  The process of Compton scattering by a free electron with subsequent
reemission of one or two photons is considered in the assumption of finite
interaction time. The corresponding cross sections are obtained in the
framework of relativistic quantum electrodynamics using a modified form of
fermion propagator with complex transmitted momentum. It is shown that finite
time effects can be observable at sufficiently low energies of scattered
photons. The proposed method also regularizes arising infrared divergence in
the cross section of the double Compton effect. Possible experimental
verification of considered theoretical approach is discussed.
