  In this paper, we consider a Hamiltonian system combining a nonlinear Schr\"
odinger equation (NLS) and an ordinary differential equation (ODE). This system
is a simplified model of the NLS around soliton solutions. Following Nakanishi
\cite{NakanishiJMSJ}, we show scattering of $L^2$ small $H^1$ radial solutions.
The proof is based on Nakanishi's framework and Fermi Golden Rule estimates on
$L^4$ in time norms.
