Energy variation of double K -shell photoionization of Ne

We report on an experimental and theoretical study of double $K$-shell photoionization of Ne over the 2.3--8.5 keV x-ray energy range. The ratio of double-to-single $K$-shell photoionization cross sections was determined experimentally by measuring the relative rates of the $KK\ensuremath{-}K{L}_{2,3}{L}_{2,3}$ ($^{2}D$) Auger hypersatellite and the $K\ensuremath{-}{L}_{2,3}{L}_{2,3}$ ($^{1}D$) diagram Auger transitions. By scaling the hypersatellite-diagram Auger-electron ratios to $KK/K$ cross-section ratios, comparison was made with theoretical cross-section ratios of He-like ${\mathrm{Ne}}^{8+}$ determined by the $R$ matrix with pseudostates method. The experimental Ne and theoretical ${\mathrm{Ne}}^{8+}$ cross-section ratios show similar variations with energy, but the experimental ratios systematically exceed the calculated ratios and also show a lower threshold energy for double $K$-shell photoionization onset compared to the computed ${\mathrm{Ne}}^{8+}$ threshold. The discrepancy is attributed to effects of $L$-shell electrons not included in the He-like ${\mathrm{Ne}}^{8+}$ calculations. Quantified scaling with nuclear charge $Z$ along the He-like isoelectronic sequence indicates that the measured 10-electron $Z=10$ double $K$-shell photoionization cross section behaves like the computed He-like $Z=8.9$ cross section, suggesting an effective nuclear screening parameter of ${s}_{L}=1.1$ by the additional eight outer $L$-shell electrons. Experimental results for the energy variations of Auger electron transitions from other multielectron hole states are also discussed.