The energy of a free gas of neutrons and protons is well known to be approximately isospin parabolic with a negligibly small quartic term of only $0.45$ MeV at the saturation density of nuclear matter $ρ_0=0.16/\rm{fm}^3$. Using an isospin-dependent single-nucleon momentum distribution including a high (low) momentum tail (depletion) with its shape parameters constrained by recent high-energy electron scattering and medium-energy nuclear photodisintegration experiments as well as the state-of-the-art calculations of the deuteron wave function and the equation of state of pure neutron matter near the unitary limit within several modern microscopic many-body theories, we show for the first time that the kinetic energy of interacting nucleons in neutron-rich nucleonic matter has a significant quartic term of $7.18\pm2.52\,\rm{MeV}$. Such a large quartic term has significant ramifications in determining the equation of state of neutron-rich nucleonic matter using both terrestrial and astrophysical observables.
Mean free paths and in-medium scattering cross sections of energetic nucleons in neutron-rich nucleonic matter within the relativistic impulse approximation
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…
Significant progress has been made recently in constraining the isospin-dependent parameters characterizing the SRC (short-range correlation)-modified single-nucleon momentum distribution in neutron-rich nucleonic matter using both experimental data and microscopic model calculations. Using the constrained single-nucleon momentum distribution in a nonlinear relativistic mean field (RMF) model, we study the equation of state (EOS) of asymmetric nucleonic matter (ANM), especially the density dependence of nuclear symmetry energy $E_{\rm{sym}}(ρ)$. Firstly, as a test of the model, the average nuc…
Based on a chiral approach to nuclear matter, we calculate the quartic term in the expansion of the equation of state of isospin-asymmetric nuclear matter. The contributions to the quartic isospin asymmetry energy $A_4(k_f)$ arising from $1π$-exchange and chiral $2π$-exchange in nuclear matter are calculated analytically together with three-body terms involving virtual $Δ(1232)$-isobars. From these interaction terms one obtains at saturation density $ρ_0 = 0.16\,$fm$^{-3}$ the value $A_4(k_{f0})= 1.5\,$MeV, more than three times as large as the kinetic energy part. Moreover, iterated $1π$-exch…
本文用核子物质的一系列势场理论模型研究了原子核和中子星中同位旋不对称性的作用。这些模型的参数是通过拟合均匀块体物质和闭壳层核的性质来确定的。讨论并揭示了重核中子皮厚度、密度为0.1 fm $^{-3}$的β平衡物质压力、密度相同的核对称能导数和中等质量中子星半径之间相关性的原因。考察了原子核结合能对核物质对称性的限制。在何种程度上即将到来的中子皮测量将进一步界定的对称性进行了研究。探讨了对称性能量约束对中子星壳内质量和转动惯量的影响以及核子直接Urca过程的阈值密度，所有这些都是潜在的可测量的。我们还评论了最小中子星半径，假设只有核子物质存在的恒星。
The neutron-proton effective $k$-mass splitting in asymmetric nucleonic matter of isospin asymmetry $δ$ and normal density is found to be $m^{*}_{n-p}\equiv(m^{*}_{n}-m^{*}_{p})/m=(0.41 \pm0.15)δ$ from analyzing globally 1088 sets of reaction and angular differential cross sections of proton elastic scattering on 130 targets with beam energies from 0.783 MeV to 200 MeV, and 1161 sets of data of neutron elastic scattering on 104 targets with beam energies from 0.05 MeV to 200 MeV within an isospin dependent non-relativistic optical potential model. It sets a useful reference for testing model p…
Besides earlier predictions based on both phenomenological models and modern microscopic many-body theories, circumstantial evidence was recently found for a reduced kinetic symmetry energy of isospin-asymmetric nucleonic matter compared to the free Fermi gas model prediction due to the short-range correlation of high-momentum neutron-proton pairs. While keeping the total symmetry energy near the saturation density of nuclear matter consistent with existing experimental constraints, we examine the correspondingly enhanced role of the isospin degree of freedom in heavy-ion collisions at interme…
Ruling out nucleonic direct Urca cooling in low-mass neutron stars using nuclear data
Université de Caen Normandie, ENSICAEN, CNRS/IN2P3, LPC Caen UMR6534（卡昂诺曼底大学，ENSICAEN，CNRS/IN2P3，LPC Caen UMR6534）；Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano（米兰大学物理系“Aldo Pontremoli”）；INFN, Sezione di Milano（意大利国家核物理研究所，米兰分部）；Department of Physics, University of Houston（休斯顿大学物理系）；Grand Accélérateur National d’Ions Lourds (GANIL), CEA/DRF-CNRS/IN2P3（重离子国家大型加速器（GANIL），CEA/DRF-CNRS/IN2P3）
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed ma…
By simultaneously describing the data of isospin sensitive nucleonic flow and pion observables, such as $v_2^n/v_2^{ch}$ and $π^-/π^+$, with ultra-relativistic quantum molecular dynamics (UrQMD) model, we got the symmetry energy at flow and pion characteristic densities which are $S(1.2ρ_0)=34\pm 4$ MeV and $S(1.5ρ_0)=36\pm 8$ MeV. Within the uncertainties, the constraints of symmetry energy at characteristic densities are consistent with the previous constraints by using other transport models. The consistency suggests that the reliable constraints on symmetry energy should be presented at th…
The isospin-asymmetry dependence of the nuclear matter equation of state obtained from microscopic chiral two- and three-body interactions in second-order many-body perturbation theory is examined in detail. The quadratic, quartic and sextic coefficients in the Maclaurin expansion of the free energy per particle of infinite homogeneous nuclear matter with respect to the isospin asymmetry are extracted numerically using finite differences, and the resulting polynomial isospin-asymmetry parametrizations are compared to the full isospin-asymmetry dependence of the free energy. It is found that in…
Equation of states (EOS) of the spin-polarized nuclear matter (NM) is studied within the Hartree-Fock (HF) formalism using the realistic density dependent nucleon-nucleon interaction. With a nonzero fraction $Δ$ of spin-polarized baryons in NM, the spin- and spin-isospin dependent parts of the HF energy density give rise to the \emph{spin symmetry} energy that behaves in about the same manner as the \emph{isospin symmetry} energy, widely discussed in literature as the nuclear symmetry energy. The present HF study shows a strong correlation between the spin symmetry energy and nuclear symmetry …
We study the composition of nuclear matter at sub-saturation densities, non-zero temperatures, and isospin asymmetry, under the conditions characteristic of binary neutron star mergers, stellar collapse, and low-energy heavy-ion collisions. The composition includes light clusters with mass number $A\le 4$, a heavy nucleus ($\isotope[56]{Fe}$), the $Δ$-resonances, the isotriplet of pions, as well as the $Λ$ hyperon. The nucleonic mean-fields are computed from a zero-range density functional, whereas the pion-nucleon interactions are treated to leading order in chiral perturbation theory. We sho…
The neutron-proton effective mass splitting in neutron-rich nucleonic matter reflects the space-time nonlocality of the isovector nuclear interaction. It affects the neutron/proton ratio during the earlier evolution of the Universe, cooling of protoneutron stars, structure of rare isotopes and dynamics of heavy-ion collisions. While there is still no consensus on whether the neutron-proton effective mass splitting is negative, zero or positive and how it depends on the density as well as the isospin-asymmetry of the medium, significant progress has been made in recent yeas in addressing these …
The well-known Migdal-Luttinger theorem states that the jump of the single-nucleon momentum distribution at the Fermi surface is equal to the inverse of the nucleon effective E-mass. Recent experiments studying short-range correlations (SRC) in nuclei using electron-nucleus scatterings at the Jefferson National Laboratory (JLAB) together with model calculations constrained significantly the Migdal-Luttinger jump at saturation density of nuclear matter. We show that the corresponding nucleon effective E-mass is consequently constrained to $M_0^{\ast,\rm{E}}/M\approx2.22\pm0.35$ in symmetric nuc…
We study the phase diagram of isospin-asymmetrical nuclear matter in the density-temperature plane, allowing for four competing phases of nuclear matter: (i) the unpaired phase, (ii) the translationally and rotationally symmetric, but isospin-asymmetrical BCS condensate, (iii) the current-carrying Larkin-Ovchinnikov-Fulde-Ferrell phase, and (iv) the heterogeneous phase-separated phase. The phase diagram of nuclear matter composed of these phases features two tri-critical points in general, as well as crossovers from the asymmetrical BCS phase to a BEC of deuterons plus a neutron gas, both for …
The radius $R_{1.4}$ of neutron stars (NSs) with a mass of 1.4 M$_{\odot}$ has been extracted consistently in many recent studies in the literature. Using representative $R_{1.4}$ data, we infer high-density nuclear symmetry energy $E_{\rm{sym}}(ρ)$ and the associated nucleon specific energy $E_0(ρ)$ in symmetric nuclear matter (SNM) within a Bayesian statistical approach using an explicitly isospin-dependent parametric Equation of State (EOS) for nucleonic matter. We found that: (1) The available astrophysical data can already improve significantly our current knowledge about the EOS in the d…
While ample evidence for the so-called empirical parabolic law of the Equation of State (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both non-relativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and non-relativistic Free Fermi Gas (FFG) models in coordinate spaces of arbitrary dimension $d$ with and without considerin…
Based on the Hugenholtz-Van Hove theorem, six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy $t(k)$, the isospin symmetric and asymmetric parts of the single-nucleon potentials $U_0(ρ,k)$ and $U_{\text{\text{sym,i}}}(ρ,k)$. The six basic quantities include the quadratic symmetry energy $E_{\text{sym,2}}(ρ)$, the quartic symmetry energy $E_{\text{sym,4}}(ρ)$, their corresponding density slopes $L_2(ρ)$ and $L_4(ρ)$, and the incompressibility coefficients $K_2(ρ)$ and $K_4(ρ)$. By using four types of well-known effective nucl…
We review a large body of predictions obtained within the framework of relativistic meson theory together with the Dirac-Brueckner-Hartree-Fock approach to nuclear matter and finite nuclei. The success of this method has been largely related to its ability to take into account important three-body effects. Therefore, the overarching theme of this article is the interpretation of the so-called "Dirac effects" as an effective three-nucleon force. We address the equation of state of isospin symmetric and asymmetric nucleonic matter and related issues, ranging from proton and neutron density distr…
Constraining the neutron-proton effective mass splitting using empirical constraints on the density dependence of nuclear symmetry energy around normal density
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 …
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…
Based on an isospin and momentum-dependent transport model, we studied the effect of momentum-dependent symmetry potential on the free neutron to proton ratio of preequilibrium nucleon emission. It is found that for $^{132}Sn+^{124}Sn$ reaction at 400 MeV/nucleon incident beam energy, free n/p ratio of preequilibrium nucleon emission mainly probe the momentum-dependence of symmetry potential at nucleon momentum around 400 $\sim$ 600 MeV/c. Whereas for 200 MeV/nucleon incident beam energy, this observable mainly probe the momentum-dependence of symmetry potential at nucleon momentum around 200 …
Various kinds of isovector nucleon effective masses are used in the literature to characterize the momentum/energy dependence of the nucleon symmetry potential or self-energy due to the space/time non-locality of the underlying isovector strong interaction in neutron-rich nucleonic matter. The multifaceted studies on nucleon isovector effective masses are multi-disciplinary in nature. Besides structures, masses and low-lying excited states of nuclei as well as nuclear reactions, studies of the isospin dependence of short-range correlations in nuclei from scatterings of high-energy electrons an…
Muons in neutron stars (NSs) play especially important roles in addressing several interesting new physics questions associated with detecting as well as understanding interactions and astrophysical effects of muonphilic dark matter particles. The key model inputs for studying the latter are the total muon mass $M_μ$, the muon mass fraction $M_μ/M_{\rm NS}$ over the NS mass $M_{\rm NS}$ and the muon radial density profile $ρ_μ(r)$ in NSs of varying masses. We investigate these quantities within a minimum model for the core of NSs consisting of neutrons, protons, electrons, and muons using an e…
Using the relativistic mean-field model with nonlinear couplings between the isoscalar and isovector mesons, we study the properties of isospin-asymmetric nuclear matter. Not only the vector mixing, $ω_μω^μ\mathbfρ_ν\mathbfρ^ν$, but also the quartic interaction due to the scalar mesons, $σ^{2}\mathbfδ^{2}$, is taken into account to investigate the density dependence of nuclear symmetry energy, $E_{\rm sym}$, and the neutron-star properties. It is found that the $δ$ meson increases $E_{\rm sym}$ at high densities, whereas the $σ$-$δ$ mixing makes $E_{\rm sym}$ soft above the saturation density.…
We present a Bayesian analysis to constrain the equation of state of dense nucleonic matter by exploiting the available data from symmetric nuclear matter at saturation and from observations of compact X-ray sources and from the gravitational wave event GW170817. For the first time, such analysis is performed by using a class of models, the relativistic mean field models, which allow to consistently construct an equation of state in a wide range of densities, isospin asymmetries and temperatures. The selected class of models contains five nuclear physics empirical parameters at saturation for …
We explore the thermodynamic properties of homogeneous cold (zero-temperature) nuclear matter including nucleons and $α$-particle condensation at low densities by using a generalized nonlinear relativistic mean-field (gNL-RMF) model. In the gNL-RMF model, the $α$-particle is included as explicit degree of freedom and treated as point-like particle with its interaction described by meson exchanges and the in-medium effects on the $α$ binding energy is described by density- and temperature-dependent energy shift with the parameters obtained by fitting the experimental Mott density. We find that …
By numerically inverting the Tolman-Oppenheimer-Volkov (TOV) equation using an explicitly isospin-dependent parametric Equation of State (EOS) of dense neutron-rich nucleonic matter, a restricted EOS parameter space is established using observational constraints on the radius, maximum mass, tidal polarizability and causality condition of neutron stars (NSs). The constraining band obtained for the pressure as a function of energy (baryon) density is in good agreement with that extracted recently by the LIGO+Virgo Collaborations from their improved analyses of the NS tidal polarizability in GW17…
Spinodal instability in nuclear matter with light cluster degrees of freedom
INFN, Laboratori Nazionali del Sud（意大利国家核物理研究所，南实验室）；Department of Physics and Astronomy “Ettore Majorana”, University of Catania（卡塔尼亚大学埃托雷·马约拉纳物理与天文学系）
Nuclear systems under constraints, with high degrees of symmetries and/or collectivities may be considered as moving effectively in spaces with reduced spatial dimensions. We first derive analytical expressions for the nucleon specific energy $E_0(ρ)$, pressure $P_0(ρ)$, incompressibility coefficient $K_0(ρ)$ and skewness coefficient $J_0(ρ)$ of symmetric nucleonic matter (SNM), the quadratic symmetry energy $E_{\rm{sym}}(ρ)$, its slope parameter $L(ρ)$ and curvature coefficient $K_{\rm{sym}}(ρ)$ as well as the fourth-order symmetry energy $E_{\rm{sym,4}}(ρ)$ of neutron-rich matter in general …
The nuclear symmetry energy is a key quantity in nuclear (astro)physics. It describes the isospin dependence of the nuclear equation of state (EOS), which is commonly assumed to be almost quadratic. In this work, we confront this standard quadratic expansion of the EOS with explicit asymmetric nuclear-matter calculations based on a set of commonly used Hamiltonians including two- and three-nucleon forces derived from chiral effective field theory. We study, in particular, the importance of non-quadratic contributions to the symmetry energy, including the non-analytic logarithmic term introduce…
Spin effects in superfluidity, neutron matter and neutron stars
Frankfurt Institute for Advanced Studies（法兰克福高等研究所）；Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Columbia Astrophysics Laboratory, Columbia University（哥伦比亚大学天体物理学实验室）
