X-ray-absorption sum rules in jj-coupled operators and ground-state moments of actinide ions

Sum rules for magnetic x-ray dichroism, relating the signals of the spin-orbit split core level absorption edges to the ground-state spin and orbital operators, are expressed in jj-coupled operators. These sum rules can be used in the region of intermediate coupling by taking into account the cross term between the j=l+/-1/2 ground-state levels and are, therefore, particularly useful in the study of actinides. The calculated expectation values for the ground-state moments of the actinide ions in intermediate coupling show that the spin-orbit-induced operators, such as the magnetic-dipole term, differ strongly from their Hund's rule ground-state values. We also prove the general rule that, when there is a perturbing interaction which is weak compared to the spin-orbit interaction, the ratio of operators with the same total moment remains constant. This rendition is usually fulfilled for the crystal-field interaction in the lanthanides and actinides. The values of the ground-state moments as a function off count give rise to an interesting trend in the dichroism of the spin-orbit split-core edges. The branching ratio of the 3d and 4d circular dichroism signal gradually increases from nearly zero for 5f(1) to similar to 0.4 for 5f(5) and is close to unity for a more than half-filled shell. The unusual behavior of the branching ratio can be related to the higher (lower) value of the magnetic dipole term, Ti, for a less (more) than half-filled shell of the actinides in the presence of spin-orbit interaction. Uranium compounds will have a much larger value of T-z than the corresponding 4f compounds. Its precise value can be used as a measure for the f count.