Sensitivity of intermediate mass fragment flows to the symmetry energy

The NIMROD-ISiS array was used to study the transverse flow of intermediate mass fragments in 35 MeV/nucleon ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, and ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ reactions. The intermediate mass fragment flow was previously shown to be sensitive to the density dependence of the symmetry energy. To explore the model dependence of the results, the antisymmetrized molecular dynamics, constrained molecular dynamics, and stochastic mean-field models were each compared to the experimental results to extract information on the form of the symmetry energy. The results demonstrate that sensitivity of the models to the nuclear equation of state can vary significantly based on the treatment of the nuclear dynamics. Despite the differences in the sensitivity, improved agreement with the experimental data is observed for each model with a stiff density dependence of the symmetry energy.

Figure 1

Transverse flow, $\overline{\langle Px\rangle }$ (left axis), for $Z=1$–9 particles from midperipheral collisions in the the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, and ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ collisions (left). The nucleon-averaged flow, $\overline{\langle Px/A\rangle /N}$ (right axis), calculated for each system is presented by the horizontal bars (right).

Figure 2

The different forms of the density dependence of the symmetry energy used in the AMD, CoMD, and SMF simulations. The soft density dependence is indicated for each calculation. Additional details on the different forms of $E_{\text{sym}}\left(\rho \right)$ are shown in Table .

Figure 3

Transverse flow, $\overline{\langle Px\rangle }$, as a function of the charge ($Z$) of the fragments from the AMD, CoMD, and SMF models. The results are presented for the midperipheral collisions from the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ reaction with the stiff parametrization of the symmetry energy for each model.

Figure 4

$R_{\text{flow}}$ value from the nucleon-averaged flow of the midperipheral reactions is shown for the different symmetry energy parametrizations of the AMD, CoMD, and SMF models. The corresponding symmetry energy slope ($L$) is shown next to each calculation. The experimental value is represented by the solid blue line with the statistical uncertainty shown as the hatched blue area.