the incident energy (not shown here), but this is mainly due to Coulomb interactions. Here we conclude that the neutron-to-proton ratio from free nucleons as well as LCPs can act as a probe of the high-density behavior of the symmetry energy.

One more interesting observation is obtained from Fig. \[fig:1\]. With increasing incident energy, the time evolution of the density is exactly opposite during the compression and expansion stages. That is, in the expansion stage the average density is found to decrease with increasing incident energy, which was earlier increasing in the compressed zone. Now, we have two aspects of the basis of the time evolution of density: one is the compressed-zone time and second is the freeze-out time. Interestingly, if the density behavior is opposite at the two times, then it would supposedly affect the magnitude of the symmetry energy as well as its effect on the nuclear matter during the whole time evolution.

![\[fig:3\](Color online) Excitation function of $(\rho/\rho_0)^{\gamma_i}$, which is proportional to $E_{Sym}$, at semicentral geometry. The left panel is at the time of maximum compression, while the right one is at the freeze-out time. Solid and open circles with a dashed line represent the contributions of 