonable predictions of parameter space and provide new hints into the constraints of hadron interactions. As a specific example, we take the relativistic mean field approximation in a widely accepted Walecka-type model to illustrate the feasibility and efficiency of the platform. The results show that the neural network can indeed estimate the parameters of the model at a certain precision such that both the properties of nuclear matter around saturation density and global properties of neutron stars can be saturated. The optimization of the present modularly designed neural network and extension to other effective models is straightforward.

Relativistic effects on the kink of nuclear charge radii in lead

The kink in the nuclear charge radii of lead isotopes is studied in the relativistic mean field approximation framework, using the parameter set NL3∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document}. Within this approach, it is shown that the small component of the single-particle Dirac spinors plays an essential role in the kink formation through its effects on the single-particle central potential. This is because the structure of this potential in terms of the σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}-scalar and ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}-vector fields and the contributions of the small component to the scalar and nucleon densities have opposite signs. The impact of the spin-orbit interaction of the valence neutrons on the kink, through its effects on their wave functions, is very small for 1i states but significant for 2g states. Due to relativistic contributions, the effects on the kink of neutrons in the valence levels of a spin-orbit doublet with j=l+1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=l+1/2$$\\end{document} and j=l-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=l-1/2$$\\end{document} are rather different from each other, even in the limit case of neglecting their spin-orbit interaction.

Isoscalar giant resonances of <inline-formula><tex-math id="M1">\begin{document}$^{{\bf{18}}}_{{\boldsymbol{\Lambda\Lambda}}}{\bf{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.png"/></alternatives></inline-formula> in relativistic approach

The interactions between hyperon-nucleon and hyperon-hyperon have been an important topic in strangeness nuclear physics, which play an important role in understanding the properties of hypernuclei and equation of state of strangeness nuclear matter. It is very difficult to perform a direct scattering experiment of the nucleon and hyperon because the short lifetime of the hyperon. Therefore, the hyperon-nucleon interaction and the hyperon-hyperon interaction have been mainly investigated experimentally by <inline-formula><tex-math id="M4">\begin{document}$\gamma$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M4.png"/></alternatives></inline-formula> spectroscopy of single-<inline-formula><tex-math id="M5">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M5.png"/></alternatives></inline-formula> hypernuclei or double-<inline-formula><tex-math id="M6">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M6.png"/></alternatives></inline-formula> hypernuclei. There are also many theoretical methods developed to describe the properties of hypernuclei. Most of these models focus mostly on the ground state properties of hypernuclei, and have given exciting results in producing the banding energy, the energy of single-particle levels, deformations, and other properties of hypernuclei. Only a few researches adopting Skyrme energy density functionals is devoted to the study of the collective excitation properties of hypernuclei. In present work, we have extended the relativistic mean field and relativistic random phase approximation theories to study the collective excitation properties of hypernuclei, and use the methods to study the isoscalar collective excited state properties of double <inline-formula><tex-math id="M7">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M7.png"/></alternatives></inline-formula> hypernuclei. First, the effect of <inline-formula><tex-math id="M8">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M8.png"/></alternatives></inline-formula> hyperons on the single-particle energy of <sup>16</sup>O and <inline-formula><tex-math id="M9">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M9.png"/></alternatives></inline-formula> are discussed in the relativistic mean field theory, the calculations are performed within TM1 parameter set and related hyperon-nucleon interaction, and hyperon-hyperon interaction. We find that it gives a larger attractive effect on the <inline-formula><tex-math id="M10">\begin{document}${{\mathrm{s}}}_{1/2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M10.png"/></alternatives></inline-formula> state of proton and neutron, while gives a weaker attractive effect on the state around Fermi surface. The self-consistent relativistic random phase approximation is used to study the collectively excited state properties of hypernucleus <inline-formula><tex-math id="M11">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M11.png"/></alternatives></inline-formula>. The isoscalar giant monopole resonance and quadrupole resonance are calculated and analysed in detail, we pay more attention to the effect of the inclusion of <inline-formula><tex-math id="M12">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M12.png"/></alternatives></inline-formula> hyperons on the properties of giant resonances. Comparing with the strength distributions of <sup>16</sup>O, changes of response function of <inline-formula><tex-math id="M13">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M13.png"/></alternatives></inline-formula> are evidently found both on the isoscalar giant monopole resonance and quadrupole resonance. It is shown that the difference comes mainly from the change of Hartree energy of particle-hole configuration and the contribution of the excitations of <inline-formula><tex-math id="M14">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M14.png"/></alternatives></inline-formula> hyperons. We find that the hyperon-hyperon residual interactions have small effect on the monopole resonance function and quadrupole response function in the low-energy region, and have almost no effect on the response functions in the high-energy region.

The Non-Linear Derivative (NLD) model for the in-medium hyperons & antihyperons dynamics

The in-medium properties of hyperons and antihyperons are studied with the Non-Linear Derivative (NLD) model and focus is made on the momentum dependence of strangeness optical potentials[1]. The NLD model is based on the Relativistic Mean Field (RMF) approximation to Relativistic Hadrodynamics (RHD) approach of nuclear systems, but it incorporates an explicit momentum dependence of mean-fields. The extension of the NLD model to the baryon and antibaryon octet is based on SU(6) and G-parity arguments. It is demonstrated that with a proper choice of momentum cut-offs, the Λ and Σ optical potentials are consistent with recent studies of the chiral effective field theory and Ξ optical potentials are consistent with Lattice-QCD calculations, over a wide momentum region. We also present NLD predictions for the in-medium momentum dependence of antiΛ, antiΣ and antiΞ hyperons. This work is important for future experimental studies, like CBM, PANDA at FAIR and is relevant to nuclear astrophysics as well.

Isotopic shift in magic nuclei within relativistic mean-field formalism

The ground-state properties such as binding energy, root-mean-square radius, pairing energy, nucleons density distribution, symmetry energy, and single-particle energies are calculated for the isotopic chain of Ca, Sn, Pb, and Z = 120 nuclei. The recently developed G3 and IOPB-I forces along with the DD-ME1 and DD-ME2 sets are used in the analysis employing the relativistic mean-field approximation. To locate the magic numbers in the superheavy region and to explain the observed kink at neutron number N = 82 for Sn isotopes, a three-point formula is used to see the shift of the observable and other nuclear properties in the isotopic chain. Unlike the electronic configuration, due to strong spin-orbit interaction, the higher spin orbitals are occupied earlier than the lower spin, causing the possible kink at the neutron magic numbers. We find peaks at the known neutron magic number with the confirmation of sub-shell, shell closure respectively at N = 40, 184 for Ca and 304120.

Relativistic mean-field corrections for interactions of dark matter particles with nucleons

We investigate the interactions of weakly interacting massive particles (WIMPS) with nucleons in nuclear medium by taking into account the effect of nuclear dynamics. We derive the nonrelativistic effective operators starting from the relativistic mean-field approximation. Certain interactions receive non-negligible corrections, which may significantly change the sensitivities of WIMP-nucleus scattering cross section to these effective operators.

Momentum dependent mean-fields of (anti)hyperons

We investigate the in-medium properties of hyperons and anti-hyperons in the framework of the Non-Linear Derivative (NLD) model. We focus on the momentum dependence of in-medium strangeness optical potentials. The NLD model is based on the simplicity of the well-established Relativistic Mean-Field (RMF) approximation, but it incorporates an explicit momentum dependence on a field-theoretical level. The extension of the NLD model to the (anti)baryon-octet is formulated in the spirit of SU(6) and G-parity arguments. It is shown that with an appropriate choice of momentum cut-offs the Λ, Σ and Ξ optical potentials are consistent with recent studies of the chiral effective field theory and Lattice-QCD calculations over a wide momentum region. In addition, we present NLD predictions for the in-medium momentum dependence of Λ‾-, Σ‾- and Ξ‾-hyperons. This work is important for future experimental studies such as CBM, PANDA at the Facility for Antiproton and Ion Research (FAIR). It is relevant for nuclear astrophysics too.

Momentum dependent mean-fields of hyperons & antihyperons

The in-medium properties of hyperons and antihyperons are studied with the Non-Linear Derivative (NLD) model and focus is made on the momentum dependence of strangeness optical potentials. The NLD model is based on the Relativistic Mean Field (RMF) approximation to Relativistic Hadrodynamics (RHD) approach of nuclear systems, but it incorporates an explicit momentum dependence of mean-fields. The extension of the NLD model to the baryon and antibaryon octet is based on SU(6) and G-parity arguments. It is demonstrated that with a proper choice of momentum cut-offs, the Λ and Σ optical potentials are consistent with recent studies of the chiral effective field theory(χ -EFT) and optical potentials are consistent with Lattice-QCD calculations, over a wide momentum region. We also present NLD predictions for the in-medium momentum dependence of ∧¯, ∑¯ and Ξ¯ hyperons. This work is important for future experimental studies, like CBM, PANDA at FAIR and is relevant to nuclear astrophysics as well.

Effect of Fock terms on nuclear symmetry energy based on Lorentz-covariant decomposition of nucleon self-energies

Using the Lorentz-covariant decomposition of nucleon self-energies with relativistic mean-field approximation, we study the effect of Fock terms on the density dependence of nuclear symmetry energy, E sym. It is found that the Fock contribution suppresses the potential part of E sym at higher densities, and the constraint from the heavy-ion collision data is in favor of the present result including exchange terms with the cutoff parameters given by the CD-Bonn potential. In addition, not only the isovector-vector (ρ) meson but also the isoscalar (σ, ω) and π mesons give influence on the potential part of E sym through the exchange diagram.

On the nature of the quantum chromodynamics phase transition in hybrid compact stars

AbstractIn this contribution, we study the nature of the quantum chromodynamics (QCD) phase transition in hybrid compact stars. In our approach, we consider a microscopic hadron–quark hybrid equation of state (EoS) to describe the structure of compact stars composed of a quark core and a hadronic shell assuming a structural first‐order phase transition at their interface. Our primary purpose in this contribution is to delineate, for a hybrid compact star, the relevant ingredients of their EoSs that simultaneously have the required stiffness and satisfy the constraints of thermodynamics (stability conditions on the free energy, accordance with the laws of thermodynamics and Gibbs' criteria for phase equilibrium). The quark matter structural description is based on the standard MIT bag model, and for the hadron phase modeling, we consider a statistical model for the EoS, which consists of an ensemble of interacting nucleons in statistical equilibrium. In the calculations, the relativistic mean field approximation is used, and the parameters of the approach are taken from experimental data and from nuclear structure calculations. Moreover, exclusion volume effects are implemented in a thermodynamically consistent way so that the transition to uniform nuclear matter can be described in a physically coherent way. We investigate the implications on the structure of a compact hybrid star of considering a Bag constant dependence on the nuclear density, as well as subsidiary aspects of the nature of QCD phase transition as the Gibbs and Maxwell construction realizations of the first‐order deconfinement phase transition inside a compact star and observational signals.

A microscopic study of spin-polarized asymmetric hot nuclear matter within the static fluctuation approximation (SFA)

In this work, the thermodynamic properties of spin-polarized asymmetric hot nuclear matter are studied within the Static Fluctuation Approximation (SFA). Specifically, the energy per unit volume, pressure, entropy per unit volume, and specific heat capacity are determined as functions of density up to 0.6 fm−3, and temperature up to 80 MeV. Also, the effects of the asymmetry and spin-polarization parameters on these quantities are explored. The main input in the formalism is the Urbana V14 nucleon–nucleon potential. It is found that these parameters have significant effects on the thermodynamic properties at high densities or low temperatures where quantum features become pronounced. As expected, the entropy results show that the system is more ordered when polarized or for large values of the asymmetry parameter. The quadratic dependence of the energy on the asymmetry and spin-polarization parameters is confirmed at different densities and temperatures. The results are compared to those obtained with different approaches, such as the lowest-order constrained variational method, the conventional variational method, and the relativistic mean-field approximation. It is found that the present results are consistent with those.

Model of multiple Dirac eikonal scattering of protons by nuclei

The model of multiple Dirac eikonal scattering (MDES) of incident proton by target-nucleus nucleons is developed, in which new expressions for the elastic [Formula: see text]-scattering amplitudes are obtained from the multiple scattering Watson series with employing the eikonal approximation for the Dirac propagators of the free proton motion between successive scattering acts on nucleons. Based on this model, calculations for the complete set of observables of the elastic [Formula: see text] and [Formula: see text]Pb at 800[Formula: see text]MeV have been performed, using proton–nucleon amplitudes determined from the phase analysis and the nucleon densities obtained from describing the target-nucleus structure in the relativistic mean-field approximation. A comparison has been made of the results of these calculations with analogous calculations on the basis of the Glauber multiple diffraction theory.

Light clusters in warm stellar matter: Explicit mass shifts and universal cluster-meson couplings

In-medium modifications of light cluster properties in warm stellar matter are studied within the relativistic mean-field approximation. In-medium effects are included by introducing an explicit binding energy shift analytically calculated in the Thomas-Fermi approximation, supplemented with a phenomenological modification of the cluster couplings to the $\sigma$ meson. A linear dependence on the $\sigma$ meson is assumed for the cluster mass, and the associated coupling constant is fixed imposing that the virial limit at low density is recovered. The resulting cluster abundances come out to be in reasonable agreement with constraints at higher density coming from heavy ion collision data. Some comparisons with microscopic calculations are also shown.

Direct Urca Processes Involving Proton 1S0 Superfluidity in Neutron Star Cooling**Supported by the National Natural Science Foundation of China under Grant Nos. 11447165, 11373047, 11404336 and U1731240, Youth Innovation Promotion Association, CAS under Grant No. 2016056, and the Development Project of Science and Technology of Jilin Province under Grant No. 20180520077JH

A detailed description of the baryon direct Urca processes A: , B: and C: related to the neutron star cooling is given in the relativistic mean field approximation. The contributions of the reactions B and C on the neutrino luminosity are calculated by means of the relativistic expressions of the neutrino energy losses. Our results show that the total neutrino luminosities of the reactions A, B and C within the mass range (1.603–2.067) M⊙ ((1.515–1.840) M⊙ for TM1 model) for GM1 model are larger than the corresponding values for neutron star without hyperons. Furthermore, although the neutrino emissivity of the reaction A is suppressed with the appearance of the proton 1S0 superfluid, the contribution of the reactions B and C can still quicken a massive neutron star cooling. In particular, the reaction C in PSR J1614-2230 and J0348+0432 is not suppressed by the proton 1S0 superfluid due to the higher threshold density of the reaction C, which will further speed up the two pulsars cooling.

Shape transitions in odd-mass γ -soft nuclei within the interacting boson-fermion model based on the Gogny energy density functional

The interacting boson-fermion model (IBFM), with parameters determined from the microscopic Hartree-Fock-Bogoliubov (HFB) approximation, based on the parametrization D1M of the Gogny energy density functional (EDF), is employed to study the structural evolution in odd-mass $\gamma$-soft nuclei. The deformation energy surfaces of even-even nuclei, single-particle energies and occupation probabilities of the corresponding odd-mass systems have been obtained within the constrained HFB approach. Those building blocks are then used as a microscopic input to build the IBFM Hamiltonian. The coupling constants of the boson-fermion interaction terms are taken as free parameters, fitted to reproduce experimental low-lying spectra. The diagonalization of the IBFM Hamiltonian provides the spectroscopic properties for the studied odd-mass nuclei. The procedure has been applied to compute low-energy excitation spectra and electromagnetic transition rates, in the case of the $\gamma$-soft odd-mass systems $^{129-137}$Ba, $^{127-135}$Xe, $^{129-137}$La and $^{127-135}$Cs. The calculations provide a reasonable agreement with the available experimental data and agree well with previous results based on the relativistic mean-field approximation.

Instability of baryonic matter in relativistic mean-field models

In this article we evaluate some of the properties of strongly interacting hadronic matter using non-linear Walecka model in relativistic mean-field approximation. We find that due to the coupling of baryons and bosons, baryonic matter develops instability that is characterised by the appearance of baryonic state with negative entropy density. In the region of instability of baryonic matter we find no evidence of negative in-medium mass of baryons or any signal of kaon condensation. Further we find that this instability of baryonic matter can halt the process of first order phase transition from strongly interacting hadronic matter consisting of coupled baryons and bosons to a weakly interacting quark–gluon plasma phase.

Particle Ratios from Strongly Interacting Hadronic Matter

We calculate the particle ratios K+/π+, K-/π-, and Λ/π- for a strongly interacting hadronic matter using nonlinear Walecka model (NLWM) in relativistic mean field (RMF) approximation. It is found that interactions among hadrons modify K+/π+ and Λ/π- particle ratios, while K-/π- is found to be insensitive to these interactions.

Hybrid Stars in the Framework of NJL Models

We compute models for the equation of state (EoS) of the matter in the cores of hybrid stars. Hadronic matter is treated in the non-linear relativistic mean-field approximation, and quark matter is modeled by three-flavor local and non-local Nambu−Jona-Lasinio (NJL) models with repulsive vector interactions. The transition from hadronic to quark matter is constructed by considering either a soft phase transition (Gibbs construction) or a sharp phase transition (Maxwell construction). We find that high-mass neutron stars with masses up to [Formula: see text] may contain a mixed phase with hadrons and quarks in their cores, if global charge conservation is imposed via the Gibbs conditions. However, if the Maxwell conditions is considered, the appearance of a pure quark matter core either destabilizes the star immediately (commonly for non-local NJL models) or leads to a very short hybrid star branch in the mass-radius relation (generally for local NJL models).

Symmetry energy and neutron star properties in the saturated Nambu–Jona-Lasinio model

In this work, we adopt the Nambu-Jona-Lasinio (NJL) model that ensures the nuclear matter saturation properties to study the density dependence of the symmetry energy. With the interactions constrained by the chiral symmetry, the symmetry energy shows novel characters different from those in conventional mean-field models. First, the negative symmetry energy at high densities that is absent in relativistic mean-field (RMF) models can be obtained in the RMF approximation by introducing a chiral isovector-vector interaction, although it would be ruled out by the neutron star (NS) stability. Second, with the inclusion of the isovector-scalar interaction the symmetry energy exhibits a general softening at high densities even for the large slope parameter of the symmetry energy. The NS properties obtained in the present NJL model can be in accord with the observations. The NS maximum mass obtained with various isovector-scalar couplings and momentum cutoffs is well above the $2M_\odot$, and the NS radius obtained well meets the limits extracted from recent measurements. In particular, the significant reduction of the canonical NS radius occurs with the moderate decrease of the slope of the symmetry energy.