Isospin-symmetric Nuclear Matter Research Articles

Tabulated equations of state from models informed by chiral effective field theory

Abstract We construct four equation of state (EoS) tables, tabulated over a range of temperatures, densities, and charge fractions, relevant for neutron star applications such as simulations of neutron star mergers. The EoS are computed from a relativistic mean-field theory constrained by the pure neutron matter EoS from chiral effective field theory, inferred properties of isospin-symmetric nuclear matter, and astrophysical observations of neutron star structure. To model nuclear matter at low densities, we attach an EoS that models inhomogeneous nuclear matter at arbitrary temperatures and charge fractions. The four EoS tables we develop are available from the CompOSE EoS repository https://compose.obspm.fr/eos/297 and gitlab.com/ahaber/qmc-rmf-tables.

Upsilon decay widths in magnetized asymmetric nuclear matter

The in-medium partial decay widths of [Formula: see text] in magnetized asymmetric nuclear matter are studied using a field theoretic model for composite hadrons with quark (and antiquark) constituents. [Formula: see text] is the lowest bottomonium state which can decay to [Formula: see text] in vacuum. The medium modifications of the decay widths of [Formula: see text] to [Formula: see text] pair in magnetized matter arise due to the mass modifications of the decaying [Formula: see text] as well as of the produced [Formula: see text] and [Formula: see text] mesons. The in-medium masses of the open bottom meson in magnetized nuclear matter are computed from their interactions with the nucleons and the scalar mesons within a chiral effective model. The mass modification of the [Formula: see text] arises due to the medium modification of a scalar dilaton field, which is introduced in the model to simulate the gluon condensates of QCD. The effects of the anomalous magnetic moments for the proton and neutron are taken into consideration in the present investigation. The presence of the external magnetic field is observed to lead to different mass modifications within the [Formula: see text] as well as the [Formula: see text] doublets, even in isospin symmetric nuclear matter. This is due to the difference in the interactions of the proton and the neutron to the electromagnetic field. The charged [Formula: see text] mesons have additional contributions from the Landau energy levels, leading to positive shifts in their masses in the presence of a magnetic field. In the presence of an external magnetic field, there are contributions to the masses of the B, [Formula: see text] mesons and [Formula: see text] state (longitudinal component) due to the pseudoscalar meson–vector meson (PV) mixing ([Formula: see text], [Formula: see text] and [Formula: see text] mixings), which are also considered in this study. The PV mixing effects are observed to be the dominant contributions to the mass shifts of these mesons, which lead to appreciable modifications in the decay widths of [Formula: see text] to the neutral ([Formula: see text]) and the charged ([Formula: see text]) pairs in the presence of a magnetic field. These should have observable consequence in the production of open bottom mesons and bottomonium states at LHC and RHIC, where huge magnetic fields are produced in ultra-relativistic peripheral heavy-ion collisions.

Structure Functions Generated by Zero Sound Excitations

In isospin symmetric and asymmetric nuclear matter we study the structure functions connected with the zero sound excitations. In the simple model with Landau-Migdal quasiparticle interactions the density response $\Pi^R(\omega,k)$ of the nuclear matter to the small isovector external field $V_0(\omega,k)$ is considered. In the previous papers the complex branches of solutions $\omega_{si}(k)$, $i=n,p,np$ of the dispersion equation corresponding to zero sound excitations in the symmetric and asymmetric nuclear matter are obtained. Now we investigate the structure and response functions of nuclear matter based on these solutions.

Constraining the nonanalytic terms in the isospin-asymmetry expansion of the nuclear equation of state

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.

Energy per particle of nuclear and neutron matter from subleading chiral three-nucleon interactions

We derive from the subleading contributions to the chiral three-nucleon interaction [published in Phys.~Rev.~C77, 064004 (2008) and Phys.~Rev.~C84, 054001 (2011)] their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter in an analytical way. For the variety of short-range and long-range terms that constitute the subleading chiral 3N-force the pertinent closed 3-ring, 2-ring, and 1-ring diagrams are evaluated. While 3-ring diagrams vanish by a spin-trace and the results for 2-ring diagrams can be given in terms of elementary functions of the ratio Fermi-momentum over pion mass, one ends up in most cases for the closed 1-ring diagrams with one-parameter integrals. The same treatment is applied to the subsubleading chiral three-nucleon interactions as far as these have been constructed up to now.

Density-dependent NN interaction from subsubleading chiral 3N forces: Intermediate-range contributions

From the subsubleading chiral three-nucleon force [intermediate-range contributions, published in Phys. Rev. C\,87, 054007 (2013)] a density-dependent NN-interaction $V_\text{med}$ is derived in isospin-symmetric nuclear matter. Following the division of the pertinent 3N-diagrams into two-pion-one-pion exchange topology and ring topology, one evaluates for these all selfclosings and concatenations of nucleon-lines to an in-medium loop. In the case of the $2\pi 1\pi$-exchange topology, the momentum- and $k_f$-dependent potentials associated with the isospin-operators ($1$ and $\vec\tau_1 \!\cdot\! \vec\tau_2$) and five independent spin-structures require at most one numerical integration. For the more challenging (concatenations of the) ring diagrams proportional to $c_{1,2,3,4}$, one ends up with regularized double-integrals $\int_0^\lambda dr\,r \int_0^{\pi/2} d\psi$ from which the $\lambda^2$-divergence has been subtracted and the logarithmic piece $\sim \ln (m_\pi/\lambda)$ is isolated. The derived semi-analytical results are most helpful to implement the subsubleading chiral 3N-forces into nuclear many-body calculations.

Properties of the nuclear symmetry energy studied by the radioactivity of unstable nuclei

In this paper, the properties of the symmetry energy in asymmetric nuclear matter, including the quadratic and quartic symmetry energies as well as their density slopes at the saturation density, are studied by the radioactivity of unstable nuclei. The symmetry energy was initially introduced as a quantum correction energy in the Weizsacker-Bethe liquid-drop model, which was proposed to describe the binding energies of finite nuclei. In order to systematically study the properties of the symmetry energy, the concept of the nuclear matter was introduced, which consists of neutrons and protons with finite neutron and proton densities but infinite neutron and proton numbers. By comparing the properties of the isospin symmetric nuclear matter, in which the neutron density is equal to the proton density, and those of the isospin asymmetric nuclear matter, in which the two densities are unequal, the symmetry energy is found to approximately represent the difference of the energy per nucleon in them. That is to say, the symmetry energy is an evaluation of the energy cost to convert protons in symmetric nuclear matter to neutrons in asymmetric nuclear matter. Since the symmetry energy characterizes the isospin asymmetric effect in nuclear matter, it plays critical roles in not only nuclear physics but also astrophysics. For example, the symmetry energy is closely related to the nuclear masses, the structures and properties of nuclei far away from stability line and near drip lines, the mechanism of heavy-ion reactions, the structures and component of neutron stars, the masses and radii of neutron stars, the cooling process of neutron stars, and so on. Besides of the quadratic symmetry energy, the quartic symmetry energy can have obvious effects on the properties of neutron stars as well. The quartic symmetry energy can significantly affect both the proton fraction in β-stable neutron stars and the critical density for the direct Urca process, which leads to faster cooling of neutron stars. In addition, the quartic symmetry energy is found to be very important for the location of the inner edge of crusts and the core-crust transition density and pressure in neutron stars. So the quartic symmetry energy can also have an influence on the structure of neutron stars. Because of the very important roles of the symmetry energy playing in not only nuclear physics but also astrophysics, it is of great significance to study the properties of both the quadratic and quartic symmetry energies. Based on the fundamental Hugenholtz-Van Hove (HVH) theorem, the properties of the symmetry energy are found to be closely related to the isoscalar and the isovector parts of the nucleon single-particle potentials, where the latter two parts can be extracted from the nuclear radioactivity. So by linking both the symmetry energy and the nuclear radioactivity to the nucleon single-particle potentials, the symmetry energy can be directly studied by nuclear radioactivity. In this paper, both the heavy-cluster radioactivity and the proton radioactivity are employed to constrain the properties of not only the quadratic symmetry energy but also the quartic symmetry energy. Besides, the effect of both the spectroscopic factor of proton radioactivity and the deformation in the daughter nucleus on the extracted results are also discussed, which are subsequently found to be very limited.

Implications of the Mass M⊙ of PSR J0740+6620 on the Equation of State of Super-dense Neutron-rich Nuclear Matter

Abstract We study the implications of the very recently reported mass M ⊙ of PSR J0740+6620 on the equation of state (EOS) of super-dense neutron-rich nuclear matter with respect to existing constraints on the EOS based on the mass M = 2.01 ± 0.04 M ⊙ of PSR J0348+0432, the maximum tidal deformability of GW170817, and earlier results of various terrestrial nuclear laboratory experiments. The lower limit of the skewness J 0 measuring the stiffness of super-dense isospin-symmetric nuclear matter is raised from about −220 MeV to −150 MeV, significantly reducing its current uncertainty range. The lower bound of the high-density symmetry energy also increases appreciably leading to a rise of the minimum proton fraction in neutron stars at β-equilibrium from about 0% to 5% around three times the saturation density of nuclear matter. The difficulties for some of the most widely used and previously well tested model EOSs to simultaneously predict both a maximum mass higher than 2.17 M ⊙ and a pressure consistent with that extracted from GW170817 present some interesting new challenges for nuclear theories.

Density-dependent NN interaction from subleading chiral 3N forces: Short-range terms and relativistic corrections

We derive from the subleading contributions to the chiral three-nucleon force (short-range terms and relativistic corrections, published in Phys. Rev. C84, 054001 (2011)) a density-dependent two-nucleon interaction $V_\text{med}$ in isospin-symmetric nuclear matter. The momentum and $k_f$-dependent potentials associated with the isospin operators ($1$ and $ \vec\tau_1\!\cdot\!\vec\tau_2$) and five independent spin-structures are expressed in terms of loop functions, which are either given in closed analytical form or require at most one numerical integration. Our results for $V_\text{med}$ are most helpful to implement subleading chiral 3N-forces into nuclear many-body calculations.

Phase transitions and symmetry energy in nuclear pasta

Cold and isospin-symmetric nuclear matter at sub-saturation densities is known to form the so-called pasta structures, which, in turn, are known to undergo peculiar phase transitions. Here we investigate if such pastas and their phase changes survive in isospin asymmetric nuclear matter, and whether the symmetry energy of such pasta configurations is connected to the isospin content, the morphology of the pasta and to the phase transitions. We find that indeed pastas are formed in isospin asymmetric systems with proton to neutron ratios of x=0.3, 0.4 and 0.5, densities in the range of 0.05 fm−3<ρ<0.08 fm−3, and temperatures T<2 MeV. Using tools (such as the caloric curve, Lindemann coefficient, radial distribution function, Kolmogorov statistic, and Euler functional) on the composition of the pasta, determined the existence of homogeneous structures, tunnels, empty regions, cavities and transitions among these regions. The symmetry energy was observed to attain different values in the different phases showing its dependence on the morphology of the nuclear matter structure.

Nucleons in Nuclear Matter and Properties of Nuclei

In this contribution we discuss the properties of nucleons and atomic nuclei in the framework of in-medium modified chiral soliton model. The mesonic Lagrangian of the model takes into account an influence of surrounding nuclear environment to the nucleon properties. The model correctly describes the Equations of State of isospin-symmetric and isospin-asymmetric nuclear matter near the nuclear saturation density ρ0. An extrapolation of the results to high density region allows to describe the properties of neutron stars. The model also can be applied to analysis of the properties of mirror nuclei.

Zero-sound condensate in a Fermi liquid

We consider a normal Fermi liquid with a local scalar interaction given by the Landau parameter f0. The system becomes unstable for f0 < −1 against a growth of scalar-mode excitations (Pomeranchuk instability). We show that the instability may be tamed by the formation of a static Bose condensate of the scalar modes. We study a possible reconstruction of the isospin-symmetric nuclear matter owing to the appearance of the condensate. Possibility of a novel metastable state at subnuclear densities is demonstrated.

Superfluid Gap in Neutron Matter from a Microscopic Effective Interaction

Correlated Basis Function (CBF) perturbation theory and the formalism of cluster expansions have been recently employed to obtain an effective interaction from a nuclear Hamiltonian strongly constrained by phenomenology. We report the results of a study of the superfluid gap in pure neutron matter, associated with the formation of Cooper pairs in the $^1S_0$ channel. The calculations have been carried out using an improved version of the CBF effective interaction, in which three-nucleon forces are taken into account using a microscopic model. Our results show that a non-vanishing superfluid gap develops at densities in the range $2 \times 10^{-4} \lesssim \rho/\rho_0 \lesssim 0.1 $, where $\rho_0 = 2.8 \times 10^{14}$ g cm$^{-3}$ is the equilibrium density of isospin-symmetric nuclear matter, corresponding mainly to the neutron star inner crust.

Scalar quanta in Fermi liquids: Zero sounds, instabilities, Bose condensation, and a metastable state in dilute nuclear matter

Spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with a local scalar interaction is investigated for various values and momentum dependence of the scalar Landau parameter $f_0$ in the particle-hole channel. For $f_0 >0$ the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$ the spectrum becomes unstable against a growth of scalar-mode excitations. An effective Lagrangian for the scalar excitation modes is derived after performing a bosonization procedure. We demonstrate that the instability may be tamed by the formation of a static Bose condensate of the scalar modes. The condensation may occur in a homogeneous or inhomogeneous state relying on the momentum dependence of the scalar Landau parameter. We show that in the isospin-symmetric nuclear matter there may appear a metastable state at a subsaturation nuclear density owing to the condensate. Then we consider a possibility of the condensation of the zero-sound-like excitations in a state with a non-zero momentum in Fermi liquids moving with overcritical velocities, provided an appropriate momentum dependence of the Landau parameter $f_0 (k)>0$. We also argue that in peripheral heavy-ion collisions the Pomeranchuk instability may occur already for $f_0 >-1$.

Di-nucleon structures in homogeneous nuclear matter based on two- and three-nucleon interactions

We investigate homogeneous nuclear matter within the Brueckner-Hartree-Fock (BHF) approach in the limits of isospin-symmetric nuclear matter (SNM) as well as pure neutron matter at zero temperature. The study is based on realistic representations of the internucleon interaction as given by Argonne v18, Paris, Nijmegen I and II potentials, in addition to chiral N$^{3}$LO interactions, including three-nucleon forces up to N$^{2}$LO. Particular attention is paid to the presence of di-nucleon bound states structures in $^1\textrm{S}_0$ and $^3\textrm{SD}_1$ channels, whose explicit account becomes crucial for the stability of self-consistent solutions at low densities. A characterization of these solutions and associated bound states is discussed. We confirm that coexisting BHF single-particle solutions in SNM, at Fermi momenta in the range $0.13-0.3$~fm$^{-1}$, is a robust feature under the choice of realistic internucleon potentials.

Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule.

In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q|≳0.5 GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum MonteCarlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.

Reducible chiral four-body interactions in nuclear matter

The method of unitary transformations generates five classes of leading-order reducible chiral four-nucleon interactions which involve pion-exchanges and a spin-spin contact-term. Their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter are evaluated in detail. For most of the closed four-loop diagrams the occurring integrals over four Fermi-spheres can be reduced to easily manageable one- or two-parameter integrals. One observes substantial cancelations among the different contributions arising from 2-ring and 1-ring diagrams. Altogether, the net attraction generated by the chiral four-nucleon interaction does not exceed values of $-1.3$\,MeV for densities $\rho<2\rho_0$.

Thermal properties of hot and dense matter with finite range interactions

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 nucleonic matter and the maximum neutron star mass, but fails to account for heavy-ion flow data due to the lack of an appropriate momentum dependence in its mean field. Similarities and differences in the thermal state variables and the specific heats between the two models are highlighted. Checks of our exact numerical calculations are performed from formulas derived in the strongly degenerate and non-degenerate limits. Our studies of the thermal and adiabatic indices, and the speed of sound in hot and dense matter for conditions of relevance to core-collapse supernovae, the thermal evolution of neutron stars from their birth and mergers of compact binary stars reveal that substantial variations begin to occur at sub-saturation densities before asymptotic values are reached at supra-nuclear densities.

Thermodynamics of isospin-asymmetric nuclear matter from chiral effective field theory

The density and temperature dependence of the nuclear symmetry free energy is investigated using microscopic two- and three-body nuclear potentials constructed from chiral effective field theory. The nuclear force models and many-body methods are benchmarked to properties of isospin-symmetric nuclear matter in the vicinity of the saturation density as well as the virial expansion of the neutron matter equation of state at low fugacities. The free energy per particle of isospin-asymmetric nuclear matter is calculated assuming a quadratic dependence of the interaction contributions on the isospin asymmetry. The spinodal instability at subnuclear densities is examined in detail.

Nuclear thermodynamics from chiral low-momentum interactions

We investigate the thermodynamic equation of state of isospin-symmetric nuclear matter with microscopic nuclear forces derived within the framework of chiral effective field theory. Two- and three-body nuclear interactions constructed at low resolution scales form the basis for a perturbative calculation of the finite-temperature equation of state. The nuclear force models and many-body methods are benchmarked against bulk properties of isospin-symmetric nuclear matter at zero temperature, which are found to be well reproduced when chiral nuclear interactions constructed at the lowest resolution scales are employed. The calculations are then extended to finite temperatures, where we focus on the liquid-gas phase transition and the associated critical point. The Maxwell construction is applied to construct the physical equation of state, and the value of the critical temperature is determined to be T_c =17.2-19.1 MeV, in good agreement with the value extracted from multifragmentation reactions of heavy ions.