Shear-Viscosity to Entropy-Density Ratio from Giant Dipole Resonances in Hot Nuclei

The Green-Kubo relation and fluctuation-dissipation theorem are employed to calculate the shear viscosity $\eta$ of a finite hot nucleus directly from the width and energy of the giant dipole resonance (GDR) of this nucleus. The ratio $\eta/s$ of shear viscosity $\eta$ to entropy density $s$ is extracted from the experimental systematics of the GDR in copper, tin and lead isotopes at finite temperature $T$. These empirical results are then compared with the predictions by several independent models, as well as with almost model-independent estimations. Based on these results, it is concluded that the ratio $\eta/s$ in medium and heavy nuclei decreases with increasing temperature $T$ to reach $(1.3 - 4)\times\hbar/(4\pi k_{B})$ at $T=$ 5 MeV.