The single-atom approximation for the $K\beta -\mathrm{to}-K\alpha$ x-ray intensity ratios for chemical compounds of $3d$ elements has been tested with the discrete-variational $X\alpha (\mathrm{DV}-X\alpha )$ molecular-orbital (MO) method. The effective numbers of electrons in each atomic shell are obtained with the $\mathrm{DV}-X\alpha$ method and used to calculate the $I\left(K\beta \right)/I\left(K\alpha \right)$ ratio in the single-atom approximation. The calculated results are in good agreement with the $\mathrm{DV}-X\alpha$ MO values for octahedral symmetry, but systematically smaller for tetrahedral symmetry. The reason for this discrepancy is ascribed to be the $K{\beta }_{2,5}$ component, which is appreciable in some compounds with the tetrahedral symmetry.

• Received 2 February 2000

DOI:https://doi.org/10.1103/PhysRevA.63.042514