Correlation between elliptic flow and shear viscosity in intermediate-energy heavy-ion collisions

The correlation between the elliptic flow $v_2$ scaled by the impact parameter $b$ and the shear viscosity $\eta$ as well as the specific viscosity $\eta /s$, defined as the ratio of the shear viscosity to the entropy density $s$, is investigated for the first time in intermediate-energy heavy-ion collisions based on an isospin-dependent quantum molecular dynamic model. The elliptic flow is calculated at balance energies to exclude the geometric influence such as the blocking effect from the spectators. Our study shows that $v_2/b$ decreases almost linearly with increasing $\eta$, consistent with that observed in ultrarelativistic heavy-ion collisions. On the other hand, $v_2/b$ is found to increase with increasing $\eta /s$.

Figure 1

The extracted slope parameter $F_d$ of the directed flow as a function of the impact parameter $b$ in heavy-ion collisions at different beam energies.

Figure 2

The extracted average shear viscosity (a), entropy density (b), and specific viscosity (c) at balance energies and corresponding impact parameters. Dashed lines are guides for the eye.

Figure 3

The elliptic flow and that scaled by the impact parameter at balance energies and corresponding impact parameters. Dashed lines are guides for the eye.

Figure 4

The scaled elliptic flow as a function of the average shear viscosity and specific viscosity at balance energies and corresponding impact parameters. Dashed lines are guides for the eye.