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Abstract

In the presence of an electromagnetic background plane-wave field, electron,
positron, and photon states are not stable, because electrons and positrons
emit photons and photons decay into electron-positron pairs. This decay of the
particle states leads to an exponential damping term in the probabilities of
single nonlinear Compton scattering and nonlinear Breit-Wheeler pair
production. In this paper we investigate analytically and numerically the
probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair
production including the particle states' decay. For this we first compute
spin- and polarization-resolved expressions of the probabilities, provide some
of their asymptotic behaviors and show that the results of the total
probabilities are independent of the spin and polarization bases. Then, we
present several plots of the total and differential probabilities for different
pulse lengths and for different spin and polarization quantum numbers. We
observe that it is crucial to take into account the damping of the states in
order for the probabilities to stay always below unity and we show that the
damping factors also scale with the intensity and pulse duration of the
background field. In the case of nonlinear Compton scattering we show
numerically that the total probability behaves like a Poissonian distribution
in the regime where the photon recoil is negligible. In all considered cases,
the kinematic conditions are such that the final particles momenta transverse
to the propagation direction of the plane wave are always much smaller than the
particles longitudinal momenta and the main spread of the momentum distribution
on the transverse plane is along the direction of the plane-wave electric
field.