Scandium Kα and Kβ x-ray spectra with ab initio satellite intensities and energy eigenvalues

Characteristic x-ray spectra offer insight into the structure and composition of atoms and molecules at a fundamental level where discrepancies in asymmetry, peak energy, and shape between theory and experiment motivate investigations. This work calculates highly convergent electron wavefunctions using the multiconfiguration Dirac-Hartree-Fock method and reveals the capability of recreating x-ray spectra from first principles, with eigenvalue convergence of order 0.1 eV and amplitude convergence of order 1--4%. The canonical Kα and Kβ transitions, [1s]→[2p] and [1s]→[2p], respectively, where square brackets denote hole states, are not sufficient to recreate major features present in the data. Shake-off satellites, where the transitions take place in the presence of a secondary $nl$ hole, are necessary to account for observed asymmetries. The probabilities for these shake-off events are determined and used to obtain ab initio satellite intensities. The Auger effect is considered for these satellite intensities through an Auger suppression factor. This work presents the full energy eigenvalue spectrum for several scandium transitions: [1s²] hypersatellites (Kαʰ and Kβʰ), the n=2 Kα3,4 and Kβ equivalent satellites, and double shake-off satellites. Calculations are compared with deconvolved experimental data using several fitting models which yield compelling goodness of fit χᵣ²=1.14 for Kα and χᵣ²=1.72 for Kβ. The selected best model is chosen through the statistical F-test and this model is fitted with raw (not deconvolved) experimental data with χᵣ²=0.92 (Kα) and χᵣ²=1.31 (Kβ).