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Our paper concerns the scattering of intense laser radiation on free electrons and it is focused on the relation between nonlinear Compton and nonlinear Thomson scattering. The analysis is performed for a laser field modeled by an ideal pulse with a finite duration, a fixed direction of propagation and indefinitely extended in the plane perpendicular to it. We derive the classical limit of the quantum spectral and angular distribution of the emitted radiation, for an arbitrary polarization of the laser pulse. We also rederive our result directly, in the framework of classical electrodynamics, obtaining, at the same time, the distribution for the emitted radiation with a well defined polarization. The results reduce to those established by Krafft et al. [G. A. Krafft, A. Doyuran and J. B. Rosenzweig, Phys. Rev. E 72, 056502 (2005)] in the particular case of linear polarization of the pulse, orthogonal to the initial electron momentum. Conditions in which the differences between classical and quantum results are visible are discussed and illustrated by graphs.

We present an elementary proof based on a direct calculation of the property of completeness at constant time of the solutions of the Klein-Gordon equation for a charged particle in a plane wave electromagnetic field. We also review different forms of the orthogonality and completeness relations previously presented in the literature and we discuss the possibility to construct the Feynman propagator for the particle in a plane-wave laser pulse as an expansion in terms of Volkov solutions. We show that this leads to a rigorous justification for the expression of the transition amplitude, currently used in the literature, for a class of laser assisted or laser induced processes.

We present high-accuracy calculations of ionization rates of helium at UV (195 nm) wavelengths. The data are obtained from full-dimensionality integrations of the helium-laser time-dependent Schrödinger equation. Comparison is made with our previously obtained data at 390 nm and 780 nm. We show that scaling laws introduced by Parker et al extend unmodified from the near-infrared limit into the UV limit. Static-field ionization rates of helium are also obtained, again from time-dependent full-dimensionality integrations of the helium Schrödinger equation. We compare the static-field ionization results with those of Scrinzi et al and Themelis et al, who also treat the full-dimensional helium atom, but with time-independent methods. Good agreement is obtained.

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Based on quantum theory, we investigate the distribution of the electrons scattered in nonlinear Compton effect by an electromagnetic plane wave. Deviations of the final electron momentum from its initial value are solely due to quantum effects. The monochromatic case, examined in detail, reveals features of the electron distribution, useful in the understanding of the pulsed plane wave case for particular intensity and electron energy regimes. The graphs displayed focus on the case of head-on or near head-on collision of an energetic electron with an electromagnetic circularly polarized pulsed plane wave and show that the deviation in direction is extremely small, while the distribution in energy can be visibly different from that of the initial electron. Two pulse shapes, several laser intensities and high incident electron energies are considered.Comment: accepted by Phys. Rev.

Within the framework of the classical electrodynamics, we investigate the scattering of a very intense laser pulse on ultrarelativistic electrons. The laser pulse is modeled by a plane wave with finite length. For a circularly polarized laser pulse, we focus on the angular distribution of the emitted radiation in its dependence on the electron energy for the cases of head-on and 90 degrees collisions. We investigate the relation between dW/dΩ and the trajectory followed by the velocity of the electron during the laser pulse and, for the case of a short laser pulse, we discuss the carrierenvelope phase effects. We also present an analysis of the polarization of the emitted radiation. We find two scaling laws allowing to predict the behaviour of the angular distributions for a broader range of parameters.