  The relations among the components of the exit momenta of ultrarelativistic
electrons scattered on a strong electromagnetic wave of a low (optical)
frequency and linear polarization are established using the exact solutions to
the equations of motion with radiation reaction included (the Landau-Lifshitz
equation). It is found that the momentum components of the electrons traversed
the electromagnetic wave depend weakly on the initial values of the momenta.
These electrons are mostly scattered at the small angles to the direction of
propagation of the electromagnetic wave. The maximum Lorentz factor of the
electrons crossed the electromagnetic wave is proportional to the work done by
the electromagnetic field and is independent of the initial momenta. The
momentum component parallel to the electric field strength vector of the
electromagnetic wave is determined only by the diameter of the laser beam
measured in the units of the classical electron radius. As for the reflected
electrons, they for the most part lose the energy, but remain relativistic.
There is a reflection law for these electrons that relates the incident and the
reflection angles and is independent of any parameters.
