Hot Asymmetric Nuclear Matter Research Articles

Effect of Λv coupling on liquid gas phase transition in warm asymmetric nuclear matter

We present a comprehensive analysis on several features of liquid gas (LG) phase transition in warm asymmetric nuclear matter using relativistic mean field model with isoscalar-isovector Λv coupling. At subsaturation as well as supranormal densities, the Λv coupling systematically controls the density dependence of nuclear symmetry energy in the relativistic mean field model. We found that the boundary of LG phase-coexistence region increases with the higher values of Λv coupling. Similarly the maximal isospin asymmetry, critical pressure and critical temperature increases with the increasing values of Λv, which shows that the liquid gas phase transition is quite sensitive to the density dependence of symmetry energy in hot asymmetric nuclear matter.

Charmonia and bottomonia in asymmetric magnetized hot nuclear matter

We investigate the mass-shift of P-wave charmonium ( , ), and S and P-wave bottomonium ( , , , and ) states in magnetized hot asymmetric nuclear matter using the unification of QCD sum rules (QCDSR) and the chiral model. Within QCDSR, we use two approaches, i.e., the moment sum rule and the Borel sum rule. The magnetic field induced scalar gluon condensate and the twist-2 gluon operator calculated in the chiral ) model are utilised in QCD sum rules to calculate the in-medium mass-shift of the above mesons. The attractive mass-shift of these mesons is observed, which is more sensitive to magnetic field in the high density regime for charmonium, however less so for bottomonium. These results may be helpful to understand the decay of higher quarkonium states to the lower quarkonium states in asymmetric heavy ion collision experiments.

Effects of energy conservation on equilibrium properties of hot asymmetric nuclear matter

Based on the relativistic Vlasov-Uehling-Uhlenbeck transport model, which includes relativistic scalar and vector potentials on baryons, we consider a $N-\Delta-\pi$ system in a box with periodic boundary conditions to study the effects of energy conservation in particle production and absorption processes on the equilibrium properties of the system. The density and temperature of the matter in the box are taken to be similar to the hot dense matter formed in heavy ion collisions at intermediate energies. We find that to maintain the equilibrium numbers of $N$, $\Delta$ and $\pi$, which depend on the mean-field potentials of $N$ and $\Delta$, requires the inclusion of these potentials in the energy conservation condition that determines the momenta of outgoing particles after a scattering or decay process. We further find that the baryon scalar potentials mainly affect the $\Delta$ and pion equilibrium numbers, while the baryon vector potentials have considerable effects on the effective charged pion ratio at equilibrium. Our results thus indicate that it is essential to include in the transport model the effect of potentials in the energy conservation of a scattering or decay process, which is ignored in most transport models, for studying pion production in heavy ion collisions.

Warm unstable asymmetric nuclear matter: Critical properties and the density dependence of the symmetry energy

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 equation of state of asymmetric nuclear matter at sub-saturation densities is not sufficiently constrained. The distillation effects are sensitive to the density dependence of the symmetry energy at low temperatures which tend to wash out with increasing temperature.

Bulk and isospin instabilities in hot nuclear matter

The instability of hot asymmetric nuclear matter with respect to bulk density distortions is considered. The equation of state of the extended Thomas-Fermi approximation is used. The origin of the anomalous dispersion and the influence of the Fermi-surface distortion effects on the bulk and isospin instabilities in homogenous nuclear matter are investigated. It is shown that the development of both instabilities is reduced significantly due to the Fermi-surface distortion effects. The dependence of the bulk instability on the temperature and on the multipolarity of the particle density distortions are shown for the nucleus of $^{208}\mathrm{Pb}$. The dependence of the formation of the decay modes (fission or multifragmentation) of the nuclei on the temperature and the Fermi-surface distortion effects are demonstrated. It is shown that in the case of low temperatures the preferable mode for the bulk instability is binary fission. For higher temperatures, the preferred modes are the multifragmentations for small clusters. The number of clusters increases with increasing temperature.

Mean-field study of hotβ-stable protoneutron star matter: Impact of the symmetry energy and nucleon effective mass

A consistent Hartree-Fock study of the equation of state (EOS) of asymmetric nuclear matter at finite temperature has been performed using realistic choices of the effective, density dependent nucleon-nucleon (NN) interaction, which were successfully used in different nuclear structure and reaction studies. Given the importance of the nuclear symmetry energy in the neutron star formation, EOS's associated with different behaviors of the symmetry energy were used to study hot asymmetric nuclear matter. The slope of the symmetry energy and nucleon effective mass with increasing baryon density was found to affect the thermal properties of nuclear matter significantly. Different density dependent NN interactions were further used to study the EOS of hot protoneutron star (PNS) matter of the $npe\mu\nu$ composition in $\beta$-equilibrium. The hydrostatic configurations of PNS in terms of the maximal gravitational mass $M_{\rm max}$ and radius, central density, pressure and temperature at the total entropy per baryon $S/A= 1,2$ and 4 have been determined in both the neutrino-free and neutrino-trapped scenarios. The obtained results show consistently a strong impact of the symmetry energy and nucleon effective mass on thermal properties and composition of hot PNS matter. $M_{\rm max}$ values obtained for the (neutrino-free) $\beta$-stable PNS at $S/A=4$ were used to assess time $t_{\rm BH}$ of the collapse of 40 $M_\odot$ protoneutron progenitor to black hole, based on a correlation between $t_{\rm BH}$ and $M_{\rm max}$ found from the hydrodynamic simulation by Hempel {\it et al.}.

Application of the nuclear equation of state obtained by the variational method to core-collapse supernovae

The equation of state (EOS) for hot asymmetric nuclear matter which is constructed with the variational method starting from the Argonne v18 and Urbana IX nuclear forces is applied to spherically symmetric core-collapse supernovae (SNe). We first investigate the EOS of isentropic beta-stable SN matter, and find that the matter with the variational EOS is more neutron-rich than that with the Shen EOS. Using the variational EOS for uniform matter supplemented by the Shen EOS of non-uniform matter at low densities, we perform general-relativistic spherically symmetric simulations of core-collapse SNe with and without neutrino transfer, starting from a presupernova model of 15 solar mass. In the adiabatic simulation without neutrino transfer, the explosion is successful, and the explosion energy with the variational EOS is larger than that with the Shen EOS. In the case of the simulation with neutrino transfer, the shock wave stalls and then the explosion fails, as in other spherically symmetric simulations. The inner core with the variational EOS is more compact than that with the Shen EOS, due to the relative softness of the variational EOS. This implies that the variational EOS is more advantageous for SN explosions than the Shen EOS.

Nuclear equation of state with the variational method and its application to supernova simulations

We report on an equation of state (EOS) of hot asymmetric nuclear matter constructed using the variational method and its application to hydrodynamic simulations of core-collapse supernovae. This nuclear EOS is based on the AV18 two-body potential and UIX three-body potential, and the energy per nucleon at zero temperature is constructed with the cluster variational method. At finite temperatures, the free energies per nucleon are calculated with an extension of the variational method devised by Schmidt and Pandharipande. This EOS is in good agreement with that by the Fermi hypernetted chain variational calculations at zero and finite temperatures, and the structure of neutron stars calculated with this EOS is consistent with recent observational data. Using this nuclear EOS, we perform a spherically symmetric general-relativistic adiabatic simulation of the SN explosion. The explosion energy calculated with our EOS in the present simulation is larger than that obtained with the Shen EOS, implying that the variational EOS is softer than the Shen EOS.

Liquid–gas phase transition in hot asymmetric nuclear matter with density-dependent relativistic mean-field models

The liquid–gas phase transition in hot asymmetric nuclear matter is studied within density-dependent relativistic mean-field models where the density dependence is introduced according to the Brown–Rho scaling and constrained by available data at low densities and empirical properties of nuclear matter. The critical temperature of the liquid–gas phase transition is obtained to be 15.7 MeV in symmetric nuclear matter falling on the lower edge of the small experimental error bars. In hot asymmetric matter, the boundary of the phase-coexistence region is found to be sensitive to the density dependence of the symmetry energy. The critical pressure and the area of phase-coexistence region increases clearly with the softening of the symmetry energy. The critical temperature of hot asymmetric matter separating the single-phase region from the two-phase region is analyzed to have a moderate sensitivity to the symmetry energy and is higher for the model possessing the softer symmetry energy.

Nuclear symmetry energy and incompressibility of hot asymmetric nuclear matter in the Thomas-Fermi model

The density dependence of nuclear symmetry energy and incompressibility of asymmetric nuclear matter have been investigated in the framework of the Thomas-Fermi approximation using the effective nucleon - nucleon interaction of Myers and Swiatecki in the new approach. The symmetry energy of about QUOTE is obtained at the saturation density. The symmetry energy and incompressibility of asymmetric nuclear matter are all in excellent agreement with the other many-body calculations. Key words: Nuclear matter – symmetry energy-incompressibility-nucleon–nucleon interactions.

Liquid-gas phase transition in hot asymmetric nuclear matter

We use a density-dependent relativistic mean field model to study the properties of nuclear systems at finite temperature. The liquid-gas phase transition of symmetric and asymmetric nuclear matter is discussed. A limiting pressure plim for hot asymmetric nuclear matter has been found because of the density dependence of the nucleon-nucleon-rho meson coupling. It is found that the liquid-gas phase transition cannot take place if p > plim. The binodal surface for this model is addressed. In addition, we calculated the asymmetry parameter dependence of the critical temperature.

Density matrix expansion for the isospin- and momentum-dependent MDI interaction

By assuming that the isospin- and momentum-dependent MDI interaction has a form similar to the Gogny-like effective two-body interaction with a Yukawa finite-range term and the momentum dependence originates only from the finite-range exchange interaction, we determine its parameters by comparing the predicted potential energy density functional in uniform nuclear matter with what has been usually given and used extensively in transport models for studying isospin effects in intermediate-energy heavy-ion collisions as well as in investigating the properties of hot asymmetric nuclear matter and neutron star matter. We then use the density matrix expansion to derive from the resulting finite-range exchange interaction an effective Skyrme-like zero-range interaction with density-dependent parameters. As an application, we study the transition density and pressure at the inner edge of neutron star crusts using the stability conditions derived from the linearized Vlasov equation for the neutron star matter.

Finite-temperature calculations for spin-polarized asymmetric nuclear matter with the lowest order constrained variational method

The lowest order constrained variational (LOCV) technique has been used to investigate some of the thermodynamic properties of spin polarized hot asymmetric nuclear matter, such as the free energy, symmetry energy, susceptibility and equation of state. We have shown that the symmetry energy of the nuclear matter is substantially sensitive to the value of spin polarization. Our calculations show that the equation of state of the polarized hot asymmetric nuclear matter is stiffer for the higher values of the polarization as well as the isospin asymmetry parameter. Our results for the free energy and susceptibility show that the spontaneous ferromagnetic phase transition cannot occur for hot asymmetric matter.

MEDIUM EFFECTS ON CHARGED PION RATIO IN HEAVY ION COLLISIONS

We have recently studied in the delta-resonance–nucleon-hole model the dependence of the pion spectral function in hot dense asymmetric nuclear matter on the charge of the pion due to the pion p-wave interaction in nuclear medium. In a thermal model, this isospin-dependent effect enhances the ratio of negatively charged to positively charged pions in neutron-rich nuclear matter, and the effect is comparable to that due to the uncertainties in the theoretically predicted stiffness of nuclear symmetry energy at high densities. This effect is, however, reversed if we also take into account the s-wave interaction of the pion in nuclear medium as given by chiral perturbation theory, resulting instead in a slightly reduced ratio of negatively charged to positively charged pions. Relevance of our results to the determination of the nuclear symmetry energy from the ratio of negatively to positively charged pions produced in heavy ion collisions is discussed.

Nuclear symmetry energy effects on liquid-gas phase transition in hot asymmetric nuclear matter

The liquid-gas phase transition in hot asymmetric nuclear matter is investigated within relativistic mean-field model using the density dependence of nuclear symmetry energy constrained from the measured neutron skin thickness of finite nuclei. We find symmetry energy has a significant influence on several features of liquid-gas phase transition. The boundary and area of the liquid-gas coexistence region, the maximal isospin asymmetry and the critical values of pressure and isospin asymmetry all of which systematically increase with increasing softness in the density dependence of symmetry energy. The critical temperature below which the liquid-gas mixed phase exists is found higher for a softer symmetry energy.

Temperature and momentum dependence of single-particle properties in hot asymmetric nuclear matter

We have studied the effects of momentum-dependent interactions on the single-particle properties of hot asymmetric nuclear matter. In particular, the single-particle potential of protons and neutrons as well as the symmetry potential have been studied within a self-consistent model using a momentum-dependent effective interaction. In addition, the isospin splitting of the effective mass has been derived from the above model. In each case temperature effects have been included and analyzed. The role of the specific parametrization of the effective interaction used in the present work has been investigated. It has been concluded that the behavior of the symmetry potential depends strongly on the parametrization of the interaction part of the energy density and the momentum dependence of the regulator function. The effects of the parametrization have been found to be less pronounced on the isospin mass splitting.

Effects of isospin and momentum dependent interactions on thermal properties of asymmetric nuclear matter

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 equation of state and the symmetry energy are not so sensitive to the momentum dependence of the interaction. The symmetry energy at fixed density is found to generally decrease with temperature and for the MDI interaction the decrement is essentially due to the potential part. It is further shown that only the low momentum part of the single-particle potential and the nucleon effective mass increases significantly with temperature for the momentum-dependent interactions. For the MDI interaction, the low momentum part of the symmetry potential is significantly reduced with increasing temperature. For the mechanical and chemical instabilities as well as the liquid-gas phase transition in hot asymmetric nuclear matter, our results indicate that the boundaries of these instabilities and the phase-coexistence region generally shrink with increasing temperature and are sensitive to the density dependence of the symmetry energy and the isospin and momentum dependence of the nuclear interaction, especially at higher temperatures.

Effects of isospin and momentum dependent interactions on liquid–gas phase transition in hot asymmetric nuclear matter

The liquid–gas phase transition in hot neutron-rich nuclear matter is investigated 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). The boundary of the phase-coexistence region is shown to be sensitive to the density dependence of the nuclear symmetry energy with a softer symmetry energy giving a higher critical pressure and a larger area of phase-coexistence region. Compared with the momentum-independent MID interaction, the isospin and momentum-dependent MDI interaction is found to increase the critical pressure and enlarge the area of phase-coexistence region. For the isoscalar momentum-dependent eMDYI interaction, a limiting pressure above which the liquid–gas phase transition cannot take place has been found and it is shown to be sensitive to the stiffness of the symmetry energy.

Weak interactions in hot nucleon matter

The reaction rates for electron capture, neutrino absorption, and neutrino scattering in hot asymmetric nuclear matter are calculated with two-body effective interactions and one-body effective weak operators obtained from realistic models of nuclear forces by use of correlated basis theory. The infinite system is modeled in a box with periodic boundary conditions, and the one-quasiparticle quasi-hole response functions are calculated with a large microcanonical sample and the Tamm-Dancoff approximation. Results for matter at a temperature of 10 MeV, proton fraction 0.4, and densities $\ensuremath{\rho}=(\frac{1}{2},1,\frac{3}{2}){\ensuremath{\rho}}_{0}$, where ${\ensuremath{\rho}}_{0}$ is the equilibrium density of symmetric nuclear matter, are presented to illustrate the method. In general, the strength of the response is shifted to higher-energy transfers when compared with that of a noninteracting Fermi gas. The shift in the response and the weakness of effective operators as compared with the bare operators significantly reduce the cross sections for electron capture and neutrino scattering by factors of $~2.5$--$3.5$. In contrast, the symmetry energy enhances the neutrino absorption reaction rate relative to the Fermi gas. However, this reaction rate is still quite small because of Pauli blocking.

Correlations in hot asymmetric nuclear matter

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 Hartree Fock approach. This effect increases with density and thereby modifies the saturation density and leads to smaller symmetry energies.