  We investigate the low-temperature behavior of the ratio between the shear
viscosity \eta and the entropy density s in the unitary Fermi gas by using a
model based on the zero-temperature spectra of both bosonic collective modes
and fermonic single-particle excitations. Our theoretical curve of \eta/s as a
function of the temperature T is in qualitative agreement with the experimental
data of trapped ultracold 6Li atomic gases. We find the minimum value \eta/s
\simeq 0.44 (in units of \hbar/k_B) at the temperature T/T_F \simeq 0.27, with
T_F the Fermi temperature.
