Physical Mechanisms and Scaling Laws of $K$-Shell Double Photoionization

We report on the photon energy dependence of the $K$-shell double photoionization (DPI) of Mg, Al, and Si. The DPI cross sections were derived from high-resolution measurements of x-ray spectra following the radiative decay of the $K$-shell double vacancy states. Our data evince the relative importance of the final-state electron-electron interaction to the DPI. By comparing the double-to-single $K$-shell photoionization cross-section ratios for neutral atoms with convergent close-coupling calculations for He-like ions, the effect of outer shell electrons on the $K$-shell DPI process is assessed. Universal scaling of the DPI cross sections with the effective nuclear charge for neutral atoms is revealed.

Figure 1

$K$-hypersatellite x-ray emission spectra of Mg, Al, and Si measured at photon energies in the region of the DPI cross sections maxima.

Figure 2

Double-to-single $K$-shell photoionization cross section ratios versus atomic number. ● present results, ◇ [31], * [12, 33], △ [34], ▽ [11], × [2, 35], and nuclear electron capture (EC) [36]. For He-like ions, the $P_{KK}^{\max }$ are from Ref. 22 and this work (open circles), and from Ref. 8 (crosses). The photoabsorption asymptotic limits of Forrey et al. [30] (dashed line) are also shown.

Figure 3

Double-to-single $K$-shell photoionization ratios for neutral atoms (open circles) compared to the CCC calculations (velocity gauge) for the corresponding He-like ions (closed circles) as a function of the scaled excess energy. The best fits to our data (see text) are represented by solid thick lines, the KO by thin solid lines, and the SO by dashed lines. Dot-dashed lines show the KO terms of the He-like ions scaled by $Z^4/Z^{*4}$.

Figure 4

(a) Scaled experimental DPI cross sections for Mg, Al, and Si compared to the scaled CCC calculations for He-like ions and experimental data for higher $Z$ elements as a function of the scaled excess energy. A scaling exponent $X$ of 4.08 along the He isoelectronic series and 3.68 for neutral atoms was used (see inset). The curves (solid lines) were deduced from the fitted values of $P_{KK}$ shown in Fig. 3. (b) Shown are the power-law fits to the maximum values of ${\sigma }^{2+}$ as a function of $Z^{*}$. The error bars are smaller than the symbols.