A test of the spin-orbit sum rule for actinides using an ab-initio calculation

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The expectation value of the angular part of the spin-orbit-coupling (SOC) operator <l· s> and the branching ratio for the N₄,₅ X-ray-absorption spectroscopy in δ-Pu, α-U and face-centered-cubic (fcc) Th are calculated within the framework of the density-functional theory in combination with the local-spin-density approximation (LSDA), the generalized-gradient approximation (GGA) and the LDA+U method. The SOC contribution is calculated in terms of the first- and the second- variational schemes. A strong variation in the magnitudes of the calculated <l· s> operator along the actinide series is found. The results show that the SOC sum rule for δ-Pu and α-U is reasonably valid, whereas there is a sign mismatch for the case of fcc Th. The calculated branching ratios for the case without SOC in the valence shell strongly deviate from the statistical value.