Covariance Analysis of Symmetry Energy Observables from Heavy Ion Collision

Using covariance analysis, we quantify the correlations between the interaction parameters in a transport model and the observables commonly used to extract information of the Equation of State of Asymmetric Nuclear Matter in experiments. By simulating $^{124}$Sn+$^{124}$Sn, $^{124}$Sn+$^{112}$Sn and $^{112}$Sn+$^{112}$Sn reactions at beam energies of 50 and 120 MeV per nucleon, we have identified that the nucleon effective mass splitting are most strongly correlated to the neutrons and protons yield ratios with high kinetic energy from central collisions especially at high incident energy. The best observable to determine the slope of the symmetry energy, L, at saturation density is the isospin diffusion observable even though the correlation is not very strong ($sim$0.7). Similar magnitude of correlation but opposite in sign exists for isospin diffusion and nucleon isoscalar effective mass. At 120 MeV/u, the effective mass splitting and the isoscalar effective mass also have opposite correlation for the double n/p and isoscaling p/p yield ratios. By combining data and simulations at different beam energies, it should be possible to place constraints on the slope of symmetry energy (L) and effective mass splitting with reasonable uncertainties.

Competition between Coulomb and Symmetry Potential in Semi-peripheral Heavy-ion Collisions

The anisotropy of angular distributions of emitted nucleons and light charged particles for the asymmetric reaction system, $^{40}$Ar+$^{197}$Au, at b=6fm and $E_{beam}$=35, 50 and 100MeV/u, are investigated by using the Improved Quantum Molecular Dynamics model. The competition between the symmetry potential and Coulomb potential shows large impacts on the nucleons and light charged particles emission in projectile and target region. As a result of this competition, the angular distribution anisotropy of coalescence invariant Y(n)/Y(p) ratio at forward regions shows sensitivity to the stiffness of symmetry energy as well as the value of Y(n)/Y(p). This observable can be further checked against experimental data to understand the reaction mechanism and to extract information about the symmetry energy at subsaturation densities.

Constraints on symmetry energy and nucleon effective mass splitting with Heavy Ion Collisions

A new version of the improved quantum molecular dynamics model has been developed to include standard Skyrme interactions. Four commonly used Skyrme parameter sets, SLy4, SkI2, SkM* and Gs are adopted in the transport model code to calculate the isospin diffusion observables as well as single and double ratios of transverse emitted nucleons. While isospin diffusion observables are sensitive to the symmetry energy term, they are not very sensitive to the nucleon effective mass splitting parameters in the interactions. Our calculations show that the high energy neutrons and protons and their ratios from reactions at different incident energies provide a robust observable to study the momentum dependence of the nucleon effective mass splitting. However the sensitivity of effective mass splitting effect on the n/p yield ratios decreases with increasing beam energy, even though high energy proton and neutron are produced more abundantly at high beam energy. Our calculations show that the optimum incident energy to study nucleon effective masses is between 100-200 MeV per nucleon.

Effect of isospin dependent cluster recognition on the observables in heavy ion collisions

We introduce isospin dependence in the cluster recognition algorithms used in the Quantum Molecular Dynamics model to describe fragment formation in heavy ion collisions. This change reduces the yields of emitted nucleons and enhances the yields of fragments, especially heavier fragments. The enhancement of neutron-rich lighter fragments mainly occurs at mid-rapidity. Consequently, isospin dependent observables, such as isotope distributions, yield ratios of $n/p$, $t/^3He$, and isoscaling parameters are affected. We also investigate how equilibration in heavy ion collisions is affected by this change.

The Influence of in-medium NN cross-sections, symmetry potential and impact parameter on the isospin observables

We explore the influence of in-medium nucleon-nucleon cross section, symmetry potential and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of Quantum Molecular Dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of symmetry potential plays a more important role on the double neutron to proton ratio $DR(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total NN collision rate. We also explore both $DR(n/p)$ and $R_i$ as a function of the impact parameter. Since the copious production of intermediate mass fragments is a distinguishing feature of intermediate-energy heavy-ion collisions, we examine the isospin transport ratios constructed from different groups of fragments. We find that the values of the isospin transport ratios for projectile rapidity fragments with $Zge20$ are greater than those constructed from the entire projectile rapidity source. We believe experimental investigations of this phenomenon can be performed. These may provide significant tests of fragmentation time scales predicted by ImQMD calculations.

Isospin Diffusion and Equilibration for Sn+Sn collisions at E/A=35 MeV

Equilibration and equilibration rates have been measured by colliding Sn nuclei with different isospin asymmetries at beam energies of E/A=35 MeV. Using the yields of mirror nuclei of 7Li and 7Be, we have studied the diffusion of isospin asymmetry by combining data from asymmetric 112Sn+124Sn and 124Sn+112Sn collisions with that from symmetric 112Sn+112Sn and 124Sn+124Sn collisions. We use these measurements to probe isospin equilibration in central collisions where nucleon-nucleon collisions are strongly blocked by the Pauli exclusion principal. The results are consistent with transport theoretical calculations that predict a degree of transparency in these collisions, but inconsistent with the emission of intermediate mass fragments by a single chemically equilibrated source. Comparisons with ImQMD calculations are consistent with results obtained at higher incident energies that provide constraints on the density dependence of the symmetry energy.

Probing the density dependence of symmetry energy at subsaturation density with HICs

The reaction mechanism of the central collisions and peripheral collisions for $^{112,124}Sn+^{112,124}Sn$ at $E/A=50MeV$ is investigated within the framework of the Improved Quantum Molecular Dynamics model. The results show that multifragmentation process is an important mechanism at this energy region, and the influence of the cluster emission on the double n/p ratios and the isospin transport ratio are important. Furthermore, three observables, double n/p ratios, isospin diffusion and the rapidity distribution of the ratio $R_{7}$ for $^{112,124}Sn+^{112,124}Sn$ at E/A=50MeV are analyzed with the Improved Quantum Molecular Dynamics model. The results show that these three observables are sensitive to the density dependence of the symmetry energy. By comparing the calculation results to the data, the consistent constraint on the density dependence of the symmetry energy from these three observables is obtained.

Constraints on the density dependence of the symmetry energy

Collisions involving 112Sn and 124Sn nuclei have been simulated with the improved Quantum Molecular Dynamics transport model. The results of the calculations reproduce isospin diffusion data from two different observables and the ratios of neutron and proton spectra. By comparing these data to calculations performed over a range of symmetry energies at saturation density and different representations of the density dependence of the symmetry energy, constraints on the density dependence of the symmetry energy at sub-normal density are obtained. Results from present work are compared to constraints put forward in other recent analysis.