Shear-viscosity to entropy-density ratio from giant dipole resonances in hot nuclei

Abstract

The Green-Kubo relation and fluctuation-dissipation theorem are employed to calculate the shear viscosity $\ensuremath{\eta}$ of a finite hot nucleus directly from the width and energy of the giant dipole resonance (GDR) of this nucleus. The ratio $\ensuremath{\eta}/s$ of shear viscosity $\ensuremath{\eta}$ 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 $\ensuremath{\eta}/s$ in medium and heavy nuclei decreases with increasing temperature $T$ to reach $(1.3\text{--}4)\ifmmode\times\else\texttimes\fi{}\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$ at $T=5\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$.