Charged-particle scattering in the presence of a magnetic and a laser field and multiphoton emissions

Abstract

Charged-particle scattering by a static potential V(r) in the simultaneous presence of a magnetic and a laser field, both directed along the z axis, is studied within the Green's function formalism and the first Born approximation (FBA). For three types of scattering potential (screened Coulomb, pure Coulomb and exponential) the first-order matrix elements and the cross sections are calculated exactly and given in analytic closed form. The optical theorem is derived, with the result that the total scattering cross section is found to be expressed not through the imaginary part of the forward elastic scattering amplitude as is usually the case, but through the real part. The analytic structure of the cross sections in the presence of the two external fields is found to resemble the cross sections of collision processes involving particles with discrete internal structure. The analysis shows that the magnetic field assisted potential scattering is one of the physical processes where a beam of free electrons is found to amplify coherent radiation, especially in the low-frequency regions (infrared or less).