  Let $H:=-\Delta+V$ be a nonnegative Schr\"odinger operator on $L^2({\bf
R}^N)$, where $N\ge 2$ and $V$ is an inverse square potential. In this paper we
obtain sharp decay estimates of the operator norms of $e^{-tH}$ and $\nabla
e^{-tH}$ in Lorentz spaces.
