  We study the free expansion of a dilute two-component Fermi gas with
attractive interspecies interaction in the BCS-BEC crossover. We apply a
time-dependent parameter-free density-functional theory by using two choices of
the equation of state: an analytic formula based on Monte Carlo data and the
mean-field equation of state resulting from the extended BCS equations. The
calculated axial and transverse radii and the aspect ratio of the expanding
cloud are compared to experimental data on vapors of ^6Li atoms. Remarkably,
the mean-field theory shows a better agreement with the experiments than the
theory based on the Monte Carlo equation of state. Both theories predict a
measurable dependence of the aspect ratio on expansion time and on scattering
length.
