Ab Initio Manganese K<i>α</i> and K<i>β</i> Energy Eigenvalues, Shake-Off Probabilities, Auger Rates, with Convergence Tests

Abstract

This work presents ab initio calculations for the Kα spectrum of manganese (Z = 25, [Ar]3d54s2), a highly complex system due to the five open orbitals in the 3d shell. The spectrum is composed of the canonical diagram line [1s]→[2p] and shake-off satellite lines [1snl]→[2pnl] (nl∈{2s,2p,3s,3p,3d,4s}), where square brackets denote a hole state. The multiconfiguration Dirac–Hartree–Fock method with the active set approach provides the initial and final atomic wavefunctions. Results are presented as energy eigenvalue spectra for the diagram and satellite transitions. The calculated wavefunctions include over one hundred million configuration state functions and over 280,000 independent transition energies for the seven sets of spectra considered. Shake-off probabilities and Auger transition rates determine satellite intensities. The number of configuration state functions ensures highly-converged wavefunctions. Several measures of convergence demonstrate convergence in the calculated parameters. We obtain convergence of the transition energies in all eight transitions to within 0.06 eV and shake-off probabilities to within 4.5%.

Keywords

• X-ray fluorescence
• MCDHF
• relativistic quantum mechanics