Multiconfiguration Dirac-Hartree-Fock theory for copper Kα and Kβ diagram lines, satellite spectra, and ab initio determination of single and double shake probabilities

The x-ray spectra of copper K alpha and K beta remain a topic of great interest due to the complex open-shell processes involved, with many discrepancies among theories and experiments. We present high-accuracy theory of copper K alpha and K beta diagram and satellite spectra in the multiconfiguration Dirac-Hartree-Fock method. Diagram spectra are expanded to 5s with simultaneous convergence of 28 000 configuration state functions (CSFs) (K alpha) and to 6g with simultaneous convergence of 91 000 CSFs (10), achieving eigenvalue convergence to +/- 0.03 eV or 0.000 25%, approximately a factor of 10 improvement over past work. It is necessary to invoke biorthogonalization, developments of the active space approach, analysis of markers for theoretical convergence of eigenvalues, and the question of self-consistency for both K alpha and K beta spectra. We make use of gauge convergence, eigenvalue convergence, and A-coefficient convergence. The satellite spectra are a major outcome-without these, it is not possible to make use of the increased accuracy of the diagram computations. The Cu K alpha 3d(8) double shake satellite spectrum alone contains 1506 unique eigenvalues (transitions) and required simultaneous convergence of 593 000 CSFs. Ab initio shakeoff probabilities for 1s, 2s, 2p, 3s, 3p, 3d, and 4s subshells as a result of the K-shell photoionization process are presented. Portable spectral representations are provided in the supplemental material, discussed in the text. We investigate the meaning behind shake, shakeoff, and shakeup processes and the computational potential to investigate these at the current time. We separate the notions of total shake, single shake, and double shake, explain how these are observable in high-quality experimental spectra, and how these calculations can be used experimentally.

Automated summary

This paper presents a high-accuracy theory of copper K alpha and K beta spectra and satellite spectra using the multiconfiguration Dirac-Hartree-Fock method. It also investigates the meaning behind shake, shakeoff, and shakeup processes and their computational potential. The importance of satellite spectra is highlighted, as it enables the use of increased accuracy in diagram computations.