Smits ORIndelicato PNazarewicz WPiibeleht MSchwerdtfeger PSchwenk A2024-08-082024-08-082023-10-13Smits OR, Indelicato P, Nazarewicz W, Piibeleht M, Schwerdtfeger P. (2023). Pushing the limits of the periodic table — A review on atomic relativistic electronic structure theory and calculations for the superheavy elements. Physics Reports. 1035. (pp. 1-57).0370-1573https://mro.massey.ac.nz/handle/10179/71244We review the progress in atomic structure theory with a focus on superheavy elements and their predicted ground state configurations important for an element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is essential to correctly solve the Dirac equation in strong Coulomb fields, and to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge Zcrit≈170, where levels such as the 1s shell dive into the negative energy continuum (Enκ<−mec2). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.(c) 2023 The Author/sCC BY 4.0https://creativecommons.org/licenses/by/4.0/Dirac equationQuantum electrodynamicsSuperheavy elementsGamow statesAtomic structure theoryJournal article10.1016/j.physrep.2023.09.004journal-article1-57S0370157323003009