Near-edge structure of nonresonant inelastic x-ray scattering fromL-shell core levels studied by a real-space multiple-scattering approach

Calculations of the nonresonant inelastic x-ray spectra for $L$ edges of Si, Mg, and Na have been performed using a Bethe-Salpeter equation approach and an implementation of a real-space multiple-scattering Green's function approach. The computational results are compared with each other and with the measured spectra. It is shown to what extent both methods reproduce the general shape of the edges, their fine structure, and the dependence on the momentum transfer and thus on the weight of dipole and multipole transitions. Characteristics of the calculations concerning screening and the calculation of the density of states are also discussed in detail. The comparison between the multiple-scattering approach, the more sophisticated calculations using the Bethe-Salpeter approach, and experiment on these simple systems is essential for applications of real-space multiple-scattering calculations on more complex systems, which are not accessible by other computational methods.