We investigate the Kb 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 Kb. This supports the validity of relativistic atomic theory and sets a new benchmark even for poorly resolved characteristic spectra using current techniques of analysis.

Much discussion in relativistic atomic physics and quantum optics has related to the interaction of gauge and perturbation of the Hamiltonian or Dirac operator. It has been commented that Lorentz and gauge independence requires different forms of the perturbation operator in shifting from one gauge to another. Equally, it has been commented that gauge convergence is not possible without different operator forms in different bases and without the operator being embedded within the self-consistent kernel. We explore the logic and self-consistency of these arguments, applied to the well-known Breit operator in an area of continuing discussion. We find that convergence is now possible to a remarkable degree including a Breit interaction operator in a form consistent with the gauge for length and velocity relativistic forms of the multipole operator, implemented at the configuration-interaction level. Excellent convergence is obtained for Breit interaction energies, interaction mixing coefficients, interaction transition probabilities and eigenenergies and transition probabilities in complex open shells (transition metal K α transitions and shake satellites), and forbidden transitions.

The 557.7 nm green line and the 297.2 nm ultraviolet line in oxygen have been studied extensively due to their importance in astrophysics and atmospheric science. Despite the enormous effort devoted to these two prominent transition lines over 30 years, and in fact going back to 1934, the ratio of their transition probabilities remains a subject of major discrepancies amongst various theoretical calculations for many decades. Moreover, theoretical results are inconsistent with available laboratory results, as well as recent spacecraft measurements of Earth's airglow. This work presents new relativistic theoretical calculations of the transition probabilities of these two photoemission lines from neutral oxygen using the multi-configuration Dirac-Hartree-Fock method. Our calculations were performed in both length and velocity gauges in order to check for accuracy and consistency, with agreement to 8%. Whilst remaining a challenging computation, these results directly bear upon interpretations of plasma processes and ionization regimes in the universe.

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