  A scattering process with gravitons as an intermediate state is investigated.
To study such a scattering, the Gravitoelectromagnetism theory is considered.
It is a gravitational theory built on the analogy between gravity and
electromagnetism. The complete Lagrangian formulation of the
gravitoelectromagnetic theory includes interactions of gravitons with fermions
and photons that leads us to calculate their scattering amplitudes and
cross-sections. In this context, the gravitational cross-section of the
$e^{-}+e^{+}\longrightarrow\mu^{-}+\mu^{+}$ scattering process is obtained. A
comparison between the electromagnetic and gravitational cross-sections is
made.
