Experimental Determination of $\eta /s$ for Finite Nuclear Matter

We present, for the first time, simultaneous determination of shear viscosity ($\eta$) and entropy density ($s$) and thus, $\eta /s$ for equilibrated nuclear systems from $A\sim 30$ to $A\sim 208$ at different temperatures. At finite temperature, $\eta$ is estimated by utilizing the $\gamma$ decay of the isovector giant dipole resonance populated via fusion evaporation reaction, while $s$ is evaluated from the nuclear level density parameter ($a$) and nuclear temperature ($T$), determined precisely by the simultaneous measurements of the evaporated neutron energy spectra and the compound nuclear angular momenta. The transport parameter $\eta$ and the thermodynamic parameter $s$ both increase with temperature, resulting in a mild decrease of $\eta /s$ with temperature. The extracted $\eta /s$ is also found to be independent of the neutron-proton asymmetry at a given temperature. Interestingly, the measured $\eta /s$ values are comparable to that of the high-temperature quark-gluon plasma, pointing towards the fact that strong fluidity may be the universal feature of the strong interaction of many-body quantum systems.

Figure 1

Different fold-gated experimental (symbols) (a) neutron energy spectra (b) high-energy $\gamma$-ray spectra along with the corresponding cascade predictions (solid lines) for ${}^{31}\mathrm{P}$ at $E_{\mathrm{beam}}=42\mathrm{MeV}$.

Figure 2

Variation of the ground state (a) GDR width and (b) average GDR energy with the mass number. The symbols are (a) the accepted ground state GDR widths and (b) the average of measured GDR energies. The green solid lines are obtained by using Eqs. (36), (40) and Table (3) of Ref. [22], derived using $\eta (0)=1u$. The pink dashed lines and the blue dot-dashed lines were obtained by solving Eq. (27) along with Eqs. (25) and (28) of Ref. [22], with $\eta (0)=1.25u$ and $0.55u$, respectively, by the secant method generalized for complex functions. The errors in $E_{\mathrm{AV}}$ are included but are small enough to be distinguished from the symbols.

Figure 3

(a) Experimental data (symbols) along with the theoretical predictions (solid lines) for $\eta$ (upper panel), $s$ (middle panel), and $\eta /s$ (lower panel). Blue short-dashed line (lower panel) is the KSS bound. The errors in $\eta$ and $\eta /s$ include the statistical errors as well as the systematic error due to the lower and upper bounds of $\eta (0)$.

Figure 4

Variation of $\eta$ (upper panel, (a) & (d)), $s$ (middle panel, (b) & (e)) and $\eta /s$ (lower panel, (c) & (f)) with the mass number at the specified temperature range.