Figure 1

Feynman diagrams representing the double photoionization of a heliumlike atom. $a$ and $b$ denote the bound-electron states, ${\mathit{p}}_1$ and ${\mathit{p}}_2$ are the continuum electron states, and $\mathit{k}$ denotes the incoming photon. Double lines denote electrons propagating in the binding nuclear field.Reuse & Permissions

Figure 2

Comparison of the nonrelativistic limit of the present calculations with the experimental results for helium and the nonrelativistic theoretical high-energy limits. The solid (black) line shows our nonrelativistic results for $Z=2$, the dashed (blue) line shows those for $Z=40$, and the dashed-dotted (red) line shows those for $Z=54$. (The three lines are practically indistinguishable on the picture.) The triangles, squares, and diamonds represent the experimental results for helium obtained in Refs. [34, 35, 36, 37], respectively. The dotted line shows the nonrelativistic high-energy limit calculated to the leading order of the perturbation theory [4]. The dash-dot-dotted line shows the nonrelativistic asymptotical limit calculated with the fully correlated wave functions [5, 6].Reuse & Permissions

Figure 3

Comparison of the results of the fully relativistic calculations (solid line, black) with results of various approximate treatments. The dotted (red) line represents the nonrelativistic limit. The dashed-dotted (blue) line is obtained with the relativistic wave functions but without retardation and including the relativistic $E1$ transition only. The dashed (green) line shows the results obtained with the relativistic wave functions and the full retardation but including the relativistic $E1$ transition only. The threshold photon energy of the double photoionization is ${\omega }_{\mathrm{cr}}=2.56$ keV for Ne${}^{8+}$, ${\omega }_{\mathrm{cr}}=10.60$ keV for Ca${}^{18+}$, and ${\omega }_{\mathrm{cr}}=43.75$ keV for Zr${}^{38+}$.Reuse & Permissions

Figure 4

Relativistic results for the scaled ratio of the double photoionization cross section ${\sigma }^{++}$ to the single photoionization cross section ${\sigma }^{+}$, for heliumlike ions with different nuclear charges $Z$, as a function of the photon energy $\omega$ divided by the threshold photon energy of the double photoionization ${\omega }_{\mathrm{cr}}$.Reuse & Permissions

Figure 5

Relativistic enhancement function $f_{\mathrm{rel}}$ defined by Eq. (26), for different heliumlike ions.Reuse & Permissions

Figure 6

Normalized energy distribution of the ejected electrons as a function of the energy sharing parameter $x$ defined by Eqs. (12) and (13), for different nuclear charge numbers and photon energies.Reuse & Permissions