Laser-assisted bremsstrahlung for circular and linear polarization

We numerically evaluate the cross sections for spontaneous bremsstrahlung emission in a laser field for both circular and linear laser polarization, in a regime where the classical ponderomotive energies for the considered laser intensities are considerably larger than the rest mass of the electron. A fully relativistic quantum-electrodynamic approach using the Volkov solutions of an electron in an external field and Dirac-Volkov propagators for the intermediate electrons is applied. We compare circular to linear polarization and point out several interesting features of the laser-dressed cross sections. Regularizations in both electron and photon propagators are required. Specifically, imaginary mass and energy shifts of the electron must be implemented near resonances which correspond to Doppler-shifted harmonics of the laser frequency. We also introduce a screening to the Coulomb potential in order to avoid long-range Coulomb infinities at zero momentum transfer.