Continuum Rayleigh scattering in an intense laser beam

The problem of resonance Rayleigh scattering by an atom in an intense laser beam, whose bare spectrum consists of one discrete fundamental state and an excited continuum of states, is studied with the use of the density-matrix formalism. Evolution equations for the density-matrix elements are solved, leading to the determination of the populations of the atom in the discrete state $|g〉$ in the presence of $n$ laser photons, and to the calculation of the dipole-moment correlation function. The importance of cascade effects is discussed. The emitted spectrum is calculated and its dependence on the intensity of the laser beam and on the frequency of the incident photons is studied.