Decomposition of the sensitivity of the symmetry energy observables

To exactly answer which density region that some frequently used symmetry-energy-sensitive observables probe, for the first time, we make a study of the decomposition of the sensitivity of some symmetry-energy-sensitive observables. It is found that for the Au+Au reaction at incident beam energies of 200 and 400 MeV/nucleon, frequently used symmetry-energy-sensitive observables mainly probe the density-dependent symmetry energy around $1.25{\rho }_0$ (for pionic observables) or $1.5{\rho }_0$ (for nucleonic observables). Effects of the symmetry energy in the low-density region is in general small but observable. The fact that the symmetry-energy-sensitive observables are not sensitive to the symmetry energy in the maximal baryon-density region increases the difficulty of studying nuclear symmetry energy at superdensity.

Figure 1

Evolution of the central baryon density in the reaction of ${}^{197}\mathrm{Au}{+}^{197}\mathrm{Au}$ at beam energies of 400 and 200 MeV/nucleon with an impact parameter of $b=1$ fm. ${\rho }_0$ denotes the nuclear saturation density.

Figure 2

Evolution of the distribution percentage of baryon number in different density regions in the central reaction of ${}^{197}\mathrm{Au}{+}^{197}\mathrm{Au}$ at beam energies of 400 and 200 MeV/nucleon.

Figure 3

Relative sensitivity of the symmetry energy sensitive observable ${\pi }^{-}/{\pi }^{+}$ as a function of density.

Figure 4

Relative sensitivity of the symmetry energy sensitive observable pre-equilibrium free $n/p$ as a function of density.

Figure 5

Same as Fig. 3, but at the beam energy of 200 MeV/nucleon.

Figure 6

Same as Fig. 4, but at the beam energy of 200 MeV/nucleon.