Temperature effects on the nuclear symmetry energy and symmetry free energy with an isospin and momentum dependent interaction

Within a self-consistent thermal model using an isospin and momentum dependent interaction (MDI) constrained by the isospin diffusion data in heavy-ion collisions, we investigate the temperature dependence of the symmetry energy $E_{sym}(\rho, T)$ and symmetry free energy $F_{sym}(\rho, T)$ for hot, isospin asymmetric nuclear matter. It is shown that the symmetry energy $E_{sym}(\rho, T)$ generally decreases with increasing temperature while the symmetry free energy $F_{sym}(\rho, T)$ exhibits opposite temperature dependence. The decrement of the symmetry energy with temperature is essentially due to the decrement of the potential energy part of the symmetry energy with temperature. The difference between the symmetry energy and symmetry free energy is found to be quite small around the saturation density of nuclear matter. While at very low densities, they differ significantly from each other. In comparison with the experimental data of temperature dependent symmetry energy extracted from the isotopic scaling analysis of intermediate mass fragments (IMF's) in heavy-ion collisions, the resulting density and temperature dependent symmetry energy $E_{sym}(\rho, T)$ is then used to estimate the average freeze-out density of the IMF's.used to estimate the average freeze-out density of the IMF's.Comment: 9 pages, 7 figures, 1 figure added to show the temperature dependence of the potential and kinetic parts of the symmetry energy. Revised version to appear in PR

Differential isospin-fractionation in dilute asymmetric nuclear matter

The differential isospin-fractionation (IsoF) during the liquid-gas phase transition in dilute asymmetric nuclear matter is studied as a function of nucleon momentum. Within a self-consistent thermal model it is shown that the neutron/proton ratio of the gas phase becomes {\it smaller} than that of the liquid phase for energetic nucleons, although the gas phase is overall more neutron-rich. Clear indications of the differential IsoF consistent with the thermal model predictions are demonstrated within a transport model for heavy-ion reactions. Future comparisons with experimental data will allow us to extract critical information about the momentum dependence of the isovector strong interaction.Comment: Rapid Communication, Phys. Rev. C (2007) in pres

NUCLEAR CONSTRAINTS ON PROPERTIES OF NEUTRON STAR CRUSTS

The transition density $\rho_{t}$ and pressure $P_{t}$ at the inner edge separating the liquid core from the solid crust of neutron stars are systematically studied using a modified Gogny (MDI) and 47 popular Skyrme interactions within well established dynamical and thermodynamical methods. It is shown that the widely used parabolic approximation to the full Equation of State (EOS) of isospin asymmetric nuclear matter may lead to huge errors in estimating the \rho_{t} and P_{t}, especially for stiffer symmetry energy functionals $E_{sym}(\rho)$. The \rho_{t} and P_{t} decrease roughly linearly with the increasing slope parameter $L$ of the $E_{sym}(\rho)$ using the full EOS within both methods. It is also shown that the thickness, fractional mass and moment of inertia of neutron star crust are all very sensitive to the parameter $L$ through the $\rho_{t}$. Moreover, it is shown that the $E_{sym}(\rho)$ constrained in the same sub-saturation density range as the neutron star crust by the isospin diffusion data in heavy-ion collisions at intermediate energies limits the transition density and pressure to 0.040 fm^-3}< \rho_{t} < 0.065 fm^-3 and 0.01 MeV/fm^3 < P_{t} < 0.26$MeV/fm^3, respectively. These constrained values for the transition density and pressure are significantly lower than their fiducial values currently used in the literature. Furthermore, the mass-radius relation and several other properties closely related to the neutron star crust are studied by using the MDI interaction. It is found that the newly constrained$\rho_t$and$P_t$together with the earlier estimate of$\Delta I/I>0.014$for the crustal fraction of the moment of inertia of the Vela pulsar impose a stringent constraint of R>= 4.7+4.0M/M_sun km for the radius$R$and mass$M$ of neutron stars.Comment: 55 pages, 20 figures, 2 tables, new results and discussions added, accepted version to appear in Ap

Nuclear symmetry potential in the relativistic impulse approximation

Using the relativistic impulse approximation with the Love-Franey \textsl{NN} scattering amplitude developed by Murdock and Horowitz, we investigate the low-energy (100 MeV$\leq E_{\mathrm{kin}}\leq 400$ MeV) behavior of the nucleon Dirac optical potential, the Schr\"{o}dinger-equivalent potential, and the nuclear symmetry potential in isospin asymmetric nuclear matter. We find that the nuclear symmetry potential at fixed baryon density decreases with increasing nucleon energy. In particular, the nuclear symmetry potential at saturation density changes from positive to negative values at nucleon kinetic energy of about 200 MeV. Furthermore,the obtained energy and density dependence of the nuclear symmetry potential is consistent with those of the isospin- and momentum-dependent MDI interaction with $x=0$, which has been found to describe reasonably both the isospin diffusion data from heavy-ion collisions and the empirical neutron-skin thickness of $^{208}$Pb.Comment: 8 pages, 5 figures, revised version to appear in PR

Transition Density and Pressure at the Inner Edge of Neutron Star Crusts

Using the nuclear symmetry energy that has been recently constrained by the isospin diffusion data in intermediate-energy heavy ion collisions, we have studied the transition density and pressure at the inner edge of neutron star crusts, and they are found to be 0.040 fm$^{-3}$ $\leq \rho_{t}\leq 0.065$ fm$^{-3}$ and 0.01 MeV/fm$^{3}$ $\leq P_{t}\leq 0.26$ MeV/fm$^{3}$, respectively, in both the dynamical and thermodynamical approaches. We have also found that the widely used parabolic approximation to the equation of state of asymmetric nuclear matter gives significantly higher values of core-crust transition density and pressure, especially for stiff symmetry energies. With these newly determined transition density and pressure, we have obtained an improved relation between the mass and radius of neutron stars.Comment: 7 pages, 3 figures, proceeding of "The International Workshop on Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energy (IWND2009)

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 boundary of these instabilities and the phase-coexistence region generally shrink with increasing temperature and is sensitive to the density dependence of the symmetry energy and the isospin and momentum dependence of the nuclear interaction, especially at higher temperatures.Comment: 21 pages, 29 figure