Characterization of the copper Kβ x-ray emission profile: an ab initio multi-configuration Dirac–Hartree–Fock approach with Bayesian constraints

We investigate the K beta characteristic radiation and the complex asymmetric structure of photoemission lines of copper, which provides a benchmark for theoretical and experimental studies of x-ray calibration series in transition metals. Ab initio multi-configuration Dirac-Hartree-Fock (MCDHF) calculations have been performed to study the complex open-shell many-electron problem in copper. The biorthogonalization technique permits determination of transition intensities and Einstein A coefficients. The results from our MCDHF calculations demonstrate excellent convergence in transition energies and intensities, as well as gauge invariance to 0.6%. Shake processes caused by single and double spectator vacancies from 3d, 3p, 3s and 4s subshells have also been investigated extensively. MCDHF has been performed to calculate energies and relative intensities of 3d, 3d(2), 3p, 3s and 4s satellites, resulting in the total number of configuration states exceeding 100 000 and more than 1500 transition components. Our theoretical calculations of shake-off probabilities using the multi-configuration method in the sudden limit have a high degree of internal consistency with the best available experimental data for copper K beta. This supports the validity of relativistic atomic theory and sets a new benchmark even for poorly resolved characteristic spectra using current techniques of analysis.