Sum Rules for Neon Photoeffect

Three oscillator sum rules are evaluated for neon from available experimental cross-section data. Recent data of Ederer and Tomboulian are used for the region from threshold to 13 Ry, and standard power-law expressions are fitted for the region from 13 Ry to the $K$ edge. Beyond the $K$ edge the Stobbe law and Born approximation are utilized. An independent value for the polarizability is utilized to determine the discrete contribution to the polarizability sum rule. This discrete contribution is used to determine the discrete contributions to the remaining sum rules. Hartree-Fock wave functions are used in evaluation of terms such as $〈0\left|\Sigma {i\ne j}^{}{\mathrm{r}}_i·{\mathrm{r}}_j\right|0\mathrm{}〉$ and $〈0\left|\Sigma {i\ne j}^{}{\mathrm{p}}_i·{\mathrm{p}}_j\right|0\mathrm{}〉$. (1) The diamagnetic susceptibility by sum rule is (-7.05±0.50) ×${10}^{-6\mathrm{}}$ versus a directly measured value of (-7.65±0.1)×${10}^{-6\mathrm{}}$. (2) The neon binding energy by sum rule of 276±13 Ry contrasts with 257.88±0.01 Ry otherwise. (3) The sum rule using the squared energy yields (11.2±0.6)×${10}^4$ ${\mathrm{Ry}}^2$ versus (10.4±1.0)×${10}^4$ ${\mathrm{Ry}}^2$ by Hartree-Fock calculation of the electron density at the nucleus.