Effects of medium-induced ρ−ω\rho-\omega meson mixing on the equation of state in isospin-asymmetric nuclear matter

We reexamine effects of the $\rho-\omega$ meson mixing mediated by nucleon polarizations on the symmetry energy in isospin-asymmetric nuclear matter. Taking into account the rearrangement term neglected in previous studies by others, we evaluate the $\rho-\omega$ mixing angle in a novel way within the Relativistic Mean-Field Models with and without chiral limits. It is found that the symmetry energy is significantly softened at high densities contrary to the finding in earlier studies. As the first step of going beyond the lowest-order calculations, we also solve the RPA equation for the $\rho-\omega$ mixing. In this case, it is found that the symmetry energy is not only significantly softened by the $\rho-\omega$ mixing at supra-saturation densities, similar to the lowest-order $\rho-\omega$ mixing, but interestingly also softened at subsaturation densities. In addition, the softening of the symmetry energy at subsaturation densities can be partly suppressed by the nonlinear self-interaction of the $\sigma$ meson.Comment: Significant changes made. Accepted version to appear in PRC (2009

Constraining the Skyrme effective interactions and the neutron skin thickness of nuclei using isospin diffusion data from heavy ion collisions

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$_\sigma$, and R$_\sigma$ are found to give $L$ values that are consistent with the extracted one. Further study on the correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy in the Skyrme Hartree-Fock approach leads to predicted thickness of the neutron skin of $0.22\pm 0.04$ fm for $^{208}$Pb, $0.29\pm 0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $^{124}$Sn.Comment: 10 pages, 4 figures, 1 Table, Talk given at 1) International Conference on Nuclear Structure Physics, Shanghai, 12-17 June, 2006; 2) 11th China National Nuclear Structure Physics Conference, Changchun, Jilin, 13-18 July, 200

Magnetic effects in heavy-ion collisions at intermediate energies

The time-evolution and space-distribution of internal electromagnetic fields in heavy-ion reactions at beam energies between 200 and 2000 MeV/nucleon are studied within an Isospin-dependent Boltzmann-Uhling-Uhlenbeck transport model IBUU11. While the magnetic field can reach about $7\times 10^{16}$ G which is significantly higher than the estimated surface magnetic field ($\sim 10^{15}$ G) of magnetars, it has almost no effect on nucleon observables as the Lorentz force is normally much weaker than the nuclear force. Very interestingly, however, the magnetic field generated by the projectile-like (target-like) spectator has a strong focusing/diverging effect on positive/negative pions at forward (backward) rapidities. Consequently, the differential $\pi^-/\pi^+$ ratio as a function of rapidity is significantly altered by the magnetic field while the total multiplicities of both positive and negative pions remain about the same. At beam energies above about 1 GeV/nucleon, while the integrated ratio of total $\pi^-$ to $\pi^+$ multiplicities is not, the differential $\pi^-/\pi^+$ ratio is sensitive to the density dependence of nuclear symmetry energy $E_{\rm{sym}}(\rho)$. Our findings suggest that magnetic effects should be carefully considered in future studies of using the differential $\pi^-/\pi^+$ ratio as a probe of the $E_{\rm{sym}}(\rho)$ at supra-saturation densities.Comment: 12 pages including 8 figures and 1 tabl

High-energy behavior of the nuclear symmetry potential in asymmetric nuclear matter

Using the relativistic impulse approximation with empirical NN scattering amplitude and the nuclear scalar and vector densities from the relativistic mean-field theory, we evaluate the Dirac optical potential for neutrons and protons in asymmetric nuclear matter. From the resulting Schr\"{o}% dinger-equivalent potential, the high energy behavior of the nuclear symmetry potential is studied. We find that the symmetry potential at fixed baryon density is essentially constant once the nucleon kinetic energy is greater than about 500 MeV. Moreover, for such high energy nucleon, the symmetry potential is slightly negative below a baryon density of about $$ fm$^{-3}$ and then increases almost linearly to positive values at high densities. Our results thus provide an important constraint on the energy and density dependence of nuclear symmetry potential in asymmetric nuclear matter.Comment: 6 pages, 5 figures, revised version, to appear in PR

Determination of the stiffness of the nuclear symmetry energy from isospin diffusion

With an isospin- and momentum-dependent transport model, we find that the degree of isospin diffusion in heavy ion collisions at intermediate energies is affected by both the stiffness of the nuclear symmetry energy and the momentum dependence of the nucleon potential. Using a momentum dependence derived from the Gogny effective interaction, recent experimental data from NSCL/MSU on isospin diffusion are shown to be consistent with a nuclear symmetry energy given by $E_{\text{sym}}(\rho)\approx 31.6(\rho /\rho_{0})^{1.05}$ at subnormal densities. This leads to a significantly constrained value of about -550 MeV for the isospin-dependent part of the isobaric incompressibility of isospin asymmetric nuclear matter.Comment: 4 pages, 4 figures, 1 table, revised version, to appear in PR

Mean free paths and in-medium scattering cross sections of energetic nucleons in neutron-rich nucleonic matter within the relativistic impulse approximation

The mean free paths and in-medium scattering cross sections of energetic nucleons in neutron-rich nucleonic matter are investigated using the nucleon optical potential obtained within the relativistic impulse approximation with the empirical nucleon-nucleon scattering amplitudes and the nuclear densities obtained in the relativistic mean field model. It is found that the isospin-splitting of nucleon mean free paths, sensitive to the imaginary part of the symmetry potential, changes its sign at certain high kinetic energy. The in-medium nucleon-nucleon cross sections are analytically and numerically demonstrated to be essentially independent of the isospin asymmetry of the medium and increase linearly with density in the high energy region where the relativistic impulse approximation is applicable.Comment: 13 pages, 6 figure

Generic Constraints on the Relativistic Mean-Field and Skyrme-Hartree-Fock Models from the Pure Neutron Matter Equation of State

We study the nuclear symmetry energy S(rho) and related quantities of nuclear physics and nuclear astrophysics predicted generically by relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simple prescription for preparing equivalent RMF and SHF parametrizations starting from a minimal set of empirical constraints on symmetric nuclear matter, nuclear binding energy and charge radii, enforcing equivalence of their Lorenz effective masses, and then using the pure neutron matter (PNM) equation of state (EoS) obtained from ab-initio calculations to optimize the pure isovector parameters in the RMF and SHF models. We find the resulting RMF and SHF parametrizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of <~2 MeV and <~6 MeV respectively, but that clear model dependence shows up in the predictions of higher-order symmetry energy parameters, leading to important differences in (a) the slope of the correlation between J and L from the confidence ellipse, (b) the isospin-dependent part of the incompressibility of nuclear matter K_tau, (c) the symmetry energy at supra-saturation densities, and (d) the predicted neutron star radii. The model dependence can lead to about 1-2 km difference in predictions of the neutron star radius given identical predicted values of J, L and symmetric nuclear matter (SNM) saturation properties. Allowing the full freedom in the effective masses in both models leads to constraints of 30<~J<~31.5 MeV, 35<~L<~60 MeV, -330<~K_tau<~-216 MeV for the RMF model as a whole and 30<~J<~33 MeV, 28<~L<~65 MeV, -420<~K_tau<~-325 MeV for the SHF model as a whole. Notably, given PNM constraints, these results place RMF and SHF models as a whole at odds with some constraints on K_tau inferred from giant monopole resonance and neutron skin experimental results.Comment: 15 pages, 7 figures, 4 table

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

Effect of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei

Using an isospin-dependent transport model, we study the effects of nuclear symmetry energy on two-nucleon correlation functions in heavy ion collisions induced by neutron-rich nuclei. We find that the density dependence of the nuclear symmetry energy affects significantly the nucleon emission times in these collisions, leading to larger values of two-nucleon correlation functions for a symmetry energy that has a stronger density dependence. Two-nucleon correlation functions are thus useful tools for extracting information about the nuclear symmetry energy from heavy ion collisions.Comment: Revised version, to appear in Phys. Rev. Let

Isospin Effect on the Process of Multifragmentation and Dissipation at Intermediate Energy Heavy Ion Collisions

In the simulation of intermediate energy heavy ion collisions by using the isospin dependent quantum molecular dynamics, the isospin effect on the process of multifragmentation and dissipation has been studied. It is found that the multiplicity of intermediate mass fragments $N_{imf}$ for the neutron-poor colliding system is always larger than that for the neutron-rich system, while the quadrupole of single particle momentum distribution $Q_{zz}$ for the neutron-poor colliding system is smaller than that of the neutron-rich system for all projectile-target combinations studied at the beam energies from about 50MeV/nucleon to 150MeV/nucleon. Since $Q_{zz}$ depends strongly on isospin dependence of in-medium nucleon-nucleon cross section and weakly on symmetry potential at the above beam energies, it may serve as a good probe to extract the information on the in-medium nucleon-nucleon cross section. The correlation between the multiplicity $N_{imf}$ of intermediate mass fragments and the total numer of charged particles $N_c$ has the behavior similar to $Q_{zz}$, which can be used as a complementary probe to the in-medium nucleon-nucleon cross section.Comment: 18 pages, 9 figure