Abstract
Volkov wave functions describe the motion of an electron in a plane-wave laser field and are widely used in the treatment of multiphoton ionization and laser-assisted scattering. These functions are not applicable for fields of a more general type in which the various modes propagate in different directions. Recent work on the development of generalized Volkov solutions, applicable when the field is not a plane wave, is extended here to account for the effect of virtual Compton scattering involving photon pairs that transfer only a small amount of momentum. When such processes occur as initial- or final-state interactions in which the energy of the electron is nearly conserved, near degeneracies are introduced requiring special care in the solution of the wave equation. Methods for constructing approximate solutions that treat these effects accurately are described here for both nonrelativistic and relativistic wave equations. The solutions are used in an analysis of the Kapitza-Dirac effect---the scattering of an electron in a standing-wave laser field---and more general results are obtained than have been in earlier treatments of this problem. In a different class of applications, the generalized Volkov solutions are adopted in a study of the (relativistic) potential scattering of an electron in the presence of a two-mode laser field. A variational formulation, evaluated in the weak-field limit, is used to generate a low-frequency approximation for two-photon bremsstrahlung. A sum rule is derived that provides a simple relation between the true cross section and that obtained with the omission of virtual Compton scattering effects.
Published Version
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