We analyze the spinodal instabilities of spin polarized asymmetric nuclear matter at zero temperature for several configurations of the neutron and proton spins. The calculations are performed with the Brueckner--Hartree--Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential plus a three-nucleon force of Urbana type. An analytical parametrization of the energy density, which reproduces with good accuracy the BHF results, is employed to determine the spinodal instability region. We find that, independently of the of the orientation of the neutron and proton spins, the spinodal instability region shinks when the system is polarized, being its size smaller smaller when neutron and proton spins are antiparallel than when they are oriented in a parallel way. We find also that the spinodal instability is always dominated by total density fluctuation independently of the degree of polarization of the system, and that restoration of the isospin symmetry in the liquid phase, {\it i.e.,} the so-called isospin distillation or fragmentation effect, becomes less efficient with the polarization of the system.
Self consistent quantum approaches are used to study the instabilities of finite nuclear systems. The frequencies of multipole density fluctuations are determined as a function of dilution and temperature, for several isotopes. The spinodal region of the phase diagrams is determined and it appears that instabilities are reduced by finite size effects. The role of surface and volume instabilities is discussed. It is indicated that the important chemical effects associated with mechanical disruption may lead to isospin fractionation.
A density dependent relativistic mean-field model is determined to reproduce the components of the nucleon self-energy at low densities. This model is used to investigate spinodal instabilities in isospin asymmetric nuclear matter at finite temperatures. The inhomogeneous density distributions in the spinodal region are investigated through calculations in a cubic Wigner-Seitz cell. Compared to results obtained in phenomenological calculations the spinodal region is large, i.e. the spinodal region at zero temperature can reach densities above 0.12 fm$^{-3}$. The predicted spinodal region is co…
As an extension of our previous work, the growth of density fluctuations in the spinodal region of charge asymmetric nuclear matter is investigated in the basis of the stochastic mean-field approach in the non-relativistic framework. A complete treatment of density correlation functions are presented by including collective modes and non-collective modes as well.
Quantal effects on growth of spinodal instabilities in charge asymmetric nuclear matter are investigated in the framework of a stochastic mean field approach. Due to quantal effects, in both symmetric and asymmetric matter, dominant unstable modes shift towards longer wavelengths and modes with wave numbers larger than the Fermi momentum are strongly suppressed. As a result of quantum statistical effects, in particular at lower temperatures, magnitude of density fluctuations grows larger than those calculated in semi-classical approximation.
Early growth of density fluctuations of nuclear matter in spinodal region is investigated employing the stochastic mean-field approach. In contrast to the earlier treatments in which only collective modes were included in the calculations, in the present work non-collective modes are also included, thus providing a complete treatment of the density correlation functions. Calculations are carried out for symmetric matter in non-relativistic framework using a semi-classical approximation.
Using a recently developed method for the inclusion of fluctuation in the BUU dynamics, we study the self-consistent propagation of inherent thermal noise of unstable nuclear matter. The large time behaviour of the evolving system exhibits synergism between fluctuation and non-linearities in a universal manner which manifest in the appearance of macroscopic structure in the average description.
Spinodal instabilities and early growth of baryon density fluctuations in symmetric nuclear matter are investigated in the basis of stochastic extension of relativistic mean-field approach in the semi-classical approximation. Calculations are compared with the results of non-relativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher baryon densities around $ρ_{b}=0.4 ~ρ_{0}$ in the relativistic approach while most unstable behavior o…
Are spinodal instabilities the leading mechanism in the fragmentation of a fermionic system? Numerous experimental indications suggest such a scenario and stimulated much effort in giving a suitable description, without being finalised in a dedicated transport model. On the one hand, the bulk character of spinodal behaviour requires an accurate treatment of the one-body dynamics, in presence of mechanical instabilities. On the other hand, pure mean-field implementations do not apply to situations where instabilities, bifurcations and chaos are present. The evolution of instabilities should be …
Using the Polyakov-Nambu-Jona-Lasinia (PNJL) model, we study the spinodal instability of a baryon-rich quark-gluon plasma in the linear response theory. We find that the spinodal unstable region in the temperature and density plane shrinks with increasing wave number of the unstable mode and is also reduced if the effect of Polyakov loop is not included. In the small wave number or long wavelength limit, the spinodal boundaries in both cases of with and without the Polyakov loop coincide with those determined from the isothermal spinodal instability in the thermodynamic approach. Also, the vec…
We study the spinodal instabilities of asymmetric nuclear matter at finite temperature within the microscopic Brueckner--Hartree--Fock (BHF) approximation using the realistic Argonne V18 nucleon-nucleon potential plus a three-body force of Urbana type. Our results are compared with those obtained with the Skyrme force SLy230a and the relativistic mean field models NL3 and TW. We find that BHF predicts a larger spinodal region. This result is a direct consequence of the fact that our Brueckner calculation predicts a larger critical temperature and saturation density of symmetric nuclear matter …
We demonstrate that the instabilities of asymmetric nuclear matter at sub-saturation densities do not present two types of instabilities as usually discussed but a unique one. The associated order parameter is everywhere dominated by the isoscalar density and so the transition is of liquid-gas type even in the so-called chemical instability region.
Density fluctuations resulting from spinodal decomposition in a non-equilibrium first-order chiral phase transition are explored. We show that such instabilities generate divergent fluctuations of conserved charges along the isothermal spinodal lines appearing in the coexistence region. Thus, divergent density fluctuations could be a signal not only for the critical end point but also for the first order phase transition expected in strongly interacting matter. We also compute the mean-field critical exponent at the spinodal lines. Our analysis is performed in the mean-field approximation to t…
Asymmetric nuclear matter at sub-saturation densities is shown to present only one type of instabilities. The associated order parameter is dominated by the isoscalar density and so the transition is of liquid-gas type. The instability goes in the direction of a restoration of the isospin symmetry leading to a fractionation phenomenon. These conclusions are model independent since they can be related to the general form of the asymmetry energy. They are illustrated using density functional approaches.
The phase diagram of nuclear matter is quite rich - it shows such phenomena as phase-transitions, formation of condensates, clustering, etc. From the analysis of the spinodal instability, one can learn about the region of liquid-gas coexistence in nuclear matter at low densities and finite isospin asymmetries. In a recent paper, we have shown that asymmetric nuclear matter at sub-nuclear densities should undergo only one type of instability. The associated order parameter is dominated by the isoscalar density and so the transition is of liquid-gas type. The instability goes in the direction of…
We investigate the impact of pairing correlations on the behavior of unstable asymmetric nuclear matter at low temperature. We focus on the relative role of the pairing interaction, coupling nucleons of the same type (neutrons or protons), with respect to the symmetry potential, which enhances the neutron-proton attraction, along the clusterization process driven by spinodal instabilities. It is found that, especially at the transition temperature from the normal to the superfluid phase, pairing effects may induce significant variations in the isotopic content of the clusterized matter. This a…
We investigate the dynamical properties of asymmetric nuclear matter at low density. The occurrence of new instabilities, that lead the system to a dynamical fragment formation, is illustrated, discussing in particular the charge symmetry dependence of the structure of the most important unstable modes. We observe that instabilities are reduced by charge asymmetry, leading to larger size and time scales in the fragmentation process. Configurations with less asymmetric fragments surrounded by a more asymmetric gas are favoured. Interesting variances with respect to a pure thermodynamical predic…
The stability of an expanding parton plasma is analyzed within quasi-particle models. The effective mass of the parton is calculated self-consistently from a gap equation which is either obtained from the Nambu Jona-Lasinio Lagrangian or from a fit to observables calculated on the lattice. The latter shows an effective confinement. At thermal equilibrium the stability is studied within thermodynamics (mechanical stability) and via a linear response analysis of the Vlasov equation. The instabilities related to a first-order phase transition are found. For a plasma expanding in three and one dim…
We study the effect of strong magnetic fields, of the order of $10^{18}$-$10^{19}$ G, on the instability region of nuclear matter at subsaturation densities. Relativistic nuclear models both with constant couplings and with density dependent parameters are considered. It is shown that a strong magnetic field can have large effects on the instability regions giving rise to bands of instability and wider unstable regions. As a consequence we predict larger transition densities at the inner edge of the crust of compact stars with strong magnetic field. The direction of instability gives rise to a…
Within the covariant density functional theory of nuclear matter we build equations of state of $Δ$-admixed compact stars. Uncertainties in the interaction of $Δ(1232)$ resonance states with nuclear matter, due to lack of experimental data, are accounted for by varying the coupling constants to scalar and vector mesonic fields. We find that, over a wide range of the parameter space allowed by nuclear physics experiments and astrophysical observations, cold catalyzed star matter exhibits a first order phase transition which persists also at finite temperature and out of $β$-equilibrium in the n…
The effects of $δ$ mesons on the dynamical instabilities of cold and warm nuclear and stellar matter at subsaturation densities are studied in the framework of relativistic mean-field hadron models (NL3, NL$ρ$ and NL$ρδ$) with the inclusion of the electromagnetic field. The distillation effect and the spinodals for all the models considered are discussed. The crust-core transition density and pressure are obtained as a function of temperature for $β$-equilibrium matter with and without neutrino trapping. An estimation of the size of the clusters formed in the non-homogeneous phase is made. It …
This paper focuses on the isospin properties of the asymmetric nuclear-matter liquid-gas phase transition analyzed in a mean-field approach, using Skyrme effective interactions. We compare two different mechanisms of phase separation for low-density matter: equilibrium and spinodal decomposition. The isospin properties of the phases are deduced from the free-energy curvature, which contains information both on the average isospin content and on the system fluctuations. Some implications on experimentally accessible isospin observables are presented.
Effects of viscosity and thermal conductivity on the dynamics of first-order phase transitions are studied. The nuclear gas-liquid and hadron-quark transitions in heavy-ion collisions are considered. We demonstrate that at non-zero thermal conductivity, $κ\neq 0$, onset of spinodal instabilities occurs on an isothermal spinodal line, whereas for $κ=0$ instabilities take place at lower temperatures, on an adiabatic spinodal.
The evolution of dynamical perturbations is examined in nuclear multifragmentation in the frame of Vlasov equation. Both plane wave and bubble type of perturbations are investigated in the presence of surface (Yukawa) forces. An energy condition is given for the allowed type of instabilities and the time scale of the exponential growth of the instabilities is calculated. The results are compared to the mechanical spinodal region predictions. PACS: 25.70 Mn
Using the test-particle method to solve the transport equation derived from the Nambu-Jona-Lasino (NJL) model, we study how phase separation occurs in an expanding quark matter like that in a heavy ion collision. To test our method, we first investigate the growth rates of unstable modes of quark matter in a static cubic box and find them to agree with the analytical results that were previously obtained using the linear response theory. In this case, we also find the higher-order scaled density moments to increase with time and saturate at values significantly larger than one, which correspon…
We discuss the features of instabilities in asymmetric nuclear matter, in particular the relation between the nature of fluctuations, the types of instabilities and the properties of the interaction. We show a chemical instability appears as an instability against isoscalar-like fluctuations. Then starting from phenomenological hadronic field theory (QHD), including exchange terms, we discuss the symmetry energy and the relation to the dynamical response inside the spinodal region.
The numerical solutions of nonlocal and local Boltzmann kinetic equations for the simulation of central heavy ion reactions are parameterized in terms of time dependent thermodynamical variables in the Fermi liquid sense. This allows one to discuss dynamical trajectories in phase space. The nonequilibrium state is characterized by non-isobaric, non-isochoric etc. conditions, shortly called iso-nothing conditions. Therefore a combination of thermodynamical observables is constructed which allows one to locate instabilities and points of possible phase transition in a dynamical sense. We find tw…
In the present work we include the isovector-scalar $δ$-meson in the quark-meson coupling model (QMC) and study the properties of asymmetric nuclear within QMC without and with the $δ$-meson. Recent constraints set by isospin diffusion on the slope parameter of the nuclear symmetry energy at saturation density are used to adjust the model parameters. The thermodynamical spinodal surfaces are obtained and the instability region at subsaturation densities within QMC and QMC$δ$ models are compared with mean-field relativistic models. The distillation effect in the QMC model is discussed.
The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for i…
We recently introduced a fluid-dynamical model for simulating relativistic nuclear collisions in the presence of a first-order phase transition and made explorative studies of head-on lead-lead collisions. We give here a more detailed account of this novel theoretical tool and carry out more exhaustive studies of the phase-separation dynamics. Extracting the density enhancement caused by the spinodal instabilities, the associated clump size distribution, and the resulting transverse flow velocity, we examine the sensitivity of these quantities to the strength of the gradient term that promotes…
We study the effects of the Coulomb interaction on the growth of unstable modes in asymmetric nuclear matter. In order to compare with previous calculations we use a semiclassical approach based on the linearized Vlasov equation. Moreover, a quantum calculation is performed within the R.P.A.. The Coulomb effects are a slowing down of the growth and the occurrence of a minimal wave vector for the onset of the instabilities. The quantum corrections cause a further decrease of the growth rates.
The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.
The existence of phase transitions from liquid to gas phases in asymmetric nuclear matter (ANM) is related with the instability regions which are limited by the spinodals. In this work we investigate the instabilities in ANM described within relativistic mean field hadron models, both with constant and density dependent couplings at zero and finite temperatures. In calculating the proton and neutron chemical potentials we have used an expansion in terms of Bessel functions that is convenient at low densities. The role of the isovector scalar $δ$-meson is also investigated in the framework of r…
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）
We study the influence of the isovector-scalar meson on the spinodal instabilities and the distillation effect in asymmetric non-homogenous nuclear matter under strong magnetic fields, of the order of $10^{18}-10^{19}$ G. Relativistic nuclear models both with constant couplings (NLW) and with density dependent parameters (DDRH) are considered. A strong magnetic field can have large effects on the instability regions giving rise to bands of instability and wider unstable regions. It is shown that for neutron rich matter the inclusion of the $δ$ meson increases the size of the instability region…
We investigate thermodynamic properties and instability conditions in intermediate energy heavy ion reactions. We define locally thermodynamic variables, i.e. density, pressure and temperature, directly from the phase space distribution of a relativistic transport calculation. In particular, temperatures are determined by a fit to two covariant hot Fermi distributions thus taking into account possible anisotropic momentum configurations. We define instability independent from the nuclear matter spinodal by the criterion that the effective compressibility becomes negative. The method is applied…
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 isospi…
An abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation in the Fermi energy domain. On the other hand finite size effects are predicted to strongly reduce this abnormal production. High statistics quasifusion hot nuclei produced in central collisions between Xe and Sn isotopes at 32 and 45 AMeV incident energies have been used to definitively establish, through the experimental measurement of charge correlations, the presence of spinodal instabilities. N/Z influence was als…
We study the variance and kurtosis of the net-baryon number in a fluid dynamical model for heavy-ion collisions. It is based on an effective chiral model with dilatons for the strong coupling regime of QCD. Taking into account spinodal instabilities, we demonstrate that this model exhibits a diverging quark number susceptibility and kurtosis all along the spinodal lines of the first-order phase transition, with a change of universality class at the critical end point. During the (3+1) dimensional expansion of a hot and dense fireball, instabilities are created by fluctuations in the explicitly…
Asymmetric nuclear matter is investigated in the low density region below the nuclear saturation density. Microscopic calculations based on the Dirac Brueckner Hartree-Fock (DBHF) approach with realistic nucleon-nucleon potentials are used to adjust a low density functional. This functional is constructed on a density expansion of the relativistic mean field theory which allows a clear interpretation of the role of the mesons to the equation of state. It is shown that a correction term should be added to the functional in order to take into account the effects beyond the mean field. Two functi…
Self-consistent mean field methods based on phenomenological Skyrme effective interactions are known to exhibit spurious spin and spin-isospin instabilities both at zero and finite temperatures when applied to homogeneous nuclear matter at the densities encountered in neutron stars and in supernova cores. The origin of these instabilities is revisited in the framework of the nuclear energy density functional theory and a simple prescription is proposed to remove them. The stability of several Skyrme parametrizations is reexamined.
Using phenomenological equations of state, we study the chemical and mechanical instabilities in hot isospin-asymmetric nuclear matter. Both instabilities are found to depend strongly on the isospin asymmetry of the nuclear matter. For a chemically and mechanically stable asymmetric nuclear matter, a lower neutron excess is found in the liquid phase than in the gas phase. Furthermore, the neutron excess in the mixed phase at densities between that of the liquid and the gas phases is limited by certain maximum value. Also, for the nuclear equations of state considered here the boundary of chemi…
Unstable modes in asymmetric nuclear matter (ANM) at subsaturation densities are studied in the framework of relativistic mean-field density-dependent hadron models. The size of the instabilities that drive the system are calculated and a comparison with results obtained within the non-linear Walecka model is presented. The distillation and anti-distillation effects are discussed.
We discuss the features of instabilities in binary systems, in particular, for asymmetric nuclear matter. We show its relevance for the interpretation of results obtained in experiments and in "ab initio" simulations of the reaction between $^{124}Sn+^{124}Sn$ at 50AMeV.}
Thermal properties of asymmetric nuclear matter are studied within a self-consistent thermal model using an isospin and momentum dependent interaction (MDI) constrained by the isospin diffusion data in heavy-ion collisions, a momentum-independent interaction (MID), and an isoscalar momentum-dependent interaction (eMDYI). In particular, we study the temperature dependence of the isospin-dependent bulk and single-particle properties, the mechanical and chemical instabilities, and liquid-gas phase transition in hot asymmetric nuclear matter. Our results indicate that the temperature dependence of…
The nuclear-matter liquid-gas phase transition induces instabilities against finite-size density fluctuations. This has implications for both heavy-ion-collision and compact-star physics. In this paper, we study the clusterization properties of nuclear matter in a scenario of spinodal decomposition, comparing three different approaches: the quantal RPA, its semi-classical limit (Vlasov method), and a hydrodynamical framework. The predictions related to clusterization are qualitatively in good agreement varying the approach and the nuclear interaction. Nevertheless, it is shown that i) the quan…
Dynamics of dilute nuclear matter with light clusters and in-medium effects
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania（意大利国家核物理研究所（INFN）卡塔尼亚分部）；INFN, Laboratori Nazionali del Sud（意大利国家核物理研究所（INFN）南方实验室）；Dipartimento di Fisica e Astronomia（物理与天文学系）
We derive stability conditions of Asymmetric Nuclear Matter ($ANM$) and discuss the relation to mechanical and chemical instabilities of general two-component systems. We show that the chemical instability may appear as an instability of the system against isoscalar-like rather than isovector-like fluctuations if the interaction between the two constituent species has an attractive character as in the case of $ANM$. This leads to a new kind of liquid-gas phase transition, of interest for fragmentation experiments with radioactive beams.
The liquid-gas phase transition and associated instability in two component systems are investigated using a mean field theory. The importance of the role of both the Coulomb force and symmetry energy terms are studied. The addition of the Coulomb terms bring asymmetry into a mean field and thus result in important differences with previous approaches which did not include such terms. The Coulomb effects modify the chemical instability and mechanical instability domains shifting many features away from proton fraction point y=1/2 to a value closer to the valley of βstability. These features ar…
In this work we study the warm equation of state of asymmetric nuclear matter in the quark meson coupling model which incorporates explicitly quark degrees of freedom, with quarks coupled to scalar, vector and isovector mesons. Mechanical and chemical instabilities are discussed as a function of density and isospin asymmetry. The binodal section, essential in the study of the liquid-gas phase transition is also constructed and discussed. The main results for the equation of state are compared with two common parametrizations used in the non-linear Walecka model and the differences are outlined…
We present a comprehensive analysis of hot and dilute isospin-asymmetric nuclear matter employing the temperature-dependent effective-relativistic mean-field theory (E-RMF). The E-RMF is applied to study the effect of $δ$ and $ω-ρ$ meson cross-coupling on the thermal properties of asymmetric nuclear matter using two recently developed IOPB-I and G3 parameter sets. These sets are known to reproduce the nuclear matter properties in agreement with various experimental and observational constraints. We consider the nuclear matter to be homogeneous and study the equation of state (EoS) for densitie…
The spinodal instabilities in hot asymmetric nuclear matter and some important critical parameters derived thereof are studied using six different families of relativistic mean-field (RMF) models. The slopes of the symmetry energy coefficient vary over a wide range within each family. The critical densities and proton fractions are more sensitive to the symmetry energy slope parameter at temperatures much below its critical value ($T_c\sim$14-16 MeV). The spread in the critical proton fraction at a given symmetry energy slope parameter is noticeably larger near $T_c$, indicating that the warm …
We try to single out some qualitative new effects of the coupling to the $δ$-isovector-scalar meson introduced in a minimal way in a phenomenological hadronic field theory. Results for the equation of state ($EOS$) and the phase diagram of asymmetric nuclear matter ($ANM$) are discussed. We stress the consistency of the $δ$-coupling introduction in a relativistic approach. New contributions to the slope and curvature of the symmetry energy and the neutron-proton effective mass splitting appear particularly interesting. A more repulsive $EOS$ for neutron matter at high baryon densities is expec…
The thermodynamic properties of proton rich systems are explored in a mean field approach which is generated from a Skyrme interaction. The addition of Coulomb interactions result in asymmetries which modify the chemical and mechanical instability of the system and its equilibrium properties. These properties are studied for systems with proton fraction $y$ on the proton richer side of the valley of $β$-stability as well as the neutron rich side. Coulomb induced instabilities lead to proton diffusion processes on the proton richer side and also large asymmetries in chemical and mechanical inst…
We have studied the mechanical and chemical instabilities as well as the liquid-gas-like phase transition in isospin asymmetric quark matter based on the NJL and the pNJL model. Areas of the mechanical instability region and the liquid-gas coexistence region are seen to be enlarged with a larger quark matter symmetry energy or in the presence of strange quarks. Our study shows that the light cluster yield ratio observed in relativistic heavy-ion collisions may not be affected much by the uncertainties of the isospin effect, and favors a smooth hadron-quark phase transition in compact stars as …
The critical properties for the transition to warm, asymmetric, non-homogeneous nuclear matter are analysed within a thermodynamical spinodal approach for a set of well calibrated equations of state. It is shown that even though different equations of state are constrained by the same experimental, theoretical and observational data, and the properties of symmetric nuclear matter are similar within the models, the properties of very asymmetric nuclear matter, such as the one found inside of neutron stars, differ a lot for various models. Some models predict larger transition densities to homog…
