Relativistic effects on low-frequency Rayleigh scattering including spin flip for hydrogenic atoms

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Abstract
We present an approximate analytic expression for the low-frequency ground-state relativistic Rayleigh scattering matrix elements for hydrogenic atoms, including the possibility of electron spin flip as a result of the elastic photon atom scattering. Our expression is obtained by taking the long-wavelength approximation in the relativistic Coulomb matrix elements, without neglecting the photon frequency dependence in the Coulomb Green operator. By comparison with existing exact numerical calculations, we demonstrate that our approximation is appropriate for photon frequencies below the photoelectric threshold, at least for the non-spin-flip amplitude. Using our expressions, we investigate two issues: (i) the comparison of static and dynamical polarizabilities, and (ii) the behavior of the electron spin-flip amplitude, related to magnetic scattering.