Scattering and pair production by a potential barrier

Scattering and electron-positron pair production by a one-dimensional potential is considered in the framework of the $S-$matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogoliubov transformation relating the in- and out-states are given. We show that the norm of a solution of the wave equation is determined by the largest amplitude of its asymptotic form when $x_3\to \pm\infty$. For a number of potentials we give the explicit expressions for the complete in- and out-sets of orthonormalized wave functions. We note that in principle virtual vacuum processes in external field influence the phase of wave function of scattered particle..Comment: 13 pages, LATEX 2e, no figure

Non-Linear Compton Scattering of Ultrashort and Ultraintense Laser Pulses

The scattering of temporally shaped intense laser pulses off electrons is discussed by means of manifestly covariant quantum electrodynamics. We employ a framework based on Volkov states with a time dependent laser envelope in light-cone coordinates within the Furry picture. An expression for the cross section is constructed, which is independent of the considered pulse shape and pulse length. A broad distribution of scatted photons with a rich pattern of subpeaks like that obtained in Thomson scattering is found. These broad peaks may overlap at sufficiently high laser intensity, rendering inappropriate the notion of individual harmonics. The limit of monochromatic plane waves as well as the classical limit of Thomson scattering are discussed. As a main result, a scaling law is presented connecting the Thomson limit with the general result for arbitrary kinematics. In the overlapping regions of the spectral density, the classical and quantum calculations give different results, even in the Thomson limit. Thus, a phase space region is identified where the differential photon distribution is strongly modified by quantum effects.Comment: 31 pages, 10 figure