  We consider the semiclassical limit of the Hartree equation with a data
causing a focusing at a point. We study the asymptotic behavior of phase
function associated with the WKB approximation near the caustic when a
nonlinearity is supercritical. In this case, it is known that a phase shift
occurs in a neighborhood of focusing time in the case of focusing cubic
nonlinear Schr\"odinger equation. Thanks to the smoothness of the nonlocal
nonlinearities, we justify the WKB-type approximation of the solution for a
data which is larger than in the previous results and is not necessarily
well-prepared. We also show by an analysis of the limit hydrodynamical equaiton
that, however, this WKB-type approximation breaks down before reaching the
focal point: Nonlinear effects lead to the formation of singularity of the
leading term of the phase function.
