  We present a measurement of the elastic differential cross section
$d\sigma(p\bar{p}\rightarrow p\bar{p})/dt$ as a function of the
four-momentum-transfer squared t. The data sample corresponds to an integrated
luminosity of $\approx 31 nb^{-1}$ collected with the D0 detector using
dedicated Tevatron $p\bar{p} $ Collider operating conditions at sqrt(s) = 1.96
TeV and covers the range $0.26 <|t|< 1.2 GeV^2$. For $|t|<0.6 GeV^2$,
d\sigma/dt is described by an exponential function of the form $Ae^{-b|t|}$
with a slope parameter $ b = 16.86 \pm 0.10(stat) \pm 0.20(syst) GeV^{-2}$. A
change in slope is observed at $|t| \approx 0.6 GeV^2$, followed by a more
gradual |t| dependence with increasing values of |t|.
