Emission of soft photons in collisions in an external electromagnetic field

The cross sections and probabilities for multiphoton emission by a classical electron in a Coulomb field in the presence of an external electromagnetic field are calculated. The cases of both monochromatic and thermal (Planck) radiation are considered. The case of sufficiently strong external field strengths in a single-mode field is investigated. In this case nonlinear radiation effects arise. The low-frequency (infrared) divergence of the emission probabilities in a Planck field is investigated, and a probability distribution for multiphoton processes is found which (in contrast to spontaneous emission) differs from the Poisson distribution