  In this paper, we consider a 3d cubic focusing nonlinear Schr\"odinger
equation (NLS) with slowing decaying potentials. Adopting the variational
method of Ibrahim-Masmoudi-Nakanishi \cite{IMN}, we obtain a condition for
scattering. It is actually sharp in some sense since the solution will blow up
if it's false. The proof of blow-up part relies on the method of Du-Wu-Zhang
\cite{DWZ}
