Nucleon effective masses are studied in the framework of the Brueckner-Hartree-Fock many-body approach at finite temperature. Self-consistent calculations using the Argonne $V_{18}$ interaction including microscopic three-body forces are reported for varying temperature and proton fraction up to several times the nuclear saturation density. Our calculations are based on the exact treatment of the center-of-mass momentum instead of the average-momentum approximation employed in previous works. We discuss in detail the effects of the temperature together with those of the three-body forces, the density, and the isospin asymmetry. We also provide an analytical fit of the effective mass taking these dependencies into account. The temperature effects on the cooling of neutron stars are briefly discussed based on the results for betastable matter.
We construct a new class of phenomenological equations of state for homogeneous matter for use in simulations of hot and dense matter in local thermodynamic equilibrium. We construct a functional form which respects experimental, observational and theoretical constraints on the nature of matter in various density and temperature regimes. Our equation of state matches (i) the virial coefficients expected from nucleon-nucleon scattering phase shifts, (ii) experimental measurements of nuclear masses and charge radii, (iii) observations of neutron star radii, (iv) theory results on the equation of…
We present a simple calculation of the nucleon self-energy in nuclear matter at finite temperature in a relativistic framework, using the real time thermal field theory. The imaginary parts of one-loop graphs are identified with discontinuities across the unitary and the Landau cuts. We find that in general both the cuts contribute significantly to the spectral function in the region of (virtual) nucleon mass usually considered, even though the unitary cut is ignored in the literature. Also our relativistic spectral function differs from the one in non-relativistic approximation, used in some …
The spectral function of rho meson in hot/dense hadronic matter is studied by taking into account the nucleon-loop on quantum hadrondynamics model level. Different from the hot pion gas effect which changes the spectral function slightly, the nucleon-antinucleon polarization (Dirac sea) makes the spectral function very sharp and shifted towards the low invariant mass region significantly due to the decreasing effective nucleon mass.
A consistent Hartree-Fock study of the equation of state (EOS) of asymmetric nuclear matter at finite temperature has been performed using realistic choices of the effective, density dependent nucleon-nucleon (NN) interaction, which were successfully used in different nuclear structure and reaction studies. Given the importance of the nuclear symmetry energy in the neutron star formation, EOS's associated with different behaviors of the symmetry energy were used to study hot asymmetric nuclear matter. The slope of the symmetry energy and nucleon effective mass with increasing baryon density wa…
A semiphenomenological approach to the nucleon self-energy in nuclear matter at finite temperatures is followed. It combines elements of Thermo Field Dynamics for the treatment of finite temperature with a model for the self-energy, which evaluates the second order diagrams taking the needed dynamics of the NN interaction from experiment. The approach proved to be accurate at zero temperature to reproduce Im(Sigma) and other properties of nucleons in matter. In the present case we apply it to determine Im(Sigma) at finite temperatures. An effective NN cross section is deduced which can be easi…
By using the Nikiforov-Uvarov method, the hyper-radial Schrodinger equation is analytically solved, in which the real modified potential is employed at finite temperature and baryon chemical potential. The eigenvalue of energy and corresponding wave function are obtained in the isotropic and anisotropic media in hot and dense media. The present results show that the binding energy of nucleon and some heavy baryon decrease strongly in hot medium and decreases slightly with increasing baryon chemical potential. In addition, binding energy for each baryon is more bound in an anisotropic medium in…
We apply the variational theory for fermions at finite temperature and high density, developed in an earlier paper, to symmetric nuclear matter and pure neutron matter. This extension generalizes to finite temperatures, the many body technique used in the construction of the zero temperature Akmal-Pandharipande-Ravenhall equation of state. We discuss how the formalism can be used for practical calculations of hot dense matter. Neutral pion condensation along with the associated isovector spin longitudinal sum rule is analyzed. The equation of state is calculated for temperatures less than 30 M…
Modifications of Delta(1232) and nucleon spectral functions at finite temperature and baryon density are evaluated in terms of resonant scattering off thermal pions, as well as a renormalization of the vacuum Delta-width including vertex corrections. The interactions are based on effective Lagrangians of pions and baryon resonances, with underlying parameters (coupling constants and form factors) determined by the elastic pi N scattering phase shift in the isobar channel, and by empirical decay branchings of excited resonances. Pion modifications are included via interactions in a pion gas, as…
Neutrinos play an important role in compact star astrophysics: neutrino-heating is one of the main ingredients in core-collapse supernovae, neutrino-matter interactions determine the composition of matter in binary neutron star mergers and have among others a strong impact on conditions for heavy element nucleosynthesis and neutron star cooling is dominated by neutrino emission except for very old stars. Many works in the last decades have shown that in dense matter medium effects considerably change the neutrino-matter interaction rates, whereas many astrophysical simulations use analytic app…
We develop a variational theory of hot nuclear matter in neutron stars and supernovae. It can also be used to study charged, hot nuclear matter which may be produced in heavy-ion collisions. This theory is a generalization of the variational theory of cold nuclear and neutron star matter based on realistic models of nuclear forces and pair correlation operators. The present approach uses microcanonical ensembles and the variational principle obeyed by the free energy. In this paper we show that the correlated states of the microcanonical ensemble at a given temperature $T$ and density $ρ$ can …
In this contribution I summarize and discuss the results of the bulk thermodynamic characteristics, meson and nucleon structure in hot matter obtained in the framework of a chiral quark-meson theory. A hybrid NJL model is used in which a Dirac sea of quarks is combined with a Fermi sea of quarks or of nucleons. In the model mesons are described as collective $\bar qq$ excitations and the nucleon appears as a baryon-number-one soliton of $N_c$ valence quarks coupled to both Dirac and Fermi sea. According to the model at some critical density and/or temperature phase transitions from nucleons to…
We calculate the mean free path in a hot and dense nuclear environment for a fermionic dark matter particle candidate in the $\sim$GeV mass range interacting with nucleons via scalar and vector effective couplings. We focus on the effects of density and temperature in the nuclear medium in order to evaluate the importance of the final state blocking in the scattering process. We discuss qualitatively possible implications for opacities in stellar nuclear scenarios, where dark matter may be gravitationally accreted.
To describe nuclear matter at high temperature and high baryon density appropriate for RHIC and LHC, an effective theory is proposed. Three developments underlie the effective theory: (1) relativistic mean field theory description of nuclear matter with mesons mediating interactions; (2) topological soliton description of the nucleon with hidden local symmetry; (3) phenomenological knowledge of nucleon-nucleon interaction and nucleon structure obtained from elastic NN scattering at c.m. energies of hundreds of GeV. When these developments are combined together, a gauged linear sigma-model with…
Internal Nucleon Properties and the Equation of State of Ultra-Dense Matter
Institut de Physique des 2 infinis de Lyon, CNRS/IN2P3, Université de Lyon, Université Claude Bernard Lyon 1（里昂无穷大物理研究所，法国国家科学研究中心/法国国家核子与粒子物理研究所，里昂大学，克洛德·贝尔纳里昂大学）；International Research Laboratory on Nuclear Physics and Astrophysics, Michigan State University and CNRS（核物理与天体物理学国际研究实验室，密歇根州立大学和法国国家科学研究中心）
A set of microscopic, covariant density-functional, and non-relativistic Skyrme-type equations of state is employed to study the structure of purely nucleonic neutron stars at finite temperature. After examining the agreement with presently available astrophysical observational constraints, we find that the magnitude of thermal effects depends on the nucleon effective mass as well as on the stiffness of the cold equation of state. We evidence a fairly small but model-dependent effect of finite temperature on stellar stability that is correlated with the relative thermal pressure inside the sta…
We obtain the RPA summed one-meson exchange potential between nucleons in symmetric nuclear matter at zero temperature, from a model which includes $ρ$, $σ$, $ω$ and $π$ mesons. The behavior of rho mesons inside the medium is first discussed using different schemes to extract a finite contribution from the vacuum polarization. These schemes give qualitatively different results for the in-medium rho mass. The results are discussed in connection with the non-renormalizability of the model. We next study the modified potential as density increases. In the intermediate distance range, it is qualit…
The effect of nucleon-nucleon correlations in symmetric nuclear matter at finite temperature is studied beyond BCS theory. Starting from a Hartree-Fock description of nuclear matter with the Gogny effective interaction, we add correlations corresponding to the formation of preformed pairs and scattering states above the superfluid critical temperature within the in-medium T-matrix approach, which is analogous to the Nozieres-Schmitt-Rink theory. We calculate the critical temperature for a BEC superfluid of deuterons, of a BCS superfluid of nucleons, and in the crossover between these limits. T…
We study the role of pions in hot dense matter encountered in astrophysics. We find that strong interactions enhance the number density of negatively charged pions and that this enhancement can be calculated reliably for a relevant range of density and temperature using the virial expansion. We assess the influence of pions and muons on the equation of state (EOS) and weak interaction rates in hot dense matter. We find that thermal pions increase the proton fraction and soften the EOS. We also find that charged current weak reactions involving pions and muons $\barν_μ+μ^- \rightarrow π$ and $ν…
Fluctuations are included in a chiral nucleon-meson model within the framework of the functional renormalization group. The model, with parameters fitted to reproduce the nuclear liquid-gas phase transition, is used to study the phase diagram of QCD. We find good agreement with results from chiral effective field theory. Moreover, the results show a separation of the chemical freeze-out line and chiral symmetry restoration at large baryon chemical potentials.
In a sufficiently hot and dense astrophysical environment the rate of the triple-alpha (3alpha) reaction can increase greatly over the value appropriate for helium burning stars owing to hadronically induced de-excitation of the Hoyle state. In this paper we use a statistical model to evaluate the enhancement as a function of temperature and density. For a density of $10^6 gm cm^{-3}$ enhancements can exceed a factor of one-hundred. In high temperature/density situations, the enhanced 3alpha rate is a better estimate of this rate and should be used in these circumstances. We then examine the e…
A model to study the sound wave in hot dense matter created in heavy ion collisions by jet is proposed.The preliminary data of jet shape analysis of PHENIX Collaboration for all centralities and two directions is well explained in this model. Then the wavelength of the sound wave, the natural frequency of the hot dense matter and the speed of sound wave are estimated from the fit.
We present a relativistic in-medium three-body equation to study correlations in hot and dense quark matter. The equation is solved for a zero-range force for parameters close to the phase transition of QCD.
Impact of the in-medium modified nucleon weak and electromagnetic form factors on the neutrino mean free path in dense matter is studied by considering both the weak and electromagnetic interactions of neutrinos with the constituents of the matter. A relativistic mean field model and the quark-meson coupling model are respectively adopted for the in-medium effective nucleon mass and nucleon form factors. We find that the cross sections of neutrino scattering in cold nuclear medium decreases when the in-medium modification of the nucleon weak and electromagnetic form factors are taken into acco…
By using the Furnstahl, Serot and Tang's model, the effect of density dependence of the effective nucleon-nucleon-rho-meson (NN-rho) coupling on the liquid-gas phase transition in hot asymmetric nuclear matter is investigated. A limit pressure p_lim has been found. We found that the liquid-gas phase transition cannot take place if p>p_lim. The binodal surface for density dependent NN-rho coupling situation is addressed.
We discuss the role of kaon-nucleon and nucleon-nucleon correlations in kaon condensation in dense matter. Correlations raise the threshold density for kaon condensation, possibly to densities higher than those encountered in stable neutron stars.
Recent developments in the theory of pure neutron matter and experiments concerning the symmetry energy of nuclear matter, coupled with recent measurements of high-mass neutron stars, now allow for relatively tight constraints on the equation of state of dense matter. We review how these constraints are formulated and describe the implications they have for neutron stars and core-collapse supernovae. We also examine thermal properties of dense matter, which are important for supernovae and neutron star mergers, but which cannot be nearly as well constrained at this time by experiment. In addit…
Within the Dirac-Brueckner-Hartree-Fock approach, using the Bonn potentials, we investigate the properties of dense, asymmetric nuclear matter and apply it to neutron stars. In the actual calculations of the nucleon self-energies and the energy density of matter, we study in detail the validity of an angle-averaged approximation and an averaging of the total momentum squared of interacting two-nucleons in nuclear matter. For practical use, we provide convenient parametrizations for the equation of state for symmetric nuclear matter and pure neutron matter. We also parametrize the nucleon self-…
Effects of the in-medium modifications of nucleon form factors on neutrino interaction in dense matter are presented by considering both the weak and electromagnetic interactions of neutrinos with the constituents of the matter. A relativistic mean field and the quark-meson coupling models are respectively adopted for the effective nucleon mass and in-medium nucleon form factors. We calculate the cross-section of neutrino scattering as well as the neutrino mean free path. We found the cross sections of neutrino scattering in cold nuclear medium decreases when the in-medium modifications of the…
A Bayesian analysis of the possible behaviors of the dense matter equation of state informed through recent LIGO-Virgo as well as NICER measurements reveals that all the present observations are compatible with a fully nucleonic hypothesis for the composition of dense matter, even in the core of the most massive pulsar PSR J0740+6620. Under the hypothesis of a nucleonic composition, we extract the most general behavior of the energy per particle of symmetric matter and density dependence of the symmetry energy, compatible with the astrophysical observations as well as our present knowledge of …
We consider deuteron formation in hot and dense nuclear matter close to equilibrium and evaluate the life-time of the deuteron fluctuations within the linear response theory. To this end we derive a generalized linear Boltzmann equation where the collision integral is related to equilibrium correlation functions. In this framework we then utilize finite temperature Green functions to evaluate the collision integrals. The elementary reaction cross section is evaluated within the Faddeev approach that is suitably modified to reflect the properties of the surrounding hot and dense matter.
Effects of neutrino charge radius and magnetic moment constraints obtained from the astrophysical observations and reactor experiments, as well as in-medium modifications of the weak and electromagnetic nucleon form factors of the matter on the neutrino electroweak interaction with dense matter, are estimated. We use a relativistic mean-field model for the in-medium effective nucleon mass and quark-meson coupling model for nucleon form factors. We analyze the neutrino scattering cross section and mean free path in cold nuclear matter. We find that the increase of the cross section relative to …
The strongly isospin-dependent tensor force leads to short-range correlations (SRC) between neutron-proton (deuteron-like) pairs much stronger than those between proton-proton and neutron-neutron pairs. As a result of the short-range correlations, the single-nucleon momentum distribution develops a high-momentum tail above the Fermi surface. Because of the strongly isospin-dependent short-range correlations, in neutron-rich matter a higher fraction of protons will be depleted from its Fermi sea and populate above the Fermi surface compared to neutrons. This isospin-dependent nucleon momentum d…
We review efforts to describe the approach to chiral symmetry restoration in neutron matter from the low-energy realization of QCD, chiral effective field theory.
The dilaton-limit fixed point and the scaling properties of hadrons in the close vicinity of the fixed point in dense baryonic matter uncovered in hidden local symmetry implemented with spontaneously broken scale symmetry are shown to reveal a surprisingly intricate interplay, hitherto unsuspected, between the origin of the bulk of proton mass and the renormalization-group flow of the ω-nuclear interactions. This rends a theoretical support to the previous (phenomenologically) observed correlation between the dropping nucleon mass and the behavior of the ω-nuclear interactions in dense matter …
Within the framework of a multi-phase transport model, we study the equation of state and pressure anisotropy of the hot dense matter produced in central relativistic heavy ion collisions. Both are found to depend on the hadronization scheme and scattering cross sections used in the model. Furthermore, only partial thermalization is achieved in the produced matter as a result of its fast expansion.
The initial conditions in heavy-ion collisions are calculated in many different frameworks. The importance of nucleon position fluctuations within the nucleus and sub-nucleon structure has been established when modeling initial conditions for input to hydrodynamic calculations. However, there remain outstanding puzzles regarding these initial conditions, including the measurement of the near equivalence of the elliptical $v_{2}$ and triangular $v_{3}$ flow coefficients in ultra-central 0-1% Pb+Pb collisions at the LHC. Recently a calculation termed MAGMA incorporating gluonic hot spots via two…
The low-energy neutron-Sigma^- interactions determine, in part, the role of the strange quark in dense matter, such as that found in astrophysical environments. The scattering phase shifts for this system are obtained from a numerical evaluation of the QCD path integral using the technique of Lattice QCD. Our calculations, performed at a pion mass of m_pi ~ 389 MeV in two large lattice volumes, and at one lattice spacing, are extrapolated to the physical pion mass using effective field theory. The interactions determined from QCD are consistent with those extracted from hyperon-nucleon experim…
Nucleon-nucleon short-range correlations (SRCs) induce a high momentum tail (HMT) in the single-nucleon momentum distribution function $n_{ǩ}^J(ρ,δ)$ in cold neutron-rich matter. While there are clear experimental evidences that the SRC/HMT effects are different for neutrons and protons and their strengths depend strongly on the isospin asymmetry of finite nuclei mostly based on electron-nucleus scattering experiments, much less is known experimentally about the SRC/HMT effects in the dense neutron-rich matter. To facilitate further explorations of SRC/HMT effects in dense neutron-rich matter …
In these lectures we discuss the uses of effective field theory in studying dense hadronic matter. We focus on two regimes in the phase diagram. At low baryon density nucleons can be described as non-relativistic point particles interacting via short range forces. Interesting effects arise because of the large nucleon-nucleon scattering length. At very large density QCD matter can be described in terms of quarks and gluons. Unusual many body effects arise because of long range gluons fields, and because of the way color and flavor get entangled in the superconducting state.
The description of excitations in hot and dense (hadronic) matter is discussed with emphasis on the use of correlation functions as a common framework for comparing different model (and QCD lattice) calculations with each other. Typical regimes of applicability of hadronic approaches are assessed, together with possibilities to confront them with experiment. We also elaborate on recent developments to relate baryonic in-medium effects to chiral symmetry restoration.
We study the $ρ$-meson spectral function in hot nuclear matter by taking into account the isospin-symmetric pion and the nucleon loops within the quantum hadrodynamics (QHD) model as well as using an effective chiral SU(3) model. The spectral function of the $ρ$ meson is studied in the mean field approximation (MFA) as well as in the relativistic Hartree (RHA) approximation. The inclusion of the nucleon loop considerably changes the $ρ$-meson spectral function. Due to a larger mass drop of $ ρ$ meson in the RHA, it is seen that the spectral function shifts towards the low invariant mass region…
Neutrino processes in dense matter play a key role in the dynamics, deleptonization and early cooling of hot protoneutron stars formed in the gravitational collapse of massive stars. Here we calculate neutrino mean free paths from neutrino-hyperon interactions in dense matter containing hyperons. Significant contributions to the neutrino opacity arise from scattering and absorption reactions involving the sigma minus particle. The estimates given here emphasise the need for (a) opacities which incoparate many-body effects in a multi-component mixture, and (b) new calculations of thermal and le…
We estimate the electrical and thermal conductivities of hot and dense hadronic matter in the relaxation time approximation of the Boltzmann equation. We estimate the thermodynamical quantities of hot and dense hadronic matter within the ambit of the excluded volume hadron resonance gas model. The relaxation time for all the hadrons is estimated assuming the constant cross section with uniform as well as mass dependent hard-core radius. We compare our results with various existing results. Finally we give an estimate of electrical and thermal conductivities in the context of heavy ion collisio…
The vector manifestation (VM) was proposed as a novel manifestation of chiral symmetry in which the massless vector meson becomes the chiral partner of pion. In this write-up, I briefly summarize the following main ingredients to formulate the VM in hot and/or dense matter: Effective field theory (EFT) based on the hidden local symmetry; Wilsonian matching between the EFT and QCD; Intrinsic thermal and/or dense effects.
Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University（复旦大学现代物理研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学理论核物理上海研究中心）；Department of Physics and Astronomy, East Texas A&M University（东德克萨斯农工大学物理与天文学系）；College of Physics, East China Normal University（华东师范大学物理学院）
The dispersion relation of $ρ$ meson in both timelike and spacelike regimes in hot and dense nuclear medium is analyzed and compared with $σ$ meson based on the quantum hadrodynamics model. The pole and screening masses of $ρ$ and $σ$ are discussed. The behavior of screening mass of $ρ$ is different from that of $σ$ due to different Dirac- and Fermi-sea contributions at finite temperature and density.
The description of nuclear matter bulk properties in the framework of quark-based hadron models in curved unit cells is extended to finite temperature. We discuss the analogy and interplay of density and temperature effects in this formulation and study, as an application, the temperature and density dependence of chiral vacuum properties in the Nambu-Jona-Lasinio (NJL) model.
We evaluate thermodynamical quantities and transport coefficients of a dense and hot hadronic matter based on an event generator URASiMA (Ultra-Relativistic AA collision Simulator based on Multiple Scattering Algorithm). The statistical ensembles in equilibrium with fixed temperature and chemical potential are generated by imposing periodic boundary condition to the simulation of URASiMA, where energy density and baryon number density is conserved. Achievement of the thermal equilibrium and the chemical equilibrium are confirmed by the common value of slope parameter in the energy distribution…
Previous studies have indicated that the peak of the quarkonium entropy at the deconfinement transition can be related to the entropic force which would induce the dissociation of heavy quarkonium. In this paper, we study the entropic force in a rotating hot and dense medium using AdS/CFT correspondence. It turns out that the inclusion of angular velocity increases the entropic force thus enhancing quarkonium dissociation, while chemical potential has the same effect. Furthermore, the results imply that the quarkonium dissociates easier in rotating medium compared to static case.
We explore the abundance of light clusters in asymmetric nuclear matter at subsaturation density. With increasing density, binding energies and wave functions are modified due to medium effects. The method of Albergo, Costa, Costanzo and Rubbino (ACCR) for determining the temperature and free nucleon density of a disassembling hot nuclear source from fragment yields is modified to include, in addition to Coulomb effects and flow, also effects of medium modifications of cluster properties, which become of importance when the nuclear matter density is above 10$^{-3}$ fm$^{-3}$. We show how the a…
Chiral restoration phase transition in hot and/or dense hadronic matter is discussed in terms of the BR scaling based on chiral symmetry and scale anomaly of QCD. The precise connection between the scalar field that figures in the trace anomaly and the sigma field that figures in the linear $σ$ model is established. It is suggested that in hot and/or dense medium, the nonlinear $σ$ model linearizes with the help of a dilaton to a linear $σ$ model with medium-renormalized constants. The relevance of Georgi's vector symmetry and/or Weinberg's ``mended symmetry" in chiral restoration is pointed o…
We study here hot nuclear matter in the quark meson coupling (QMC) model which incorporates explicitly quark degrees of freedom, with quarks coupled to scalar and vector mesons. The equation of state of nuclear matter including the composite nature of the nucleons is calculated at finite temperatures. The calculations are done taking into account the medium-dependent bag constant. Nucleon properties at finite temperatures as calculated here are found to be appreciably different from the value at $T=0.$
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 modifications of hadronic masses and decay widths at finite temperature and baryon density are investigated using a phenomenological model of hadronic interactions in the Relativistic Hartree Approximation. We consider an exhaustive set of hadronic reactions and vector meson decays to estimate the photon emission from hot and dense hadronic matter. The reduction in the vector meson masses and decay widths is seen to cause an enhancement in the photon production. It is observed that the effect of $ρ$-decay width on photon spectra is negligible. The effects on dilepton production from pion a…
We study the behavior of the rho^0 vector mass during the hadronic phase of an ultra-relativistic heavy-ion collision at finite temperature. We show that scattering with the most abundant particles during this stage, namely, pions, kaons and nucleons, leads to an overall temperature dependent, decrease of the rho^0 intrinsic mass at rest, compared to its value in vacuum. The main contributions arise from s-channel scattering with pions through the formation of a_1 resonances as well as with nucleons through the formation of even parity, spin 3/2 [N(1720)] and 5/2 [$Δ$(1905)] nucleon resonances…
We calculate neutrino processes involving two nucleons at subnuclear densities using chiral effective field theory. Shorter-range noncentral forces reduce the neutrino rates significantly compared with the one-pion exchange approximation currently used in supernova simulations. For densities rho < 10^{14} g cm^{-3}, we find that neutrino rates are well constrained by nuclear interactions and nucleon-nucleon scattering data. As an application, we calculate the mean-square energy transfer in scattering of a neutrino from nucleons and find that collision processes and spin-dependent mean-field ef…
