Entrance-channel dependence of isospin effects on double n/p ratio in HIC

Within the hadronic transport model IBUU04, we investigate the effect of density-dependent symmetry energy on double neutron/proton (n/p) ratio of free nucleons in heavy ion collisions by taking four isotopic Sn+Sn reaction systems. Especially the entrance-channel asymmetry and impact-parameter dependence of the effect of symmetry energy are discussed. It is found that in both central and semi-central collisions the sensitivity of the double n/p ratio to the density-dependent symmetry energy is more pronounced in neutron-richer systems. Our results also indicate clearly that the effect of symmetry energy is stronger in central collisions than that in semi-central collisions.

DETERMINING THE DENSITY DEPENDENCE OF THE NUCLEAR SYMMETRY ENERGY USING HEAVY-ION REACTIONS

We review recent progress in the determination of the subsaturation density behavior of the nuclear symmetry energy from heavy-ion collisions as well as the theoretical progress in probing the high density behavior of the symmetry energy in heavy-ion reactions induced by high energy radioactive beams. We further discuss the implications of these results for the nuclear effective interactions and the neutron skin thickness of heavy nuclei.

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 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.

Probing balance energy using momentum- and isospin-dependent potential

Using the momentum- and isospin-dependent Boltmann-Uehling-Uhlenbeck (BUU) model, we investigate the transverse flow and balance energy in two isotopic colliding systems Ca-48+Fe-58 and Cr-48+Ni-58 by adopting different symmetry potentials. By comparing the results between the two colliding systems, we find that the difference between the balance energies of two isotopic systems can be considered as a sensitive probe to the density dependence of symmetry energy.

Isospin- and momentum-dependent interaction in isospin-dependent quantum molecular dynamics

An isospin-dependent quantum molecular dynamical model (IQMD) is developed, with the isospin degree of freedom in the momentum-dependent interaction(MDI) included in IQMD, to obtain an isospin- and momentum-dependent interaction (IMDI) in IQMD. We investigate the effect of IMDI on the isospin fractionation ratio and its dynamical mechanism in the intermediate energy heavy ion collisions. It is found that the IMDI induces the significant reductions in the isospin fractionation ratio for all of beam energies, impact parameters, neutron-proton ratios and mass number of colliding systems. However, the strong dependence of isospin fractionation ratio on the symmetrical potential is preserved, with the isospin degree of freedom included in the MDI, i.e. the isospin fractionation ratio is still a good probe for extracting the information about the equation of state of isospin asymmetrical nuclear matter.

Entrance channel effects on the role of isospin-dependent momentum interaction in isospin fractionation in heavy ion collisions

An isospin degree of freedom is inserted into the momentum dependent interaction in the quantum molecular dynamics model to obtain an isospin dependent momentum interaction given in a form practically usable in isospin dependent quantum molecular dynamics model. We investigate the entrance channel effects for the role of isospin momentum dependent interaction on the isospin fractionation ratio and its dynamical mechanism in the intermediate energy heavy ion collisions. It is found that the isospin dependent momentum interaction induces a significant reduction of isospin fractionation ratio under all entrance channel conditions. However the strong dependence of isospin fractionation ratio on the symmetry potential is preserved after considering the isospin degree of freedom in the momentum dependent interaction.

Isospin diffusion and equilibration for Sn plus 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 Li-7 and Be-7, we have studied the diffusion of isospin asymmetry by combining data from asymmetric Sn-112 + Sn-124 and Sn-124 + Sn-112 collisions with those from symmetric Sn-112 + Sn-112 and Sn-124 + Sn-124 collisions. We use these measurements to probe isospin equilibration in central collisions where nucleon-nucleon collisions are strongly blocked by the Pauli exclusion principle. 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 quantum molecular dynamics calculations are consistent with results obtained at higher incident energies that provide constraints on the density dependence of the symmetry energy.

CONSTRAINTS ON THE DENSITY DEPENDENCE OF THE SYMMETRY ENERGY

Collisions involving Sn-112 and Sn-124 nuclei have been calculated with the ImQMD transport model in order to place constraints on the density dependences of the nuclear symmetry energy. Consistent constraints on the symmetry energy at sub-saturation density have been obtained by comparing these transport calculations to measurements of isospin diffusion and to the ratios of neutron and proton spectra. New isospin diffusion results from E/A = 35 MeV are also presented.