Linear relation between x-ray absorption branching ratio and valence-band spin-orbit expectation value

The fraction of the total line strength of one of the core-hole spin-orbit-split manifolds in x-ray absorption is proved to be related to the expectation value of the valence-band spin-orbit operator. The relation obtained, by angular momentum algebra, is valid if the total angular momentum of the core hole is a good quantum number, which is true for deep core levels. Therefore, the branching ratio of deep-core-hole manifolds is probably the most direct probe to measure the valence-band spin-orbit interactions, especially in transition-metal compounds. The branching ratio measures the angular part of the spin-orbit operator and is complementary to magnetic measurements which determine the Landé g factor.