Systematics of moments of dipole oscillator-strength distributions for atoms of the first and second row

Abstract

The moments $S(\ensuremath{\mu})$ and $L(\ensuremath{\mu})=\frac{dS(\ensuremath{\mu})}{d\ensuremath{\mu}}$ for $\ensuremath{-}6\ensuremath{\le}\ensuremath{\mu}\ensuremath{\le}1$ are derived from comprehensive Hartree-Slater oscillator-stength distributions for He through Ar. For $\ensuremath{\mu}\ensuremath{\le}\ensuremath{-}2$, these moments are governed by valence excitations only, and therefore exhibit a pronounced periodic variation that repeats in each row. Inner shells begin to contribute appreciably to $S(\ensuremath{-}1)$, which retains a periodic variation superimposed upon an over - all increase with increasing atomic number $Z$. For $\ensuremath{\mu}\ensuremath{\ge}0$, the $Z$ dependence of the moments becomes dominated by inner-shell contributions; as $\ensuremath{\mu}$ increases, the over-all increase with $Z$ becomes more rapid. Another perspective of the voluminous data is gained by plotting $logS(\ensuremath{\mu})$ vs $\ensuremath{\mu}$. The plot reveals three classes of behavior---tight, intermediate, and loose atoms. Comparisons with experiment and more detailed calculations are made where possible.