  In this paper, we study the real analyticity of the scattering operator for
the Hartree equation $ i\partial_tu=-\Delta u+u(V*|u|^2)$. To this end, we
exploit interior and exterior cut-off in time and space, and combining with the
compactness argument to overcome difficulties which arise from absence of good
properties for the nonlinear Klein-Gordon equation, such as the finite speed of
propagation and ideal time decay estimate. Additionally, the method in this
paper allows us to simplify the proof of analyticity of the scattering operator
for the nonlinear Klein-Gordon equation with cubic nonlinearity in Kumlin.
