Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen

Abstract

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second-order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and are expressed in terms of B splines and B polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization of the scattered light are investigated as a function of scattering angle and photon energy. Analytical expressions are derived for the polarization-dependent angular distribution which can be used for scattering by both hydrogenic as well as many-electron systems. Detailed computations are performed for Rayleigh scattering by atomic hydrogen within the incident photon energy range 0.5 to 5 keV. Particular attention is paid to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction.

Spin effects probed by Rayleigh X-ray scattering off hydrogenic ions

“…The investigated energy range for all targets lies above their 1s ionization thresholds. It has been recently showed by us that, within that energy range, the finite basis set approach to Rayleigh scattering gives good agreement with NIST (National Institute of Standards and Technology) data values and other calculations [17,18]. Finally, a summary of our findings and links to future prospects are given in Sec.…”

“…As seen in the figure, for the E1E1 curve,P cc 3 is zero for all energy values. This can be understood in view of the symmetric shape of angular distribution for E1E1 term [17,18]: The photon is scattered at small angles (in which case helicity is conserved) or large angles (in which case helicity is flipped) with the same probability. This naturally determines a vanishing third ISP.…”

“…The amplitude for linear polarization scenario is linked to the amplitude for circular polarization scenario as [17] …”

“…The second-order transition amplitude for Rayleigh (and Raman) scattering is given by [17][18][19][20] …”

Analytical evaluation of atomic form factors: Application to Rayleigh scattering

“…During the last decades, calculations of Rayleigh scattering amplitudes have been widely performed, both within relativistic and nonrelativistic frameworks [26,[38][39][40][41][42][43]. Up to now, there have been two main methods to perform such calculations, namely relativistic second-order S-matrix (SM) and FF approaches [26].…”