Two-photon bremsstrahlung processes in atoms: Polarization effects and analytic results for the Coulomb potential

Abstract

The partial wave analysis of two-photon free-free (bremsstrahlung) electron transition cross sec- tions during scattering by a static potential U(r), as well as by an atom with a nonzero angular momentum, is carried out. The dipole interaction with radiation is taken into account in the second order of perturbation theory for the general case of elliptic polarization of photons. The polarization and angular dependences of the two- photon potential scattering amplitude is presented as a combination of the scalar product of electron momenta and photon polarization vectors and five atomic parameters containing Legendre polynomials of the scattering angle as well as radial matrix elements depending on the initial ( E) and final (E') electron energies. The results are applicable both for spontaneous double bremsstrahlung at nonrelativistic energies and for induced absorp- tion and emission in the field of a light wave. Specific polarization effects (circular and elliptic dichroism) are analyzed for two-photon bremsstrahlung processes associated with the interference of the Hermite and anti- Hermite parts of the amplitude and depending on the sign of photon helicity. The limiting cases of high and low photon frequencies are investigated analytically, and the asymptotic forms of radial matrix elements and ampli- tudes for the general form of the U(r) potential are determined. Closed analytic expressions are derived for the radial matrix elements of the Coulomb potential in the form of integrals of hypergeometric function, and sin- gularities are singled out in explicit form for E' E. The methods of approximate calculation of the radial matrix elements are discussed, and the results of their exact numerical calculation, as well as angular distribu- tions and the cross sections of induced one- and two-photon emission and absorption, are given for the case of the Coulomb potential. The numerical results show that dichroism effects are quite accessible for experimental observations. © 2002 MAIK Nauka/Interperiodica.