We examine the properties of the isospin-asymmetry expansion of the nuclear equation of state from chiral two- and three-body forces. We focus on extracting the high-order symmetry energy coefficients that consist of both normal terms (occurring with even powers of the isospin asymmetry) as well as terms involving the logarithm of the isospin asymmetry that are formally nonanalytic around the expansion point of isospin-symmetric nuclear matter. These coefficients are extracted from numerically precise perturbation theory calculations of the equation of state coupled with a new set of finite difference formulas that achieve stability by explicitly removing the effects of higher-order terms in the expansion. We consider contributions to the symmetry energy coefficients from both two- and three-body interactions. It is found that the coefficients of the logarithmic terms are generically larger in magnitude than those of the normal terms from second-order perturbation theory diagrams, but overall the normal terms give larger contributions to the ground state energy. The high-order isospin-asymmetry terms are especially relevant at large densities where they affect the proton fraction in beta-equilibrium matter.
The isospin diffusion of the quasi-projectile formed in the $^{64,58}Ni$ on $^{64,58}Ni$ reactions in the Fermi energy domain is investigated in the framework of the Boltzmann-Uehling-Uhlenbeck transport model. The well known isospin transport ratio observable is revisited, with the aim of insuring an optimal comparison between experimental data and theoretical calculations and reducing the present uncertainties in the extraction of empirical equation of state parameters. We show that isospin transport ratios are sensitive to all the low order isovector parameters ($E_{sym}$, $L_{sym}$ and $K_…
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this work we present a selection of reaction observables in dissipative collisions particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS). At low energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. We will first discuss the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation during t…
The computation of the thermodynamic properties of nuclear matter is a central task of theoretical nuclear physics. The nuclear equation of state is an essential quantity in nuclear astrophysics and governs the properties of neutron stars and core-collapse supernovæ. The framework of chiral effective field theory provides the basis for the description of nuclear interactions in terms of a systematic low-energy expansion. In this thesis, we apply chiral two- and three-nucleon interactions in perturbative many-body calculations of the thermodynamic equation of state of infinite homogeneous nucle…
The quest for the nuclear equation of state (EoS) at high densities and/or extreme isospin is one of the longstanding problems of nuclear physics. Ab initio calculations for the nuclear many-body problem make predictions for the density and isospin dependence of the EoS far away from the saturation point of nuclear matter. On the other hand, in recent years substantial progress has been mode to constrain the EoS both, from the astrophysical side and from accelerator based experiments. Heavy ion experiments support a soft EoS at moderate densities while recent neutron star observations require …
With a newly improved isospin- and momentum-dependent interaction and an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, we have investigated the effects of the slope parameter $L$ of the nuclear symmetry energy and the isospin splitting of the nucleon effective mass $m_{n-p}^*=(m_n^*-m_p^*)/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in $^{208}$Pb. With the isoscalar nucleon effective mass $m_s^*=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm11.84 (\rm MeV)$ and $m_{n-p}^*=…
Recent analysis of the isospin diffusion data from heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections has led to the extraction of a value of $L=88\pm 25$ MeV for the slope of the nuclear symmetry energy at saturation density. This imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Among the 21 sets of Skyrme interactions commonly used in nuclear structure studies, the 4 sets SIV, SV, G$_σ$, and R$_σ$ are found to give $L$ values tha…
Neutron star radii are primarily determined by the pressure of isospin asymmetric matter which is proportional to the slope of the nuclear symmetry energy. Available terrestrial laboratory data on the isospin diffusion in heavy-ion reactions at intermediate energies constrain the slope of the symmetry energy. Using this constraint, we show that the radius (radiation radius) of a 1.4 solar mass neutron star is between 11.5 (14.4) and 13.6 (16.3) km.
In this work we extend our formalism to study meson-baryon interactions by including $s$- and $u$-channel diagrams for pseudoscalar-baryon systems. We study the coupled systems with strangeness $-1$ and focus on studying the isospin-1 resonance(s), especially in the energy region around 1400 MeV. By constraining the model parameters to fit the cross section data available on several processes involving relevant channels, we find resonances in the isoscalar as well as the isovector sector in the energy region around 1400 MeV.
Quantitative information on the tensor force induced isospin-dependence of short-range nucleon-nucleon correlation (SRC) extracted from recent J-Lab experiments was used in constraining the high-momentum tails of single nucleon momentum distributions in both symmetric nuclear matter (SNM) and pure neutron matter (PNM). Its effects on the Equations of State of SNM and PNM as well as the nuclear symmetry energy are investigated. It is found that the tensor force induced isospin-dependence of SRC softens significantly the nuclear symmetry energy especially at supra-saturation densities.
Within an isospin and momentum dependent transport model, the dynamics of isospin particles (nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The mass splitting of $m^{*}_{n}>m^{*}_{p}$ and $m^{*}_{n}<m^{*}_{p}$ in nuclear matter and the different stiffness of symmetry energy are used in the model. The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of …
Temperature dependence of the nucleon-nucleon inelastic cross section in an isospin-asymmetric nuclear medium
School of Science, Huzhou University（湖州学院理学院）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；School of Nuclear Science and Engineering, Shenyang Institute of Engineering（沈阳工程学院核科学与工程学院）
Based on the current measurement of the neutron distribution radius ($R_n$) of $^{208}$Pb through the PREX-2 data, we re-visited the recently developed G3 and IOPB-I force parameter by fine-tuning some of the specific couplings within the relativistic mean-field model. The $ω-ρ-$mesons coupling $Λ_ω$ and the $ρ-$meson coupling $g_ρ$ are refitted to reproduce the experimental neutron radius of $^{208}$Pb without compromising the bulk properties of finite nuclei and infinite nuclear matter observables. The modified parameter sets are applied to calculate the gross properties of finite nuclei for…
We show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. Using this correlation analysis to existing data on the neutron skin thickness of Sn isotopes, we find important constraints on the value E_{sym}(rho_0) and density slope L of the nuclear symmetry energy at saturation density. Combining these constraints with those from recent analyses of isospin diffusion and double neutron/proton ratio in heavy ion collisions leads to a value of L=58\pm 18 MeV approximately independent of E_{sym}(ρ_0).
Recent analyses of several isospin effects in heavy-ion reactions have allowed us to constrain the density dependence of nuclear symmetry energy at sub-saturation densities within a narrow range. Combined with constraints on the Equation of State (EOS) of symmetric nuclear matter obtained previously from analyzing the elliptic flow in relativistic heavy-ion collisions, the EOS of neutron-rich nuclear matter is thus partially constrained. Here we report effects of the partially constrained EOS of neutron-rich nuclear matter on the mass-radius correlation, moment of inertia, elliptical deformati…
Probing the density dependence of nuclear symmetry energy through isospin transport in heavy-ion reactions
Variable Energy Cyclotron Centre（可变能量回旋加速器中心）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Université de Caen Normandie（诺曼底卡昂大学）；ENSICAEN（恩西曹昂高等师范学院）；CNRS/IN2P3, LPC Caen（法国国家科学研究中心/法国原子能和替代能源委员会，卡昂低能物理实验室）；Institut Universitaire de France (IUF)（法兰西学院）；Grand Accelerateur National d’Ions Lourds (GANIL)（重离子大加速器（GANIL））；CEA/DRF - CNRS/IN2P3（法国原子能和替代能源委员会/法国国家科学研究中心-法国原子能和替代能源委员会）
Testing the constancy of the gravitational constant G has been a longstanding fundamental question in natural science. As first suggested by Jofré, Reisenegger and Fernández [1], Dirac's hypothesis of a decreasing gravitational constant $G$ with time due to the expansion of the Universe would induce changes in the composition of neutron stars, causing dissipation and internal heating. Eventually, neutron stars reach their quasi-stationary states where cooling due to neutrino and photon emissions balances the internal heating. The correlation of surface temperatures and radii of some old neutro…
According to the Hugenholtz-Van Hove theorem, nuclear symmetry energy \esym and its slope \lr at an arbitrary density $ρ$ are determined by the nucleon isovector (symmetry) potential \usym and its momentum dependence $\frac{\partial U_{sym}}{\partial k}$. The latter determines uniquely the neutron-proton effective k-mass splitting $m^*_{n-p}(ρ,δ)\equiv (m_{\rm n}^*-m_{\rm p}^*)/m$ in neutron-rich nucleonic matter of isospin asymmetry $δ$. Using currently available constraints on the \es0 and \l0 at normal density $ρ_0$ of nuclear matter from 28 recent analyses of various terrestrial nuclear la…
A Gaussian Process framework for constraining the nuclear equation of state from microscopic calculations with correlated uncertainties
Ohio University（俄亥俄大学）；Argonne National Laboratory（阿贡国家实验室）；University of Washington（华盛顿大学）；University of California, Berkeley（加州大学伯克利分校）；Michigan State University（密歇根州立大学）
Understanding the differences between the distribution of quarks bound in protons and neutrons is key for constraining the mechanisms of SU(6) spin-flavor symmetry breaking in Quantum Chromodynamics (QCD). While vast amounts of proton structure measurements were done, data on the structure of the neutron is much more spars as experiments typically extract the structure of neutrons from measurements of light atomic nuclei using model-dependent corrections for nuclear effects. Recently the MARATHON collaboration performed such an extraction by measuring inclusive deep-inelastic electron-scatteri…
Properties, structure, and thermal evolution of neutron stars are determined by the equation of state of stellar matter. Recent data on isospin-diffusion and isoscaling in heavy-ion collisions at intermediate energies as well as the size of neutron skin in $^{208}Pb$ have constrained considerably the density dependence of the nuclear symmetry energy and, in turn, the equation of state of neutron-rich nucleonic matter. These constraints could provide useful information about the global properties of rapidly rotating neutron stars. Models of rapidly rotating neutron stars are constructed applyin…
The radial overlap correction, $δ_{RO}$ is re-examined for 30 superallowed $β$ decays using the shell model with Hartree-Fock (HF) radial wave functions. Our calculation is based on the Skyrme interaction including Coulomb, Charge-Symmetry-Breaking (CSB) and Charge-Independence-Breaking (CIB) terms. The corrections due to the gradient of charge density, vacuum polarization, Coulomb spin-orbit and finite size of nucleons are also considered. To avoid the spurious isospin mixing, the local equivalent potential is constructed from the solution of a HF calculation for the $Z=N$ nucleus without cha…
Significant progress has been made in recent years in constraining nuclear symmetry energy at and below the saturation density of nuclear matter using data from both terrestrial nuclear experiments and astrophysical observations. However, many interesting questions remain to be studied especially at supra-saturation densities. In this lecture note, after a brief summary of the currently available constraints on nuclear symmetry energy near the saturation density we first discuss the relationship between the symmetry energy and the isopin and momentum dependence of the single-nucleon potential …
Neutron Skin Effects on Particle Emission in Heavy-Ion Collisions: A Topic Review with Astrophysical and Nuclear Structure Connections
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（复旦大学理论核物理上海研究中心）；School of Physics, East China Normal University（华东师范大学物理系）
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…
