Cu Kα3,4 satellite spectrum with ab initio Auger-rate calculations

This work investigates the capability of the multiconfiguration Dirac-Hartree-Fock (MCDHF) method in predicting the Cu $K{\ensuremath{\alpha}}_{3,4}$ spectrum. Ab initio energy eigenvalues, relative intensities, and radiative widths are calculated for the Cu $2p$ and $2s$ satellite transitions. By fitting to the most accurate experimental Cu $K{\ensuremath{\alpha}}_{3,4}$ spectra available, we show that our $2p$ satellite energy eigenvalues agree with experiment to within 0.35 eV and that our $2p$ shake probability agrees with the $2p$ fitted intensity to within 0.05%. Our fits suggest a $I(2s)$:$I(2p)$ satellite intensity ratio (as a percentage of the total $K\ensuremath{\alpha}$ spectrum) of 0.03(1):0.76(1) Theoretical predictions of this ratio can be examined using shake probabilities. We calculate the probability of shake-off due to the sudden creation of a $1s$ hole in Cu, yielding an ab initio $I(2s)$:$I(2p)$ shake probability ratio of 0.194:0.742. Using MCDHF, the rates at which hole states, created through the shake processes, depopulate via Auger transitions are determined. These results explain the apparent discrepancy between experimental satellite intensities and shake probabilities, and characterize the Cu $K{\ensuremath{\alpha}}_{3,4}$ spectrum with a satellite intensity ratio of 0.04(1):0.76, consistent with the experiment.