Neutron-proton differential transverse flow in ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions at 270 MeV/nucleon

Within a transport model, we study the neutron-proton differential transverse flow and its excitation function in central ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions at 270 MeV/nucleon. To more accurately evaluate effects of the high-density behavior of symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$ on this observable, we also consider the uncertainties of $E_{\mathrm{sym}}\left(\rho \right)$ around the saturation density ${\rho }_0$. It is shown that the neutron-proton differential transverse flow and its excitation function are mainly sensitive to the slope $L$ of $E_{\mathrm{sym}}\left(\rho \right)$ at ${\rho }_0$. However, the effects of low-density behavior of $E_{\mathrm{sym}}\left(\rho \right)$ on this observable should also be considered. Therefore, it is suggested that measurements of the neutron-proton differential transverse flow and its excitation function may provide useful complements to the constraints on $L$ extracted from the spectral pion ratio in $\mathrm{S}\pi \mathrm{RIT}$ experiments.

Figure 1

Density dependence of the $E_{\mathrm{sym}}\left(\rho \right)$ for Case I and Case II.

Figure 2

Upper: Kinetic-energy dependent isoscalar potential (a) at ${\rho }_0$ in comparison with the Schrödinger-equivalent one obtained by Hama et al. Lower: Kinetic-energy dependent isovector potential (b) at ${\rho }_0$ for Case I and Case II.

Figure 3

Differential transverse flows of free neutrons $p_x^n$ and protons $p_x^p$ as a function of the center-of-mass rapidity $y_{\text{c.m.}}$.

Figure 4

$N_n\left(y\right)/N\left(y\right)$ and $N_p\left(y\right)/N\left(y\right)$ with $L=30.3$ MeV and 125.6 MeV as a function of the center-of-mass rapidity $y_{\text{c.m.}}$.

Figure 5

Kinetic-energy dependent isovector potential at $\rho =0.5{\rho }_0$ and $\rho =2{\rho }_0$ for Case I and Case II.

Figure 6

Neutron-proton differential transverse flows as a function of the center-of-mass rapidity $y_{\text{c.m.}}$.

Figure 7

Excitation function of the neutron-proton differential transverse flows at midrapidity $|y_{\text{c.m.}}|\le 0.1$ as a function of $L$. The lines are drawn to guide the eye.