Probing the density dependence of the symmetry energy by nucleon flow

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, sensitive regions of some nucleon observables to the nuclear symmetry energy are studied. It is found that the symmetry-energy-sensitive observable $n/p$ ratio in the ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction at 0.3 GeV/nucleon in fact just probes the density-dependent symmetry energy below the density of $1.5{\rho }_0$ and effectively probes the density-dependent symmetry energy around or somewhat below the saturation density. Nucleon elliptic flow can probe the symmetry energy from the low-density region to the high-density region when changing the incident beam energies from 0.3 to 0.6 GeV/nucleon in the semi-central ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction. And nucleon transverse and elliptic flows in the semi-central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 0.6 GeV/nucleon are more sensitive to the high-density behavior of the nuclear symmetry energy. One thus concludes that nucleon observables in the heavy reaction system and with higher incident beam energy are more suitable to be used to probe the high-density behavior of the symmetry energy. The present study may help one to get more specific information about the density-dependent symmetry energy from nucleon flow observable in heavy-ion collisions at intermediate energies.

Figure 1

The relative sensitivity of the symmetry-energy-sensitive observable free neutron to proton ratio $n/p$ as a function of kinetic energy in the central ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction at 0.3 GeV/nucleon.

Figure 2

The relative sensitivity of neutron and proton elliptic flows as a function of transverse momentum in the semi-central ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction at 0.3 GeV/nucleon.

Figure 3

The relative sensitivity of neutron and proton elliptic flows as a function of transverse momentum in the semi-central ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction at 0.6 GeV/nucleon.

Figure 4

The relative sensitivity of the difference between neutron elliptic flow and proton elliptic flow as a function of transverse momentum in the semi-central ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction at 0.6 GeV/nucleon.

Figure 5

The relative sensitivity of the difference between neutron elliptic flow and proton elliptic flow as a function of transverse momentum in the semi-central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 0.6 GeV/nucleon.

Figure 6

The relative sensitivity of the difference between neutron transverse flow and proton transverse flow as a function of rapidity in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 0.6 GeV/nucleon.