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

The moments $S\left(\mu \right)$ and $L\left(\mu \right)=\frac{dS\left(\mu \right)}{d\mu }$ for $-6\mathrm{}\le \mu \le 1$ are derived from comprehensive Hartree-Slater oscillator-stength distributions for He through Ar. For $\mu \le -2\mathrm{}$, 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 $S(-1\mathrm{})\mathrm{}$, which retains a periodic variation superimposed upon an over - all increase with increasing atomic number $Z$. For $\mu \ge 0$, the $Z$ dependence of the moments becomes dominated by inner-shell contributions; as $\mu$ increases, the over-all increase with $Z$ becomes more rapid. Another perspective of the voluminous data is gained by plotting $logS\left(\mu \right)$ vs $\mu$. The plot reveals three classes of behavior—"tight," "intermediate," and "loose" atoms. Comparisons with experiment and more detailed calculations are made where possible.