Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{sym,4}(ρ)$. Based on two accurately calibrated interactions FSUGold and IU-FSU, our results show that the value of $E_{sym,4}(ρ)$ at normal nuclear matter density $ρ_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $ρ_{0}$. On the other hand, we find that the $E_{sym,4}(ρ)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{sym,4}(ρ)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{sat}(δ)=K_{0}+K_{sat,2}δ^{2}+K_{sat,4}δ^{4}+\mathcal{O}(δ^{6})$ where $δ=(ρ_{n}-ρ_{p})/ρ$ is the isospin asymmetry, and we find that the value of $K_{sat,4}$ is generally small compared with that of the $K_{sat,2}$. In addition, we study the effects of the $E_{sym,4}(ρ)$ on the proton fraction $x_{p}$ and the core-crust transition density $ρ_{t}$ and pressure $P_{t}$ in neutron stars. Interestingly, we find that, compared with the results from the empirical parabolic approximation, including the $E_{sym,4}(ρ)$ contribution can significantly enhance the $x_{p}$ at high densities and strongly reduce the $ρ_{t}$ and $P_{t}$ in neutron stars, demonstrating that the widely used empirical parabolic approximation may cause large errors in determining the $x_{p}$ at high densities as well as the $ρ_{t}$ and $P_{t}$ in neutron stars within the nonlinear relativistic mean field model, consistent with previous nonrelativistic calculations.
We establish a relation between the equation of state (EOS) of nuclear matter and the fourth-order symmetry energy $a_{\rm{sym,4}}(A)$ of finite nuclei in a semi-empirical nuclear mass formula by self-consistently considering the bulk, surface and Coulomb contributions to the nuclear mass. Such a relation allows us to extract information on nuclear matter fourth-order symmetry energy $E_{\rm{sym,4}}(ρ_0)$ at normal nuclear density $ρ_0$ from analyzing nuclear mass data. Based on the recent precise extraction of $a_{\rm{sym,4}}(A)$ via the double difference of the "experimental" symmetry energy…
Recently, we have shown that the continuity equation for the nuclear vector and axial current operators acquires additional terms if the latter depend on the energy transfer. We analyze in detail the electromagnetic single-nucleon four-current operators and verify the validity of the modified continuity equation for all one- and two-nucleon contributions up to fourth order in the chiral expansion. We also derive, for the first time, the leading contribution to the three-nucleon charge operator which appears at this order. Our study completes the derivation of the electroweak nuclear currents t…
We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators…
We present and discuss predictions for a cross section of bulk and single-particle properties in symmetric nuclear matter based on recent high-quality nucleon-nucleon potentials at N3LO and including all subleading three-nucleon forces. We begin with the equation of state and its saturation properties and proceed to the single-nucleon potential. We also explore short-range correlations as seen through the defect function. The various predictions which we present have a common foundation in an internally consistent ab initio approach.
Relativistic energy density functionals have become a standard framework for nuclear structure studies of ground-state properties and collective excitations over the entire nuclide chart. We review recent developments in modeling nuclear weak-interaction processes: charge-exchange excitations and the role of isoscalar proton-neutron pairing, charged-current neutrino-nucleus reactions relevant for supernova evolution and neutrino detectors, and calculation of beta-decay rates for r-process nucleosynthesis.
Measurements of atomic transitions in different isotopes offer key information on the nuclear charge radius. The anticipated high-precision experimental techniques, augmented by atomic calculations, will soon enable extraction of the higher-order radial moments of the charge density distribution. To assess the value of such measurements for nuclear structure research, we study the information content of the fourth radial moment $\rf$ by means of nuclear density functional theory and a multiple correlation analysis. We show that $\rf$ can be directly related to the surface thickness of nuclear …
Adopting the density dependent relativistic mean-field (RMF) and relativistic Hartree-Fock (RHF) approaches, the properties of the nuclear fourth-order symmetry energy $S_4$ are studied within the covariant density functional (CDF) theory. It is found that the fourth-order symmetry energies are suppressed in RHF at both saturation and supranuclear densities, where the extra contribution from the Fock terms is demonstrated, specifically via the isoscalar meson-nucleon coupling channels. The reservation of $S_4$ and higher-order symmetry energies in the nuclear equation of state then affects ess…
This article summarizes our present knowledge about nuclear matter at the highest energy densities and its formation in relativistic heavy ion collisions. We review what is known about the structure and properties of the quark-gluon plasma and survey the observables that are used to glean information about it from experimental data.
The expression for the radial moments $\left\langle r^{n}\right\rangle_{c}$ of the nuclear charge density has been discussed under the plane wave Born approximation (PWBA) method recently, which is significant to investigate the nuclear surface thickness and neutron distribution radius. In this paper, we extend the studies of extracting second-order moment $\left\langle r^{2}\right\rangle_{c}$ and fourth-order moment $\left\langle r^{4}\right\rangle_{c}$ from the Coulomb form factors $|F_{C}(q)|^2$ by the distorted wave Born approximation (DWBA) at the small momentum transfer $ q $ region. Bas…
We briefly review highlights for ultra-relativistic light-heavy collisions (p-Pb, d-Au, 3He-Au, 12C-Au) which display collective evolution, with the same very characteristic features as in the A-A systems.
Based on systematic analyses of several popular non-relativistic energy density functionals with mean-field approximation, we estimate the value of the fourth-order symmetry energy $E_{\text{sym,4}}(ρ)$ at nuclear normal density $ρ_0$ and its density dependence, and explore the correlation between $E_{\text{sym,4}}(ρ_0)$ and other macroscopic quantities of nuclear matter properties. We use the empirical values of some nuclear macroscopic quantities to construct model parameter sets by Monte Carlo method for the conventional Skyrme-Hartree-Fock (SHF) model, the extended Skyrme-Hartree-Fock (eSH…
The relation between the fourth-order symmetry energy $E_{\rm{sym,4}}(ρ_0)$ of nuclear matter at saturation density $ρ_0$ and its counterpart $a_{\rm{sym,4}}(A)$ of finite nuclei in a semiempirical nuclear mass formula is revisited by considering the high-order isospin-dependent surface tension contribution to the latter. We derive the full expression of $a_{\rm{sym,4}}(A)$, which includes explicitly the high-order isospin-dependent surface tension effects, and find that the value of $E_{\rm{sym,4}}(ρ_0)$ cannot be extracted from the measured $a_{\rm{sym,4}}(A)$ before the high-order surface t…
Many probes are proposed to determine the quark-gluon plasma and explore its properties in ultra-relativistic heavy-ion collisions. Some of them are related to initial states of the collisions, such as collective flow, Hanbury-Brown-Twiss (HBT) correlation, chiral magnetic effects and so on. The initial states can come from geometry overlap of the colliding nuclei, fluctuations or nuclear structure with the intrinsic geometry asymmetry. The initial geometry asymmetry can transfer to the final momentum distribution in the aspect of hydrodynamics during the evolution of the fireball. Different f…
This article describes calculations of the yield ratio of anti-particles to the yield of particles ($\bar{p}/p$, $\bar{d}/d$,$\overline{^{3}\mathrm{He}}$/$^{3}$He) in proton-proton and nuclear-nuclear interactions using the self-similarity parameter in the central rapidity region. The used approach is based on the study of relativistic nuclear interactions in the four-velocity space. The results of the calculations are compared with the existing experimental data in a wide center-of-mass energy range ($SPS$, $RHIC$, $LHC$). Within this approach the inclusive spectra of pions and kaons and rati…
We review direct photons in the phenomenology of nuclear collisions at relativistic energies. Direct photons carry information about the space-time evolution of nuclear collisions because the QCD medium is transparent against colorless particles. After a status summary of theoretical and experimental studies, transverse momentum spectra and azimuthal momentum anisotropies of direct photons are studied in the context of the hydrodynamic modeling of relativistic nuclear collisions with emphasis on pre-equilibrium photons. It is implied that pre-equilibrium photons can be as important as thermal …
In this talk we review some of our results for the longitudinal correlations in connection with recent experimental data, in particular for the {\em torque} effect and for the two-particle correlations in pseudorapidity, $C(η_1,η_2)$. The model framework involves event-by-event fluctuations of the initial conditions, followed with 3D viscous hydrodynamic evolution and statistical hadronization.
The exploration of the strong-interaction matter under extreme conditions is one of the main goals of relativistic heavy-ion collisions. We provide some of the main results on the novel properties of quark-gluon plasma, with particular focus given to the strong collectivity and the color opaqueness exhibited by such hot and dense matter produced in high-energy nuclear collisions at RHIC and the LHC.
The quark matter created in relativistic nuclear collisions is interpreted as a nearly-perfect fluid. The recent efforts to explore its finite-density properties in the beam energy scan programs motivate one to revisit the issue of the local rest frame fixing in off-equilibrium hydrodynamics. I first investigate full second-order relativistic hydrodynamics in the Landau and the Eckart frames. Then numerical hydrodynamic simulations are performed to elucidate the effect of frame choice on flow observables in relativistic nuclear collisions. The results indicate that the flow can differ in the L…
Extraction of ground-state nuclear deformations from ultra-relativistic heavy-ion collisions: Nuclear structure physics context
University of York（约克大学）；University of Warsaw（华沙大学）；Michigan State University（密歇根州立大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Duke University（杜克大学）
The penetrating nature of electromagnetic signals makes them suitable probes to explore the properties of the strongly-interacting medium created in relativistic nuclear collisions. We examine the effects of the initial conditions and shear relaxation time on the spectra and flow coefficients of electromagnetic probes, using an event-by-event 3+1D viscous hydrodynamic simulation (MUSIC).
The Interacting Boson Model of nuclear structure is introduced to the unitarity limit. Non relativistic conformal symmetry creates a scale invariant state from which the stationary states of atomic nuclei are obtained. A brief discussion of the nature of the conformal field theory is included along with the BCS-BEC crossover and hydrodynamic properties.
In this dissertation, we have studied the implications of nuclear interaction for nuclear structure and astrophysics within the relativistic mean-field (RMF) model.
We review the equation of state of QCD matter at finite densities. We discuss the construction of the equation of state with net baryon number, electric charge, and strangeness using the results of lattice QCD simulations and hadron resonance gas models. Its application to the hydrodynamic analyses of relativistic nuclear collisions suggests that the interplay of multiple conserved charges is important in the quantitative understanding of the dense nuclear matter created at lower beam energies. Several different models of the QCD equation of state are discussed for comparison.
With the relativistic representation of the nuclear tensor force that is included automatically by the Fock diagrams, we explored the self-consistent tensor effects on the properties of nuclear matter system. The analysis were performed within the density-dependent relativistic Hartree-Fock (DDRHF) theory. The tensor force is found to notably influence the saturation mechanism, the equation of state and the symmetry energy of nuclear matter, as well as the neutron star properties. Without introducing any additional free parameters, the DDRHF approach paves a natural way to reveal the tensor ef…
The direct photon emission model in relativistic nuclear colliders has been improved in recent years for reducing the discrepancy between theoretical estimations and experimental data and for understanding the properties of the QCD matter. In this study, the contribution of pre-equilibrium photons are investigated in addition to those of prompt and thermal photons in the framework of a relativistic hydrodynamic model. The numerical simulations at an LHC energy suggest that the pre-equilibrium photons may be relevant at intermediate transverse momentum near the saturation momentum scale, increa…
I show that the average transverse momentum, $\langle p_t \rangle$, of the hadrons emitted in relativistic nuclear collisions can be used as a ``knob'' to control the strength of the magnetic field induced by the spectator and the participant protons over the overlap region. I thus argue that any observable sensitive to this magnetic field is nontrivially correlated with $\langle p_t \rangle$ at a given collision centrality.
Electron scattering is an effective method to study the nuclear structure. For the odd-$A$ nuclei with proton holes in the outmost orbits, we investigate the contributions of proton holes to the nuclear quadrupole moments $Q$ and magnetic moments $μ$ by the multiple Coulomb scattering and magnetic scattering. The deformed nuclear charge densities are constructed by the relativistic mean-field (RMF) models. Comparing the theoretical Coulomb and magnetic form factors with the experimental data, the nuclear quadrupole moments $Q$ and nuclear magnetic moments $μ$ are investigated. From the electro…
In this paper we present a phenomenological treatment of charm quark energy loss before fragmenting into D mesons and calculate nuclear modification factor, '$R_{AA}$' and azimuthal anisotropy, '$v_2$' of D mesons for lead on lead collision at LHC energy of $\sqrt{s}$=2.76 A TeV.
Anisotropies of hadronic distribution in nuclear collisions are used for determination of properties of the nuclear matter. At the LHC it is important to account for the contribution to the flow due to momentum transferred from hard partons to the quark-gluon plasma.
