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

Abstract

We study the polarization characteristics of x-ray photons scattered by hydrogenic atoms, based on the Dirac equation and second-order perturbation theory. The relativistic states used in calculations are obtained using the finite basis set method and expressed in terms of B-splines and B-polynomials. We derive general analytical expressions for the polarization-dependent total cross sections, which are applicable to any atom and ion, and evaluate them separately for linear and circular polarization of photons. In particular, detailed calculations are performed for the integrated Stokes parameters of the scattered light for hydrogen as well as hydrogenlike neon and argon. Analyzing such integrated Stokes parameters, special attention is given to the electron-photon spin-spin interaction, which mostly stems from the magnetic-dipole contribution of the electron-photon interaction. Subsequently, we find an energy window for the selected targets in which such spin-spin interactions can be probed.

Polarization transfer in Rayleigh scattering of hard x-rays

“…Recent theoretical investigations of elastic scattering focus on the effects of photon polarization [30,31,46,47,57,58]. For all basic photon-matter processes, the features of polarization transfer from the incident to the outgoing beam are of particular importance as they enable tests of theory methods that are more stringent than measuring just total or differential interaction cross sections.…”

Many-electron effects on x-ray Rayleigh scattering by highly charged He-like ions

“…This technique enables one to replace an infinite summation in the spectral representation of the electron propagator by a summation over a finite basis set and was utilized for calculating the Rayleigh scattering in Refs. [24,27]. Still another approach is based on the exact Dirac-Coulomb Green's function which can be represented in a closed form as a superposition of the regular and irregular solutions of the Dirac equation.…”

“…[22] for a comprehensive review on this approach. In recent years [23][24][25][26][27] the angular and polarization correlation between the incident and outgoing photons have also been investigated. Unfortunately, however, the formalism of the second-order S-matrix theory does not enable one to investigate systematically the many-electron effects on the Rayleigh scattering.…”

Two-photon processes based on quantum commutators

“…The term A 12 reads plitude. As in [31,32], we shall consider light scattering as depicted in Fig. 1.…”

“…All of these approaches contain a summation over the infinite intermediate states of the target bound system. In case of one-electron atomic systems, such intermediate-state summation has been evaluated for a variety of secondorder processes, leading to high accurate values of crosssections and emissions rates [22][23][24][25][26][27][28][29][30], as well as its dependence upon photon polarizations [31][32][33][34] and geometry [35,36]. Nevertheless, in case of many-body systems or complex potentials, such a summation over the infinite intermediate states is often difficult, or impossible to be evaluated accurately [37][38][39][40][41][42].…”