Isospin Diffusion Research Articles

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 ${E}_{\mathrm{sym}}(\ensuremath{\rho},T)$ and symmetry free energy ${F}_{\mathrm{sym}}(\ensuremath{\rho},T)$ for hot, isospin asymmetric nuclear matter. It is shown that the symmetry energy ${E}_{\mathrm{sym}}(\ensuremath{\rho},T)$ generally decreases with increasing temperature while the symmetry free energy ${F}_{\mathrm{sym}}(\ensuremath{\rho},T)$ 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 ${E}_{\mathrm{sym}}(\ensuremath{\rho},T)$ is then used to estimate the average freeze-out density of the IMF's.

Nuclear symmetry potential in the relativistic impulse approximation

Using the relativistic impulse approximation with the Love-Franey $\mathit{NN}$ scattering amplitude developed by Murdock and Horowitz, we investigate the low-energy ($100\ensuremath{\leqslant}{E}_{\mathrm{kin}}\ensuremath{\leqslant}400$ MeV) behavior of the nucleon Dirac optical potential, the Schr\"odinger-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 well both the isospin diffusion data from heavy-ion collisions and the empirical neutron-skin thickness of $^{208}\mathrm{Pb}$.

Constraining the radii of neutron stars with terrestrial nuclear laboratory data

Neutron star radii are primarily determined by the pressure of isospin asymmetric matter which is proportional to the slope of the nuclear symmetry energy. Available terrestrial laboratory data on the isospin diffusion in heavy-ion reactions at intermediate energies constrain the slope of the symmetry energy. Using this constraint, we show that the radius (radiation radius) of a 1.4 solar mass (M⊙) neutron star is between 11.5 (14.4) and 13.6 (16.3) km.

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 ± 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, Gσ, and Rσ 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 ± 0.04 fm for 208 Pb , 0.29 ± 0.04 fm for 132 Sn , and 0.22 ± 0.04 fm for 124 Sn .

Progress towards Determining the Density Dependence of the Nuclear Symmetry Energy Using Heavy-Ion Reactions

The latest development in determining the density dependence of the nuclear symmetry energy using heavy-ion collisions is reviewed. Within the IBUU04 version of an isospin- and momentum-dependent transport model using a modified Gogny effective interaction, recent experimental data from NSCL/MSU on isospin diffusion are found to be consistent with a nuclear symmetry energy of E sym(ρ)≈31.6(ρ/ρ0)1.05 at subnormal densities. Predictions on several observables sensitive to the density dependence of the symmetry energy at supranormal densities accessible at GSI and the planned Rare Isotope Accelerator (RIA) are also made.

Exploring the extended density-dependent Skyrme effective forces for normal and isospin-rich nuclei to neutron stars

We parameterize the recently proposed generalized Skyrme effective force (GSEF) containing extended density dependence. The parameters of the GSEF are determined by the fit to several properties of the normal and isospin-rich nuclei. We also include in our fit a realistic equation of state for the pure neutron matter up to high densities so that the resulting Skyrme parameters can be suitably used to model the neutron star with the "canonical" mass ($\sim 1.4 M_\odot$). For the appropriate comparison we generate a parameter set for the standard Skyrme effective force (SSEF) using exactly the same set of the data as employed to determine the parameters of the GSEF. We find that the GSEF yields larger values for the neutron skin thickness which are closer to the recent predictions based on the isospin diffusion data. The Skyrme parameters so obtained are employed to compute the strength function for the isoscalar giant monopole, dipole and quadrupole resonances. It is found that in the case of GSEF, due to the the larger value of the nucleon effective mass the values of centroid energies for the isoscalar giant resonances are in better agreement with the corresponding experimental data in comparison to those obtained using the SSEF. We also present results for some of the key properties associated with the neutron star of "canonical" mass and for the one with the maximum mass.

Isospin transport at Fermi energies

In this paper we investigate isospin transport mechanisms in semiperipheral collisions at Fermi energies. The effects of the formation of a low density region (neck) between the two reaction partners and of preequilibrium emission on the dynamics of isospin equilibration are carefully analyzed. We clearly identify two main contributions to the isospin transport: isospin diffusion due to the $N/Z$ ratio and isospin drift due to the density gradients. Both effects are sensitive to the symmetry part of the nuclear equation of state (EOS), in particular to the value and slope around saturation density.

Nucleon-nucleon cross sections in neutron-rich matter and isospin transport in heavy-ion reactions at intermediate energies

Nucleon-nucleon (NN) cross sections are evaluated in neutron-rich matter using a scaling model according to density, momentum, and isospin dependent nucleon effective masses. It is found that the in-medium NN cross sections are not only reduced but also have a different isospin dependence compared with the free-space ones. Because of the neutron-proton effective mass splitting the difference between nn and pp scattering cross sections increases with the increasing isospin asymmetry of the medium. Within the transport model IBUU04, the in-medium NN cross sections are found to influence significantly the isospin transport in heavy-ion reactions. With the in-medium NN cross sections, a symmetry energy of ${E}_{\mathrm{sym}}(\ensuremath{\rho})\ensuremath{\approx}31.6(\ensuremath{\rho}/{\ensuremath{\rho}}_{0}){}^{0.69}$ was found most acceptable compared with both the MSU isospin diffusion data and the presently acceptable neutron-skin thickness in $^{208}\mathrm{Pb}$. The isospin dependent part ${K}_{\mathrm{asy}}({\ensuremath{\rho}}_{0})$ of isobaric nuclear incompressibility was further narrowed down to $\ensuremath{-}500\ifmmode\pm\else\textpm\fi{}50$ MeV. The possibility of determining simultaneously the in-medium NN cross sections and the symmetry energy was also studied. The proton transverse flow, or even better the combined transverse flow of neutrons and protons, can be used as a probe of the in-medium NN cross sections without much hindrance from the uncertainties of the symmetry energy.

Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei

Correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy are studied in the Skyrme Hartree-Fock model. From the most recent analysis of the isospin diffusion data in heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections, a value of $L=88\pm 25$ MeV for the slope of the nuclear symmetry energy at saturation density is extracted, and this imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Predicted thickness of the neutron skin is $0.22\pm 0.04$ fm for $% ^{208}$Pb, $0.29\pm 0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $% ^{124}$Sn.

Isospin diffusion in heavy-ion collisions and the neutron skin thickness of lead

The correlation between the thickness of the neutron skin in $^{208}\mathrm{Pb}$ and the degree of isospin diffusion in heavy-ion collisions is examined. The same equation of state is used to compute the degree of isospin diffusion in an isospin-depedent transport model and the neutron skin thickness in the Hartree-Fock approximation. We find that skin thicknesses less than 0.15 fm are excluded by the isospin diffusion data.

Fluctuations and Isospin Equilibration in Heavy Ion Reactions

The Boltzmann–Uehling–Uhlenbeck (BUU) approach with density fluctuations was used to study the density dependence of the asymmetry term in the nuclear equation of state (EOS). The isospin diffusion and equilibration process was investigated. The isotopic ratios of light particles were not sensitive enough to distinguish between asy-stiff and asy-soft EOS. However, the isospin ratio seems to be more sensitive to the density dependence of the asymmetry term in the nuclear equation of state and it favors a more asy-stiff equation of state.

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(sym)(rho) approximately 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.

Isospin effects on reaction dynamics from low to relativistic energies

We present several possibilities offered by the reaction dynamics of dissipative heavy ion collisions to study in detail the symmetry term of the nuclear equation of state, EOS. In the Fermi energy domain we discuss isospin effects on the nuclear liquid–gas phase transition, Isospin Distillation , and on mid-rapidity fragment formation in semicentral collisions. The correlation between isospin diffusion and deviations from the Viola systematics will be analysed. Collective flows are studied at intermediate energies in order to extract observables sensitive to the nucleon effective mass splitting at high isospin density.

Isospin diffusion in heavy ion collisions

Abstract In this talk, we will examine isoscaling, the exponential dependence of the isotope yield ratios on the neutron number and proton number, as an experimental observable to explore isospin diffusion in heavy ion collisions. Comparison to transport model such as BUU will be discussed.

Isospin diffusion in heavy ion collisions

In this talk, we will examine isoscaling, the exponential dependence of the isotope yield ratios on the neutron number and proton number, as an experimental observable to explore isospin diffusion in heavy ion collisions. Comparison to transport model such as BUU will be discussed.

Isospin effects on reaction dynamics from low to relativistic energies

We present several possibilities offered by the reaction dynamics of dissipative heavy ion collisions to study in detail the symmetry term of the nuclear equation of state, EOS. In the Fermi energy domain we discuss isospin effects on the nuclear liquid–gas phase transition, Isospin Distillation, and on mid-rapidity fragment formation in semicentral collisions. The correlation between isospin diffusion and deviations from the Viola systematics will be analysed. Collective flows are studied at intermediate energies in order to extract observables sensitive to the nucleon effective mass splitting at high isospin density.

Isospin diffusion and the nuclear symmetry energy in heavy ion reactions.

Using symmetric 112Sn+112Sn, 124Sn+124Sn collisions as references, we probe isospin diffusion in peripheral asymmetric 112Sn+124Sn, 124Sn+112Sn systems at an incident energy of E/A=50 MeV. Isoscaling analyses imply that the quasiprojectile and quasitarget in these collisions do not achieve isospin equilibrium, permitting an assessment of isospin transport rates. We find that comparisons between isospin sensitive experimental and theoretical observables, using suitably chosen scaled ratios, permit investigation of the density dependence of the asymmetry term of the nuclear equation of state.

Nuclear isospin diffusivity

The isospin diffusion and other irreversible phenomena are discussed for a two-component nuclear Fermi system. The set of Boltzmann transport equations, such as employed for reactions, are linearized, for weak deviations of a system from uniformity, in order to arrive at nonreversible fluxes linear in the nonuniformities. Besides the diffusion driven by a concentration gradient, also the diffusion driven by temperature and pressure gradients is considered. Diffusivity, conductivity, heat conduction and shear viscosity coefficients are formally expressed in terms of the responses of distribution functions to the nonuniformities. The linearized Boltzmann-equation set is solved, under the approximation of constant form-factors in the distribution-function responses, to find concrete expressions for the transport coefficients in terms of weighted collision integrals. The coefficients are calculated numerically for nuclear matter, using experimental nucleon-nucleon cross sections. The isospin diffusivity is inversely proportional to the neutron-proton cross section and is also sensitive to the symmetry energy. At low temperatures in symmetric matter, the diffusivity is directly proportional to the symmetry energy.

Neck fragmentation reaction mechanism

Based on a microscopic transport model, we study the origin of nonstatistical intermediate mass fragment (IMF) production in semicentral heavy ion collisions at the Fermi energies. We show that a fast, dynamical IMF formation process, the neck fragmentation mechanism, can explain the experimentally observed features: deviations from Viola systematics and anisotropic, narrow angular distributions. It may be regarded as the continuation of the multifragmentation mechanism towards intermediate impact parameters. Its relation to other dynamical mechanisms, the induced fission and the abrasion of the spectator zones, that can also contribute to mid-rapidity IMF production, is discussed. The dependence on beam energy and centrality of the collision is carefully analysed. The competition between volume and surface instabilities makes this mechanism very sensitive to the in-medium nucleon-nucleon interactions, from the cross sections for hard collisions to the compressibility and other equation of state (EOS) properties. For charge asymmetric collisions the sensitivity of various observables to the symmetry energy is investigated. Of particular interest appears the isospin diffusion dynamics with no signal of isospin equilibration. However, in spite of the short time scales and of the dynamical aspects, we notice isoscaling features of the neck mechanism. We observe that isospin enrichment of the neck zone as well as the isoscaling parameters are sensitive to the density dependence of asymmetry term of EOS around and below saturation value.

Reaction Dynamics with Exotic Nuclei

AbstractWe review the new possibilities offered by the reaction dynamics of asymmetricheavy ion collisions, using stable and unstable beams. We show that it represents arather unique tool to probe regions of highly Asymmetric Nuclear Matter (ANM) incompressed as well as dilute phases, and to test the in-medium isovector interactionfor high momentum nucleons. The focus is on a detailed study of the symmetryterm of the nuclear Equation of State (EOS) in regions far away from saturationconditions but always under laboratory controlled conditions.Thermodynamic properties of ANM are surveyed starting from nonrelativisticand relativistic effective interactions. In the relativistic case the role of the isovectorscalar δ-meson is stressed. The qualitative new features of the liquid-gas phase tran-sition, ”diffusive” instability and isospin distillation, are discussed. The results ofab-initio simulations of n-rich, n-poor, heavy ion collisions, using stochastic isospindependent transport equations, are analysed as a function of beam energy and cen-trality. The isospin dynamics plays an important role in all steps of the reaction,from prompt nucleon emissions to the final fragments. The isospin diffusion is alsoof large interest, due to the interplay of asymmetry and density gradients. In rela-tivistic collisions, the possibility of a direct study of the covariant structure of theeffective nucleon interaction is shown. Results are discussed for particle production,collective flows and iso-transparency.Perspectives of further developments of the field, in theory as well as in experi-ment, are presented.