Electron-electron correlation in two-photon double ionization of He-like ions

Electron correlation plays a crucial role in quantum many-body physics ranging from molecular bonding and strong-field–induced multielectron ionization, to superconducting in materials. Understanding the dynamic electron correlation in the photoionization of relatively simple quantum three-body systems, such as He and He-like ions, is an important step toward manipulating complex systems through photoinduced processes. Here we have performed ab initio investigations of two-photon double ionization (TPDI) of He and He-like ions $(\mathrm{L}{\mathrm{i}}^{+},\mathrm{B}{\mathrm{e}}^{2+}$, and ${\mathrm{C}}^{4+})$ exposed to intense attosecond x-ray pulses. Results from such fully correlated quantum calculations show weaker and weaker electron correlation effects in TPDI spectra as the ionic charge increases, which is opposite to the intuition that the absolute increase of correlation in the ground state should lead to more equal energy sharing in photoionization. These findings indicate that the final-state electron-electron correlation ultimately determines the energy sharing of the two ionized electrons in TPDI.

Figure 1

The final photoionization probability–density distribution on the plane spanned by the radial coordinates $r_1$ and $r_2$, for (a) He and He-like ions of (b) $\mathrm{L}{\mathrm{i}}^{+}$, (c) $\mathrm{B}{\mathrm{e}}^{2+}$, and (d) ${\mathrm{C}}^{4+}$ exposed to intense x-ray pulses.

Figure 2

The momentum distribution of photoinduced double ionization of (a) He and He-like ions of (b) $\mathrm{L}{\mathrm{i}}^{+}$, (c) $\mathrm{B}{\mathrm{e}}^{2+}$, and (d) ${\mathrm{C}}^{4+}$ exposed to intense x-ray pulses.

Figure 3

The triple-differential cross section (TDCS) of two-photon double ionization (in units of ${10}^{-50}\mathrm{c}{\mathrm{m}}^4\mathrm{s}/\mathrm{s}{\mathrm{r}}^2\mathrm{eV})$ as a function of the second electron ejection angle $\left({\theta }_2\right)$ and energy $\left(E_2\right)$ in the coplanar geometry $\left({\varphi }_1={\varphi }_2=0^{\circ }\right)$, for the case of the first electron ejection angle of ${\theta }_1=0^{\circ }$. The different panels correspond to the cases shown in Fig. 1, in which the horizontal dashed lines mark the expected energies from the sequential two-photon double ionization (STPDI).

Figure 4

Similar to Fig. 3 but for He and He-like ions exposed to different x-ray pulses: (a) He with $h\nu =85\mathrm{eV}$, (b) He with $h\nu =421.4\mathrm{eV}$, (c) $\mathrm{L}{\mathrm{i}}^{+}$ with $h\nu =421.4\mathrm{eV}$, and (d) $\mathrm{B}{\mathrm{e}}^{2+}$ with $h\nu =421.4\mathrm{eV}$, respectively. The same x-ray pulse intensity of $I=2\times {10}^{17}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ applies for (b)–(d), while $I=5\times {10}^{16}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ applies to (a).

Figure 5

The energy shift in the TPDI peak from the expected sequential TPDI locations as a function of $Z$ of He-like ions, for the different cases investigated.

Figure 6

TDCS versus the ejected electron energy for the back-to-back ejection geometry, for (a) He, (b) $\mathrm{L}{\mathrm{i}}^{+}$, and (c) $\mathrm{B}{\mathrm{e}}^{2+}$ interacting with different x-ray pulses at the same ratio of $E_{\mathrm{ex}}/\left(|I{p}_1|+|I{p}_2|\right)\approx 7.6\%$.