Theoretical calculation of characteristic radiation: multiconfiguration Dirac–Hartree–Fock calculations in scandium K α and K β

Abstract

The characteristic X-ray spectra of 3d transition metals are a constant source of advances in atomic physics, X-ray spectrometry, and quantum mechanics. Prior to this work, there was a discrepancy of 0.549 eV between theoretical and experimental results for the scandium Kα1 peak energy, representing a 55σ discrepancy using the experimental uncertainty. This work improves this to a 0.330 eV discrepancy with only a 4σ error between experiment and theory. Furthermore, we add considerable evidence that asymmetries in X-ray spectra are described by shake events. This work provides ab initio calculations for the diagram and shake-off satellite lines of Sc Kα and Kβ and makes significant improvement on the previous fitting between theory and experiment, from a χ2r of 7.35 and 20.85 to 1.60 and 1.45 for Kα and Kβ, respectively. Therefore, we make a strong claim that the asymmetries in scandium x-ray lines exist due to satellite lines with very little room for other hypothesised phenomena to exist, such as Kondo-like interactions and Doniac-Sunjic asymmetries. By fitting to the best experimental data for Sc Kα,β we obtain values for the width and intensity of the satellite lines which enable us to reconstruct the Kα, Kβ profiles.

High-accuracy measurement, advanced theory and analysis of the evolution of satellite transitions in manganese Kα using XR-HERFD

“…Once initial and final states are calculated, energy eigenvalues and relative intensities are obtained through biorthogonalization. Recent work outlines the success of this approach for scandium (Dean et al, 2022) and copper (Nguyen et al, 2022a,b). Results for the Mn K� 2s and 2p shake-off satellites are presented in Fig.…”