Quasiclassical results for two-photon Coulomb Bremstrahlung

Stimulated two-photon Bremstrahlung (2BrS) is investigated at the scattering of quasiclassical electrons ($Ze^2/\hbar v \gg 1$, $v$ is the electron velocity) from a Coulomb center of charge $Ze$ in the presence of a monochromatic light wave of frequency $\omega$. Despite one-photon Bremstrahlung process, the cross section of 2BrS cannot be found within the framework of classical electrodynamics and one has been obtained as a limit $\hbar \to 0$ in exact quantum results. The quasiclassical 2BrS amplitude is expressed in terms of integrals of McDonald functions $K_{2i\xi}$ dependent on the dimensionless ``classical`` frequency $\xi=Ze^2\omega/mv^3$ and the scattering angle $\theta$. Simple analytical results for differential and total cross sections of 2BrS at low ($\xi \ll 1$) and high ($\xi \gg 1$) frequencies are obtained and comparisons with existing approximate results are presented. Photon polarization dependence of the 2BrS cross section is investigated and it is found that the {\it elliptic dichroism} effect vanishes, but the {\it circular dichroism} is kept even in the quasiclassical limit. Quasiclassical results for {\it spontaneous} emission of two BrS photons (having different frequencies) are also discussed.