  We prove the local energy decay and the smoothing effect for the damped
Schr{\"o}dinger equation on R^d. The self-adjoint part is a Laplacian
associated to a long-range perturbation of the flat metric. The proofs are
based on uniform resolvent estimates obtained by the dissipative Mourre method.
All the results depend on the strength of the dissipation which we consider.
