  For the 3D focusing cubic nonlinear Schrodinger equation, Scattering of $H^1$
solutions inside the (scale invariant) potential well was established by Holmer
and Roudenko~\cite{HR2} (radial case) and Duyckaerts, Holmer and
Roudenko~\cite{DHR} (general case). In this paper, we extend this result to
arbitrary space dimensions and focusing, mass-supercritical and
energy-subcritical power nonlinearities, by adapting the method of~\cite{DHR}.
