*Article* **Shake-Off Process in Non-Sequential Single-Photon Double Ionization of Closed-Shell Atomic Targets**

**Anatoli S. Kheifets**

> Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia; a.kheifets@anu.edu.au

**Abstract:** Amusia and Kheifets in 1984 introduced a Green's function formalism to describe the effect of many-electron correlation on the ionization spectra of atoms. Here, we exploit this formalism to model the shake-off (SO) process, leading to the non-sequential single-photon two-electron ionization (double photoionization—DPI) of closed-shell atomic targets. We separate the SO process from another knock-out (KO) mechanism of DPI and show the SO prevalence away from the DPI threshold. We use this kinematic regime to validate our model by making a comparison with more elaborate techniques, such as convergen<sup>t</sup> and time-dependent close coupling. We also use our model to evaluate the attosecond time delay associated with the SO process. Typically, the SO is very fast, taking only a few attoseconds to complete. However, it can take much longer in the DPI of strongly correlated systems, such as the H− ion as well as the subvalent shells of the Ar and Xe atoms and Cl− ion.

**Keywords:** atomic photoionization; many-electron correlation; non-sequential double ionization

**PACS:** 32.80.Rm 32.80.Fb 42.50.Hz

**Citation:** Kheifets, A.S. Shake-Off Process in Non-Sequential Single-Photon Double Ionization of Closed-Shell Atomic Targets. *Atoms* **2022**, *10*, 89. https://doi.org/ 10.3390/atoms10030089

Academic Editor: Grzegorz Piotr Karwasz

Received: 17 August 2022 Accepted: 5 September 2022 Published: 7 September 2022

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