Stimulated effects upon “jarring” of an electron in an external electromagnetic field

Various elementary processes that involve imparting a large momentum to an electron, and which occur in an external laser field, stimulate effects of absorption and emission of quanta of this field. As a rule, the first stage of this process (e.g., perhaps the scattering of the electron, its motion in an inhomogeneous medium, emission or absorption of a light quantum by the electron, the Compton effect, radioactive decay, the photoelectric effect, etc.) occurs in times $\tau$ much shorter than the period $2\pi/\omega$ of the low-frequency motion of the electron caused by the external field. In this case, the second stage (stimulated emission-absorption) does not depend on the physical nature of the first stage, and it is universal for all processes. The problem of stimulated effects of the stated type can be solved for once and for all as a problem of the “jarring” of the electron in the presence of the external field. In non-relativistic fields ($v/c\ll1$), the probability of the stimulated processes is determined by the parameter $N\sim|(v/c)c\delta p/(\hbar\omega)|$, which denotes the rms number of quanta emitted or abosrbed. In the limiting cases $N\gg1$ and $N\lesssim1$, the problem of “jarring” is solved classically or quantum-mechanically, respectively. In the Compton effect, where $\delta p=\hbar(k_1-k_2)$, or in “jarring” due to emission (or absorption) of a hard photon, when $\delta p=\hbar k$, the parameter $N$ does not contain the Planck quantum. Hence one can explain the effect of satellites appearing in the emission spectrum from a purely classical standpoint for any $N$. In addition to the Compton effect, the article treats also stimulated processes in $\beta$-decay and in the photoelectric effect occurring in an external laser field.