A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the Self-Consistent Green's Function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD-BONN and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner--Hartree--Fock approximation, the variational approach and the virial expansion.
In this paper the equation of state of hot neutron matter is calculated. Involving the Oppenheimer-Volkov-Tolman equation global parameters of a neutron star at the finite temperature are obtained. The objective of our work was to study the influence of the temperature on the main parameters of a neutron star.
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.
In this chapter, we investigate the structure and composition of hot neutron star matter and proto-neutron stars. Such objects are made of baryonic matter that is several times denser than atomic nuclei and tens of thousands times hotter than the matter in the core of our Sun. The relativistic finite-temperature Green function formalism is used to formulate the expressions that determine the properties of such matter in the framework of the density-dependent mean field approach. Three different sets of nuclear parametrizations are used to solve the many-body equations and to determine the mode…
The possible exotic nuclear properties in the neutron-rich Ca, Ni, Zr, and Sn isotopes are explored with the continuum Skyrme Hartree-Fock-Bogoliubov theory formulated with the Green's function method. The available experimental two-neutron separation energies $S_{\rm 2n}$ and one-neutron separation energies $S_{\rm n}$ are well reproduced. Much shorter drip lines predicted by $S_{\rm n}$ are obtained compared with those by $S_{\rm 2n}$. The systematic studies of the neutron pairing energies $-E_{\rm pair}$ shown that values of the odd-$A$ nuclei are much smaller in comparison with those of th…
Properties of rapidly rotating hot neutron stars within Brueckner theory
INFN, Sezione di Catania, Dipartimento di Fisica, Universitá di Catania（意大利国家核物理研究所卡塔尼亚分部物理学系卡塔尼亚大学）；The Research Center for Theoretical Physics, Science School, Qingdao University of Technology（青岛理工大学理学院理论物理研究中心）；Institute of Modern Physics, Key Laboratory of Nuclear Physics and Ion-Beam Application, MOE, Fudan University（复旦大学现代物理研究所核物理与离子束应用教育部重点实验室）；School of Mathematics and Physics, University of Geosciences（中国地质大学数学与物理学院）
We calculate the neutrino mean free path and the Equation of State of pure neutron matter at finite temperature within a selfconsistent scheme based on the Brueckner--Hartree--Fock approximation. We employ the nucleon-nucleon part of the recent realistic baryon-baryon interaction (model NSC97e) constructed by the Nijmegen group. The temperatures considered range from 10 to 80 MeV. We report on the calculation of the mean field, the residual interaction and the neutrino mean free path including short and long range correlations given by the Brueckner--Hartree--Fock plus Random Phase Approximati…
Structure of cold and hot dense matter at subnuclear densities is investigated by quantum molecular dynamics (QMD) simulations. Obtained phase diagrams show that the density of the phase boundaries between the different nuclear structures decreases with increasing temperature due to the thermal expansion of nuclear matter region.
We have considered a hot neutron star with a quark core, a mixed phase of quark-hadron matter, and a hadronic matter crust and have determined the equation of state of the hadronic phase and the quark phase, we have then found the equation of state of the mixed phase under the Gibbs conditions. Finally, we have computed the structure of hot neutron star with the quark core and compared our results with those of the neutron star without the quark core. For the quark matter calculations, we have used the MIT bag model in which the total energy of the system is considered as the kinetic energy of…
We calculate the scattering rate of low energy neutrinos in hot and dense neutron matter encountered in neutrons stars and supernova in the hydrodynamic regime. We find that the Brillouin peak, associated with the sound mode, and the Rayleigh peak, associated with the thermal diffusion mode, dominate the dynamic structure factor. Although the total scattering cross section is constrained by the compressibility sum rule, the differential cross-section calculated using the hydrodynamic response function differs from results obtained in approximate treatments often used in astrophysics such as ra…
The single-particle spectral functions in asymmetric nuclear matter are computed using the ladder approximation within the theory of finite temperature Green's functions. The internal energy and the momentum distributions of protons and neutrons are studied as a function of the density and the asymmetry of the system. The proton states are more strongly depleted when the asymmetry increases while the occupation of the neutron states is enhanced as compared to the symmetric case. The self-consistent Green's function approach leads to slightly smaller energies as compared to the Brueckner Hartre…
The neutrino mean free path in neutron matter under a strong magnetic field is evaluated for the inelastic scattering reaction and studied as a function of the neutron matter density in the range $0.05 \leq ρ\leq 0.4$ fm$^{-3}$ for several temperatures up to 30 MeV and magnetic field strengths B=0 G, $10^{18}$ G and $2.5\times 10^{18}$ G. Polarized neutron matter is described within the non--relativistic Brueckner--Hartree--Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential supplemented with the Urbana IX three-nucleon force. Explicit expressions of the cross section per unit …
We have studied the spin polarized hot neutron matter in the presence of strong magnetic field. In this work, using the lowest order constrained variational method at finite temperature and employing $AV_{18}$ nuclear potential, some thermodynamic properties of spin polarized neutron matter such as spin polarization parameter, free energy, equation of state and effective mass have been calculated. It has been shown that the strong magnetic field breaks the symmetry of the free energy, leading to a magnetized equilibrium state. We have found that the equation of state becomes stiffer by increas…
We consider hot accretion disk outflows from black hole - neutron star mergers in the context of the nucleosynthesis they produce. We begin with a three dimensional numerical model of a black hole - neutron star merger and calculate the neutrino and antineutrino fluxes emitted from the resulting accretion disk. We then follow the element synthesis in material outflowing the disk along parameterized trajectories. We find that at least a weak r-process is produced, and in some cases a main r-process as well. The neutron-rich conditions required for this production of r-process nuclei stem direct…
Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a reference, the energies and widths of single-particle resonant states are extracted from the density of states without any ambiguity. As an example, the energies and widths for single-neutron resonant states in $^{120}$Sn are compared with those obtained by the scattering phase-shift method, the analytic continuation in the coupling constant approach, the rea…
We construct a new isentropic equation of state (EOS) at finite temperature "CRover" on the basis of the hadron-quark crossover at high density. By using the new EOS, we study the structure of hot neutron stars at birth with the typical lepton fraction ($Y_l=0.3-0.4$) and the typical entropy per baryon ($S=1-2$). Due to the gradual appearance of quark degrees of freedom at high density, the temperature T and the baryon density at the center of the hot neutron stars with the hadron-quark crossover are found to be smaller than those without the crossover by a factor of 2 or more. Typical energy …
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…
We study the properties of hot beta-stable nuclear matter using equations of state derived within the Brueckner-Hartree-Fock approach at finite temperature including consistent three-body forces. Simple and accurate parametrizations of the finite-temperature equations of state are provided. The properties of hot neutron stars are then investigated within this framework, in particular the temperature dependence of the maximum mass. We find very small temperature effects and analyze the interplay of the different contributions.
Using the momentum-dependent MDI effective interaction for nucleons, we have studied the transition density and pressure at the boundary between the inner crust and liquid core of hot neutron stars. We find that their values are larger in neutrino-trapped neutron stars than in neutrino-free neutron stars. Furthermore, both are found to decrease with increasing temperature of a neutron star as well as increasing slope parameter of the nuclear symmetry energy, except that the transition pressure in neutrino-trapped neutron stars for the case of small symmetry energy slope parameter first increas…
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 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…
The present thesis aims at studying the properties of symmetric nuclear and pure neutron matter from a Green's functions point of view, including two-body and three-body chiral forces. An extended self-consistent Green's function formalism is defined to consistently incorporate three-body forces in the many-body calculations. The effect of three-nucleon interactions is included via the construction of a dressed two-body density dependent force. This is obtained performing an average of the leading order three-body terms in the chiral effective field theory expansion. The dressed force correspo…
We review the equation of state (EoS) models covering a large range of temperatures, baryon number densities and electron fractions presently available on the \textsc{CompOSE} database. These models are intended to be directly usable within numerical simulations of core-collapse supernovae, binary neutron star mergers and proto-neutron star evolution. We discuss their compliance with existing constraints from astrophysical observations and nuclear data. For a selection of purely nucleonic models in reasonable agreement with the above constraints, after discussing the properties of cold matter,…
In the present work we study the effects of strongly quantizing magnetic fields and finite temperature on the properties of inner crusts of hot neutron stars. The inner crust of a neutron star contains neutron-rich nuclei arranged in a lattice and embedded in gases of free neutrons and electrons. We describe the system within the Wigner-Seitz (WS) cell approximation. The nuclear energy is calculated using Skyrme model with SkM* interaction. To isolate the properties of nuclei we follow the subtraction procedure presented by Bonche, Levit and Vautherin, within the Thomas-Fermi approximation. We…
The FSU2H equation-of-state model, originally developed to describe cold neutron star matter with hyperonic cores, is extended to finite temperature. Results are presented for a wide range of temperatures and lepton fractions, which cover the conditions met in protoneutron star matter, neutron star mergers and supernova explosions. It is found that the temperature effects on the thermodynamical observables and the composition of the neutron star core are stronger when the hyperonic degrees of freedom are considered. An evaluation of the temperature and density dependence of the thermal index l…
The prediction of the equation of state of hot, dense nuclear matter is one of the most complicated and interesting problems in nuclear astrophysics. At the same time, knowledge of it is the basic ingredient for some of the most interesting studies. In the present work, we concentrate our study on the construction of the equation of state of hot, dense nuclear matter, related mainly to the interior of the neutron star. We employ a theoretical nuclear model, which includes momentum-dependent interaction among the nucleons, along with the \textit{state-of-the-art} microscopic calculations. Therm…
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 …
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.
The symmetry energy for nuclear matter and its relation to the neutron skin in finite nuclei is discussed. The symmetry energy as a function of density obtained in a self-consistent Green function approach is presented and compared to the results of other recent theoretical approaches. A partial explanation of the linear relation between the symmetry energy and the neutron skin is proposed. The potential of several experimental methods to extract the neutron skin is examined.
Ab initio Green's function theory of superfluid neutron matter
Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学）；Institut für Kernphysik（核物理研究所）；PRISMA++ Cluster of Excellence（PRISMA++卓越集群）；Università degli Studi di Milano（米兰大学）；Dipartimento di Fisica “Aldo Pontremoli”（阿尔多·蓬特莫利物理系）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）
We study how the frequencies and damping times of oscillations of a newly born, hot proto-neutron star depend on the physical quantities which characterize the star quasi-stationary evolution which follows the bounce. Stellar configurations are modeled using a microscopic equation of state obtained within the Brueckner-Hartree-Fock, nuclear many-body approach, extended to the finite-temperature regime. We discuss the mode frequency behaviour as function of the lepton composition, and of the entropy gradients which prevail in the interior of the star. We find that, in the very early stages, gra…
The neutron and proton single-particle spectral functions in asymmetric nuclear matter fulfill energy weighted sum rules. The validity of these sum rules within the self-consistent Green's function approach is investigated. The various contributions to these sum rules and their convergence as a function of energy provide information about correlations induced by the realistic interaction between the nucleons. These features are studied as a function of the asymmetry of nuclear matter.
In order to study structure of proto-neutron stars and those in subsequent cooling stages, it is of great interest to calculate inhomogeneous hot and cold nuclear matter in a variety of phases. The finite-temperature Hartree-Fock-Bogoliubov (FT-HFB) theory is a primary choice for this purpose, however, its numerical calculation for superfluid (superconducting) many-fermion systems in three dimensions requires enormous computational costs. To study a variety of phases in the crust of hot and cold neutron stars, we propose an efficient method to perform the FT-HFB calculation with the three-dime…
We study the role of chiral nuclear forces on the propagation of neutrinos in hot neutron matter. In particular, we analyze the convergence of the dynamical structure factor and the neutrino mean free path with the order of the power counting of the chiral forces, as well as the role of the regulator cut-off of these forces in the determination of these quantities. Single-particle energies and chemical potentials needed to calculate the dynamical structure factor are obtained within the Brueckner--Hartree--Fock approximation extended to finite temperature. Our results show that the dynamical s…
We have studied the properties of hot $^{234,236}$U and $^{240}$Pu nuclei in the framework of relativistic mean field formalism. The recently developed FSUGarnet and IOPB-I parameter sets are implemented for the first time to deform nuclei at finite temperature. The results are compared with the well-known NL3 set. The said isotopes are structurally important because of the thermally fissile nature of $^{233,235}$U and $^{239}$Pu as these nuclei ($^{234,236}$U and $^{240}$Pu) are formed after the absorption of a thermal neutron, which undergoes fission. Here, we have evaluated the nuclear prop…
As we go from center toward the surface of a neutron star, the state of baryonic matter changes from the de-confined quark-gluon to a mixed phase of quark and hadronic matter, and a thin crust of hadronic matter. For the quark matter, within MIT bag model, the total energy density of the system is the kinetic energy for non-interacting quarks plus a bag constant. In this article first we have considered a density dependent bag constant obtained using the recent experimental results of CERN SPS on the formation of a quark-gluon plasma. For calculations of the hadron phase, we use the lowest ord…
Over the last few years, the detection of gravitational waves from binary neutron star systems has rekindled our hopes for a deeper understanding of the unknown nature of ultradense matter. In particular, gravitational wave constraints on the tidal deformability of a neutron star can be translated into constraints on several neutron star properties using a set of universal relations. Apart from binary neutron star mergers, supernova explosions are also important candidates for the detection of multimessenger signals. Such observations may allow us to impose significant constraints on the bindi…
Knockout nuclear reactions, in which a nucleon is removed from a nucleus as a result of the collision with another nucleus, have been widely used as an experimental tool, both to populate isotopes further removed from stability, and to obtain information about the single-particle nature of the nuclear spectrum. In order to fully exploit the experimental information, theory is needed for the description of both the structure of the nuclei involved, and the dynamics associated with the nucleon removal mechanisms. The standard approach, using theoretical shell-model spectroscopic factors for the …
It is shown that the experimentally observed decrease of the nuclear symmetry energy with the increasing centrality or the excitation energy in isotopic scaling analyses of heavy-ion reactions can be well understood analytically within a degenerate Fermi gas model. The evolution of the symmetry energy is found to be mainly due to the variation in the freeze-out density rather than temperature. The isoscaling analyses are useful for probing the interaction part of the nuclear symmetry energy, provided that both the freeze-out temperature and density of the fragments can be inferred simultaneous…
The X-ray spectra of the neutron stars located in the centers of supernova remnants Cas A and HESS J1731-347 are well fit with carbon atmosphere models. These fits yield plausible neutron star sizes for the known or estimated distances to these supernova remnants. The evidence in favor of the presence of a pure carbon envelope at the neutron star surface is rather indirect and is based on the assumption that the emission is generated uniformly by the entire stellar surface. Although this assumption is supported by the absence of pulsations, the observational upper limit on the pulsed fraction …
We formulate a new scheme of the Hartree-Fock-Bogoliubov mean-field theory applicable to weakly bound and pair correlated deformed nuclei using the coordinate-space Green's function technique. On the basis of a coupled-channel representation of the quasiparticle wave function expanded in terms of the partial waves, we impose the correct boundary condition of the asymptotically out-going waves on the continuum quasiparticle states. We perform numerical analysis for $^{38}$Mg to illustrate properties of the continuum quasiparticle states and the pair correlation in deformed nuclei near the neutr…
In part one of this paper, we use a non-local extension of the 3-flavor Polyakov-Nambu-Jona-Lasinio model, which takes into account flavor-mixing, momentum dependent quark masses, and vector interactions among quarks, to investigate the possible existence of a spinodal region (determined by the vanishing of the speed of sound) in the QCD phase diagram and determine the temperature and chemical potential of the critical end point. In part two of the paper, we investigate the quark-hadron composition of baryonic matter at zero as well as non-zero temperature. This is of great topical interest fo…
We investigate the adiabatic index $Γ_{\mathrm{th}}$ of hot and dense nuclear matter from chiral effective field theory and find that the results are systematically larger than from typical mean field models. We start by constructing the finite-temperature equation of state from chiral two- and three-nucleon forces, which we then use to fit a class of extended Skyrme energy density functionals. This allows for modeling the thermal index across the full range of densities and temperatures that may be probed in simulations of core-collapse supernovae and neutron star mergers, including the low-d…
Explosive astrophysical systems - such as supernovae or compact star binary mergers - provide conditions where exotic degrees of freedom can be populated. Within the covariant density functional theory of nuclear matter we build several general purpose equations of state which, in addition to the baryonic octet, account for $Δ(1232)$ resonance states. The thermodynamic stability of $Δ$-admixed nuclear matter is investigated in the limiting case of vanishing temperature for charge fractions $Y_Q=0.01$ and $Y_Q=0.5$ and wide ranges of the coupling constants to the scalar and vector mesonic field…
We describe the finite volume effects of CP-odd quantities, such as the neutron electric dipole moment and the anapole moment in the $θ$-vacuum, under different topological sectors. We evaluate the three-point Green's functions for the electromagnetic current in a fixed non-trivial topological sector in order to extract these CP-odd observables. We discuss the role of zero modes in the CP-odd Green's function and show that, in the quenched approximation, there is a power divergence in the quark mass for CP-odd quantities at finite volume.
We have performed three-flavor Boltzmann neutrino transport radiation hydrodynamics simulations covering a period of 3 s after the formation of a protoneutron star in a core-collapse supernova explosion. Our results show that a treatment of charged-current neutrino interactions in hot and dense matter as suggested by Reddy et al. [Phys. Rev. D 58, 013009 (1998)] has a strong impact on the luminosities and spectra of the emitted neutrinos. When compared with simulations that neglect mean field effects on the neutrino opacities, we find that the luminosities of all neutrino flavors are reduced w…
New ab initio constrained extended Skyrme equations of state for simulations of neutron stars, supernovae and binary mergers: II. Thermal response in the suprasaturation density domain
National Institute for Physics and Nuclear Engineering (IFIN-HH)（核物理与核工程国家研究所）
Based on a quasiparticle model for βstable and electrically neutral deconfined matter we address the mass-radius relation of pure quark stars. The model is adjusted to recent hot lattice QCD results for 2 + 1 flavors with almost physical quark masses. We find rather small radii and masses of equilibrium configurations composed of cold deconfined matter, well distinguished from neutron or hybrid stars.
For core-collapse and neutron star merger simulations it is important to have at hand adequate equations of state, describing the underlying dense and hot matter as realistically as possible. Here, we present two newly constructed equation of state (EoS) including the entire baryon octet. Both EoS are compatible with the main constraints from nuclear physics, both experimental and theoretical. One of the EoS is equally describing maximum mass for cold $β$-equilibrated neutron stars of $2 M_\odot$ in agreement with recent observations. The predictions obtained with the new EoS are compared with…
We explore the thermal properties of hot and dense matter using a model that reproduces the empirical properties of isospin symmetric and asymmetric bulk nuclear matter, optical model fits to nucleon-nucleus scattering data, heavy-ion flow data in the energy range 0.5-2 GeV/A, and the largest well-measured neutron star mass of 2 $\rm{M}_\odot$. Results of this model which incorporates finite range interactions through Yukawa type forces are contrasted with those of a zero-range Skyrme model that yields nearly identical zero-temperature properties at all densities for symmetric and asymmetric n…
