Effect of high angular momentum on η/s of nuclear matter

Abstract

The shear viscosity ($\ensuremath{\eta}$) of nuclear matter is investigated in different nuclei (nuclear mass $A\ensuremath{\approx}59--194$) using experimental giant dipole resonance (GDR) width ($\mathrm{\ensuremath{\Gamma}}$) at high angular momenta ($J=12--54$ $\ensuremath{\hbar}$) and temperatures ($T=1.2--2.1$ MeV) collected from the existing literature. $\ensuremath{\eta}$, calculated from $\mathrm{\ensuremath{\Gamma}}$, is found to increase with $T$ and $J$. We show that critical temperature included fluctuation model (CTFM) successfully describes $J$-induced $\ensuremath{\eta}$ 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 $\ensuremath{\eta}$ to improve the prediction at such high-$J$ region. The $\ensuremath{\eta}/s$ ratio, highly important for measuring fluidity, is calculated using $\ensuremath{\eta}$ 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 $\ensuremath{\hbar}/4\ensuremath{\pi}{k}_{\mathrm{B}}$, which is very close to those of a partonic system like quark gluon plasma at high temperature.