The origin of nonstatistical branching ratios in spin-orbit-split x-ray absorption spectra is explained. Atomic calculations for transition metals show a systematic change which is due to initial-state spin-orbit splitting and electrostatic interactions between core hole and valence electrons. We have formulated the results of these atomic calculations in general rules, which are also applicable to solids. In the free atom the branching ratio reaches a maximum for the Hund's-rule ground state and its value decreases gradually for S, L, and J levels of higher energy. The presence of a crystal field results in a lower branching ratio when it produces a low-spin ground state. The rules can be used to assess the spin state and the spin-orbit splitting from the experimental branching ratio in transition-metal and rare-earth compounds. A specific example is given for the influence of second-order spin-orbit interactions in high-spin Ni compounds.

Branching ratio in x-ray absorption-spectroscopy

http://amo-csd.lbl.gov/downloads/BIB-INNER-SHELL-BY-HITCHCOCK.pdf

Bibliography of atomic and molecular inner-shell excitation studies

A theory is presented for the x-ray absorption spectra of materials characterized by bandwidths which are somewhat larger than the (quasiatomic) electron correlation energies. Assuming that an empty-band approximation is appropriate for nearly empty bands we show that the problem is much akin to the well-known Coulomb localization problem in Auger spectroscopy, with an enhanced sensitivity for exchange and multipole effects because of the dipole selection rules. Using first-principles band structure and atomic data as input for the theory, we calculate the spectra of Ca, Ti, and V and obtain good agreement with high-resolution experimental spectra.

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l2,3 absorption-spectra of the lighter 3d transition-metals

Non-Rydberg effects in the photoabsorption spectra of atoms are described. They are observed at photon energies which correspond to the creation of a vacancy within the subvalence shells of the atom or to the simultaneous excitation of two electrons. The importance of synchrotron radiation as an experimental tool for the investigation of non-Rydberg effects is stressed, and many examples are given. Many of the non-Rydberg properties can be understood by analogy with elementary one dimensional potential well theory.

The Non-Rydberg spectroscopy of atoms

Photoionisation of Ca atoms has been investigated by means of a time-of-flight mass spectrometer coupled with a source of monochromatised synchrotron radiation and an atomic Ca beam. Relative photoionisation cross sections (q+ for single photoionisation and q2+ for double photoionisation, as well as the ratio R=q2+/q+) have been measured in the wavelength range 35-42 nm with a 0.15 nm bandwidth. Comparison with the photoabsorption data of Mansfield and Newsom (1977) shows a good correspondence in the peak structure between the absorption resonance and the Ca2+ yield for proton energies above the lowest 3p ionisation limit. The variation of R with wavelength exhibits a step behaviour which correlates with some of the 3p ionisation limits.

https://iopscience.iop.org/article/10.1088/0022-3700/19/9/010/pdf

Single and double photoionisation of Ca atoms between 35 and 42 nm

The Ca I absorption spectrum has been photographed between 10 and 120 angstrom for the first time. At least seven discrete features-all attributable to excitation of the 2p subshell - have been observed. Identifications are made by comparison with Hartree-Fock calculations. The Hartree-Fock results also support an explanation of the irregular quantum defects and remarkable breadths of the lines assigned to the 2p $\rightarrow $ 3d transition.

The Ca I Absorption Spectrum in the Extreme Ultraviolet: Excitation of the 2p Subshell

The 3d and 4s photoabsorption spectra of Cr I have been observed by using the synchrotron radiation emitted by the Bonn 500 MeV electron accelerator as the source of background continuum. The resulting spectrum is unexpectedly simple, and this is explained within the spectator electrons approximation. The more intense transitions can be arranged in Rydberg series. A prominent series of transmission windows arises by double excitation. A detailed analysis is presented, supported by some ab initio Hartree-Fock calculations and also by comparison with the semi-empirical calculations of Roth (1970) which include mixing between all the (3d + 4s)$^5$ 4p configurations.

The Spectator Electrons Approximation in the 3d and 4s Spectra of Cr I

New observations of the absorption spectrum of Mn I between 1800 and 700 A have revealed 77 new transitions, arrangeable in Rydberg series converging on to experimentally known levels of the ion. The analysis of the spectrum at wavelengths shorter than 1300 A suggests assignments for several previously unidentified transitions in the 1300-1600 A range. Comparisons with ab initio Hartree-Fock calculations are attempted, and the spectator electrons model is shown to provide the correct framework for the analysis of 3d and 4s excitation in Mn I.

G. H. Newsom

Papers

The Ca I Absorption Spectrum in the Extreme Ultraviolet: Excitation of the 2p Subshell

The Spectator Electrons Approximation in the 3d and 4s Spectra of Cr I

On the validity of the spectator electrons model in the 3d and 4s excitation spectra of Mn i