We consider the defocusing, $\dot{H}^1$-critical Hartree equation for the
radial data in all dimensions $(n\geq 5)$. We show the global well-posedness
and scattering results in the energy space. The new ingredient in this paper is
that we first take advantage of the estimate of the term $\displaystyle -
\int_{I}\int_{|x|\leq A|I|^{1/2}}|u|^{2}\Delta \Big(\frac{1}{|x|}\Big)dxdt$ in
the localized Morawetz inequality to rule out the possibility of energy
concentration, instead of the usual Morawetz estimate dependent of the
nonlinearity.