Non-linear Compton effect with a laser pulse

We theoretically investigate the scattering of intense laser radiation on energetic electrons. The laser field is described as a pulse with a fixed propagation direction; this allows the use of relativistic Volkov solutions and leads to a transition amplitude which is a product of a three-dimensional δ-function with an one-dimensional integral evaluated numerically. We study the dependence of the emitted photon spectrum on the pulse duration. In contrast with the monochromatic case, where the spectrum is discrete, in our case one obtains a continuous distribution with a succession of maxima located near the corresponding discrete values.