Theory of X-Ray Satellites

A general theory has been developed with regard to x-ray excitations, based on the method of the sudden approximation. As one application, the production probabilities of all the normal single-hole x-ray states of ${\mathrm{F}}^{-}$, Ne, ${\mathrm{Na}}^{+}$, ${\mathrm{Cl}}^{-}$, Ar, and ${\mathrm{K}}^{+}$ have been calculated in a self-consistent-field approximation. These production probabilities have been employed for derivation of the $\mathrm{KL}$-satellite intensity values 36.5% (${\mathrm{F}}^{-}$), 21.1% (Ne), and 14.3% (${\mathrm{Na}}^{+}$) relative to the $K{\alpha }_{1,2}$ line and the $\mathrm{KM}$-satellite intensity values 39.7% (${\mathrm{Cl}}^{-}$), 26.2% (Ar), and 19.3% (${\mathrm{K}}^{+}$) relative to the $K{\beta }_{1,3}$ line. In calculation of the relative satellite intensities, account has been taken of the difference between the oscillator strengths of the main line and the satellites, and the decay of $\mathrm{KL}$ to the $\mathrm{KM}$ states of ${\mathrm{Cl}}^{-}$, Ar, and ${\mathrm{K}}^{+}$. It has further been shown that the exchange probabilities can be ignored in these calculations. The satellite intensities calculated display close agreement with the experimental intensities obtained from Deslattes's measurements as concerns ${\mathrm{Cl}}^{-}$ and Ar, although there is a slight disagreement in the case of ${\mathrm{K}}^{+}$. It has been suggested that the usual criterion of validity for sudden approximation need not be fulfilled exactly in applications, and a connection between the sudden-approximation probability and the dipole-transition probability has been found. In conclusion, there is a discussion of solid-state effects on the satellite intensities.