Branching ratio in x-ray absorption spectroscopy

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Abstract
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.