  Swift discovered XRF 050416A with the BAT and began observing it with its
narrow field instruments only 64.5 s after the burst onset. Its very soft
spectrum classifies this event as an X-ray flash. The afterglow X-ray emission
was monitored up to 74 days after the burst. The X-ray light curve initially
decays very fast, subsequently flattens and eventually steepens again, similar
to many X-ray afterglows. The first and second phases end about 172 and 1450 s
after the burst onset, respectively. We find evidence of spectral evolution
from a softer emission with photon index Gamma ~ 3.0 during the initial steep
decay, to a harder emission with Gamma ~ 2.0 during the following evolutionary
phases. The spectra show intrinsic absorption in the host galaxy. The
consistency of the initial photon index with the high energy BAT photon index
suggests that the initial phase of the X-ray light curve may be the low-energy
tail of the prompt emission. The lack of jet break signatures in the X-ray
afterglow light curve is not consistent with empirical relations between the
source rest-frame peak energy and the collimation-corrected energy of the
burst. The standard uniform jet model can give a possible description of the
XRF 050416A X-ray afterglow for an opening angle larger than a few tens of
degrees, although numerical simulations show that the late time decay is
slightly flatter than expected from on-axis viewing of a uniform jet. A
structured Gaussian-type jet model with uniform Lorentz factor distribution and
viewing angle outside the Gaussian core is another possibility, although a full
agreement with data is not achieved with the numerical models explored.
