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Abstract

We show how the semiclassical formulas for radiation emission of Baier,
Katkov and Strakhovenko for arbitrary initial and final spins of the electron
and arbitrary polarization of the emitted photon can be rewritten in a form
which numerically converges quickly. We directly compare the method in the case
of a background plane wave with the result obtained by using the Volkov state
solution of the Dirac equation, and confirm that we obtain the same result. We
then investigate the interaction of a circularly polarized short laser pulse
scattering with GeV electrons and see that the finite duration of the pulse
leads to a lower transfer of circular polarization than that predicted by the
known formulas in the monochromatic case. We also see how the transfer of
circular polarization from the laser beam to the gamma ray beam is gradually
deteriorated as the laser intensity increases, entering the nonlinear regime.
However, this is shown to be recovered if the scattered photon beam is
collimated to only allow for passage of photons emitted with angles smaller
than $1/\gamma$ with respect to the initial electron direction, where $\gamma$
is the approximately constant Lorentz factor of the electron. The obtained
formulas also allow us to answer questions regarding radiative polarization of
the emitting particles. In this respect we briefly discuss an application of
the present approach to the case of a bent crystal and high-energy positrons.