  We present a measurement of the $W$-boson-pair production cross section in
$p\bar{p}$ collisions at 1.96 TeV center-of-mass energy and the first
measurement of the differential cross section as a function of jet multiplicity
and leading-jet energy. The $W^{+}W^{-}$ cross section is measured in the final
state comprising two charged leptons and neutrinos, where either charged lepton
can be an electron or a muon. Using data collected by the CDF experiment
corresponding to $9.7~\rm{fb}^{-1}$ of integrated luminosity, a total of $3027$
collision events consistent with $W^{+}W^{-}$ production are observed with an
estimated background contribution of $1790\pm190$ events. The measured total
cross section is $\sigma(p\bar{p} \rightarrow W^{+}W^{-}) = 14.0 \pm
0.6~(\rm{stat})^{+1.2}_{-1.0}~(\rm{syst})\pm0.8~(\rm{lumi})$ pb, consistent
with the standard model prediction.
