  We study the asymptotic behavior of the Schr\"odinger equation in the
presence of a nonlinearity of Hartree type in the semi-classical regime. Our
scaling corresponds to a weakly nonlinear regime where the nonlinearity affects
the leading order amplitude of the solution without altering the rapid
oscillations. We show the validity of the WKB-analysis when the potential in
the nonlinearity is singular around the origin. No new resonant wave is created
in our model, this phenomenon is inhibited due to the nonlinearity. The
nonlocal nature of this latter leads us to build our result on a high-frequency
averaging effects. In the proof we make use of the Wiener algebra and the space
of square-integrable functions.
