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The Green-Kubo relation and fluctuation-dissipation theorem are employed tocalculate the shear viscosity $\eta$ of a finite hot nucleus directly from thewidth 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 theexperimental systematics of the GDR in copper, tin and lead isotopes at finitetemperature $T$. These empirical results are then compared with the predictionsby several independent models, as well as with almost model-independentestimations. Based on these results, it is concluded that the ratio $\eta/s$ inmedium and heavy nuclei decreases with increasing temperature $T$ to reach$(1.3 - 4)\times\hbar/(4\pi k_{B})$ at $T=$ 5 MeV.

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