Widths of4sand5smultiplet components in the rare earths

For multiplets formed by adding an $s$ vacancy to an atom with a partially filled shell, it is shown that the Auger transition rate can be found from expressions that do not involve franctional-parentage coefficients of the partially filled shell. The proof requires a sum over final states and that the partially filled shell be in a state of maximum spin. Calculations are performed for the widths of the $4s$ and $5s$ multiplet components in the rare earths. The calculated $4s$ widths are considerably larger than the measured values, while the $5s$ widths are considerably smaller than the measured values. It is shown that these disagreements cannot be fully accounted for by the choice of Auger-electron energy. It is hypothesized that the cause of the disagreement is neglect of configuration interaction, and this is briefly discussed.