Scattering operator for elastic and inelastic resonant x-ray scattering

Abstract

We show that, in the fast collision approximation, the scattering operator for resonant x-ray scattering can be expressed in terms of simple spin-orbital moment operators M (fc) (l,s) of the valence shell involved in the resonance. This theory is applicable to the analysis of a broad range of resonant x-ray elastic and inelastic scattering and absorption experiments involving rare earth, actinide, and transition elements.

Unraveling Orbital Correlations with Magnetic Resonant Inelastic X-Ray Scattering

“…(2) as W α e (d j ) ∝ d j σ α |Ô j,e |d j σ α where |d j σ α is the state with a hole in the 3d orbital with spin σ along the α axis. Since one needs here only to calculate the matrix elements of the operatorÔ j,e on single site states, this can be done just by applying the dipole and fast collision approximations to the Kramers-Heisenberg formula for RIXS [33,34], so thatÔ j,e = αβ e αβD † β,jĜ jDα,j , whereD αj are the components of the dipole operator [22], and G j ∝ −ıc 1 +c 2Ŝj ·Π j is the intermediate state propagator (c 1,2 are constants depending on the resonant edge, see Fig. 1).…”

Resonant X-ray scattering in the presence of several anisotropic factors

“…We shall denote both cases as a weak-anisotropy approximation. It is similar to the fast-collision approximation (Luo et al, 1993). To explain the weakness of anisotropy in the latter case, let us suppose that the atomic resonant line is split into two levels described by the susceptibility tensors 1 and 2 and the resonant energies E 1 and E 2 .…”

“…The sum rules that allow the scattering amplitude to be calculated in terms of spherical tensors were represented by Carra et al (1993) and Luo et al (1993). In the dipole±dipole approximation, the explicit Cartesian form of susceptibility for the simultaneous existence of magnetic ordering and axially symmetric anisotropy of the local atomic environment was proposed by Blume (1994):…”

Self-interaction-corrected relativistic theory of magnetic scattering of x rays: Application to praseodymium

“…Finally, we mention few practical points about the implementation of the matrix elements of Eqs. (27) and (28).W e will derive below numerically tractable approximations for these matrix elements due to the electric dipole ͑E1͒ or magnetic dipole and electric quadrupole ͑M1+E2͒ contributions to the photon-electron interaction vertex X q ͑r͒.…”

“…25 Other approaches to interpreting MXRS spectra exist, particularly the successful methods based on group theory and angular momentum algebra that result in sum rules as described by Borgatti 26 and by Carra 27 and Luo. 28 The present work should not be regarded as a rival theory to these, but rather as an attempt to extend the range of density functional methods to describe magnetic scattering of x rays in the same way as is done for photoemission and other spectroscopies. 29 As a DFT-based theory our work is, of course, based on very different approximations to this earlier work, making direct comparison between the two theories problematic.…”