Exchange corrections of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></mml:math>x-ray emission rates

Separate relativistic Hartree-Fock solutions for atoms in their initial and final states are used for calculating the radiative decay of a $K$-vacancy state. The matrix-element calculations include the exchange effects of the nonzero overlap of wave functions from different subshells. Results are presented for the filling of the vacancy by the $p$ electrons for a set of elements from $Z=10\mathrm{to}98$. The Hartree-Fock theory is also used for calculating the rates of production of multiple-vacancy states in the decay process. In contrast to earlier single-potential calculations, the calculated values of ratios of the rates of the $K$ x-ray components are in good agreement with the experimental values.