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A new first-principles computation scheme to calculate `branching ratio' hasbeen applied to various $5d$, $4d$, and $3d$ transition metal elements andcompounds. This recently suggested method is based on a theory which assumesthe atomic core hole interacting barely with valence electrons. While itprovides an efficient way to calculate the experimentally measurable quantitywithout generating spectrum itself, its reliability and applicability should becarefully examined especially for the light transition metal systems. Here weselect 36 different materials and compare the calculation results withexperimental data. It is found that our scheme well describes 5$d$ and 4$d$transition metal systems whereas, for 3$d$ materials, the difference betweenthe calculation and experiment is quite significant. It is attributed to theneglect of core-valence interaction whose energy scale is comparable with thespin-orbit coupling of core $p$ orbitals.

First-principles-based calculation of branching ratio for 5$\boldsymbol{d}$, 4$\boldsymbol{d}$, and 3$\boldsymbol{d}$ transition metal systems