**6. Conclusions**

We have shown how two-photon above-threshold ionization can be treated in a relativistic framework from first principles. Correlation is included in the photoionization process at the level of the relativistic random phase approximation. As in the non-relativistic case, the calculation of the subsequent continuum–continuum transition relies on knowledge of the form of the intermediate wave packet when it is well outside the atomic core. For this purpose, we present a convenient recursive formula for both the large and small component of the regular and irregular solution to the relativistic Coulomb problem. The procedure have been applied to a few heavy elements, and it is shown that the separation of the atomic delay into a Wigner–Smith–Eisenbud delay and a universal continuum–continuum works reasonably well also for these systems.

We have further demonstrated qualitative agreemen<sup>t</sup> with existing experimental photoionization-delay data for ionization from the 4*d*-orbitals in xenon, and with lower energy results from the outermost orbitals in xenon and krypton. For higher photon energies, experiments report considerably larger delay differences between the fine-structure split channels than supported by the calculations. This might be connected to resonances or interfering shake-up channels, which can hopefully be resolved in the future.

**Author Contributions:** Conceptualization, E.L. and J.M.D.; methodology, E.L., J.M.D. and J.V.; software, J.V. and E.L.; validation, E.L., J.M.D. and J.V.; formal analysis, E.L., J.M.D. and J.V.; investigation, J.V.; resources, E.L. and J.M.D.; data curation, J.V.; writing—original draft preparation, E.L.; writing—review and editing, E.L. and J.M.D.; visualization, J.V. and E.L.; supervision, E.L. and J.M.D.; project administration, E.L. and J.M.D.; funding acquisition, E.L. and J.M.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Knut and Alice Wallenberg Foundation: Grant No. 2017.0104 and 2019.0154, from the Swedish Research Council: GrantNo. 2018-03845 and 2020-03315, and from the Olle Engkvist Foundation: Grant No. 194-0734.

**Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
