Rayleigh Scattering of a Laser Beam from a Massive Relativistic Two-Level Atom

$A$ relativistic two-level model of a massive atom in the presence of an external plane-wave laser beam is solved. Using the resulting wave functions, the cross sections for the scattering of a photon of the laser frequency or one of its harmonics is calculated. Many interesting nonlinear effects are found, the most striking being the rapid change of the resonance frequency in the cross section for harmonic production as the intensity of the laser is increased. Both approximate and exact numerical results are presented.