THE RESONANCE APPROACH FOR THE PROCESS OF THE PHOTO-TRIDENT IN THE FIELD OF A LINEARLY POLARIZED ELECTROMAGNETIC WAVE

The process of the creation of an electron-positron pair at the scattering of a polarized high-energy photon (photo-trident) in the field of a monochromatic linearly polarized electromagnetic wave was investigated in the framework of the resonance approximation. This approximation allows to neglect the interference of amplitudes, i.e. resonance for each amplitude occurs in different kinematic regions. Despite these simplifications the expression for the probability for the investigated process, which has a second order in the fine structure constant, is sufficiently cumbersome. That is a consequence of the polarization properties of the intermediate state. And only for the case of linear polarization of the wave and an unpolarized initial photon, the probability of a photo-trident is factorized into the product of the probabilities of the first-order subprocesses into which the sequence of the studied process is divided.