The quantity $-rV\left(r\right)\mathrm{}$ for ions, formed by removing a $1s$ electron from the neutral atom, is computed by the approach of Herman and Skillman. A straight-line approximation of $-rV\left(r\right)\mathrm{}$ is made, leading to an exactly solvable one-electron Schrödinger equation. The discrete and continuum orbitals are used to compute Auger $\mathrm{KLL}$ and $\mathrm{KLM}$ transition rates, radiative rates, and fluorescence yields for the elements Be-Ar. Comparison with experimental $K$-shell fluorescence yields indicates the calculations are 25% too high for Mg and Al and within 5% for Ar. Comparison of the individual Auger transition intensities for F, Ne, Na, and Mg indicates differences of 50%. This 50% difference between calculated and measured individual Auger transition intensities persists up to Ar, where the sum of the individual intensities is in better than 7% agreement with that derived from the fluorescence yield and $K$-state width.

• Received 13 March 1969

DOI:https://doi.org/10.1103/PhysRev.185.1