Nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the damping of particle states

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. We present analytical and numerical investigations for the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the particle states decay. For this we first give new spin- and polarization-resolved expressions of the probabilities, verify that they are gauge invariant, provide some of their asymptotic behaviors, and show that the results of the total probabilities are independent of the spin and polarization bases. In plots from numerical computations we observe that it is crucial to take into account the damping of the states in order the probabilities to stay always below unity and we show that the damping factors also scale with the 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 for sufficiently low initial electron energies such that the photon recoil is negligible. In all considered cases, the final particles momentum transverse to the propagation direction of the plane wave is always much smaller than the particles energies and the main spread of the momentum on the transverse plane is along the direction of the plane-wave electric field.