On the recoil effect during radiation of relativistic particles

Recoil effect during photon emission by relativistic particles in the external field is considered. It is shown that the effect can be taken into account not only on the basis of the Schwinger operator method but also by the generalization of the WKB method known in quantum mechanics. A formula, determining the prbability of photon emission by spinless particle in quasiclassical approximation, is derived. The formula applicability conditions are ascertained. The conditions during the particle motion in different external fields are analyzed. The method presented can be generalized for the case of radiation in the external field of a particle possessing a spin (electron, positron), as well as for the case of formation of high-energy electron-positron pair in the external field