Effect of high angular momentum on $\eta /s$ of nuclear matter

The shear viscosity ($\eta$) of nuclear matter is investigated in different nuclei (nuclear mass $A\approx 59–194$) using experimental giant dipole resonance (GDR) width ($\mathrm{\Gamma }$) at high angular momenta ($J=12–54$ $\hslash$) and temperatures ($T=1.2–2.1$ MeV) collected from the existing literature. $\eta$, calculated from $\mathrm{\Gamma }$, is found to increase with $T$ and $J$. We show that critical temperature included fluctuation model (CTFM) successfully describes $J$-induced $\eta$ even beyond critical angular momentum $J_c$ at different values of $T$. However, the Fermi liquid drop model (FLDM) could not explain the data at higher angular momenta. We propose the addition of a $J$-dependent term with the FLDM $\eta$ to improve the prediction at such high-$J$ region. The $\eta /s$ ratio, highly important for measuring fluidity, is calculated using $\eta$ and the entropy density $s$. The latter is estimated using the Fermi gas formula. Interestingly, the experimental value of the ratio is independent of $J$ and $A$ and comes within 2.6–6.0 $\hslash /4\pi k_{\mathrm{B}}$, which is very close to those of a partonic system like quark gluon plasma at high temperature.

Figure 1

(Online color) [Panels (a)-(f) clockwise from top left] Experimental $\eta$ at different $J$ plotted (red filled circles and yellow filled squares) against $T$ for the nuclei ${}^{59}\mathrm{Cu}$, ${}^{109-110}\mathrm{Sn}$, ${}^{113}\mathrm{Sb}$, ${}^{144}\mathrm{Sm}$, ${}^{152}\mathrm{Gd}$, ${}^{176}\mathrm{W}$ and ${}^{194}\mathrm{Hg}$. The CTFM calculations at different $J$ values are shown using blue short and medium dashed curves. The modified FLDM calculations (J-FLDM) for different $J$ values are shown using dark green dotted and dashed-dotted curves. The FLDM calculation, without any modification, is also shown using black continuous line.

Figure 2

The term ${\eta }_{\mathrm{add}}$ plotted as a function of $J$ for different nuclei. The continuous curve denotes the exponential fit to ${\eta }_{\mathrm{add}}$.

Figure 3

[(a)–(f)] clockwise from top left] Entropy density plotted against $T$ for the nuclei ${}^{59}\mathrm{Cu}$, ${}^{109,110}\mathrm{Sn}$, ${}^{113}\mathrm{Sb}$, ${}^{144}\mathrm{Sm}$, ${}^{152}\mathrm{Gd}$, ${}^{176}\mathrm{W}$, and ${}^{194}\mathrm{Hg}$. The data points (shown by red filled circles and yellow filled squares) are calculated at experimental T values. The theoretical Fermi gas model calculation (using Ignatyuk's [45] and Baumann's [46] approaches) is also shown for different $k$ values.

Figure 4

Panels (a)–(f) clockwise from top left] Experimental $\eta /s$ at different $J$ plotted (shown by red filled circles and yellow filled squares) against $T$ for the nuclei ${}^{59}\mathrm{Cu}$, ${}^{109-110}\mathrm{Sn}$ and ${}^{113}\mathrm{Sb}$, ${}^{144}\mathrm{Sm}$, ${}^{152}\mathrm{Gd}$, ${}^{176}\mathrm{W}$ and ${}^{194}\mathrm{Hg}$. The CTFM calculations at different $J$ values are shown using blue short and medium dashed curves. The modified FLDM calculations (J-FLDM) are shown using dark green dotted and dash-dotted curves. The KSS bound is also shown with black continuous line in the same plot.