Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

TL;DR

This review discusses advances in atomic structure theory for superheavy elements, emphasizing relativistic effects, quantum electrodynamics, and challenges in solving the many-particle Dirac equation at high atomic numbers.

Contribution

It highlights recent progress and future prospects in relativistic atomic calculations for superheavy elements, including beyond the critical nuclear charge.

Findings

Understanding of electronic structure in superheavy elements

Challenges in solving the many-particle Dirac equation

Potential for calculations beyond Z=170

Abstract

We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is important to correctly solve the Dirac equation in strong Coulomb fields, and also 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 \(Z_{\rm crit}\approx 170\), where levels such as the \(1s\) shell dive into the negative energy continuum (\(E_{n\kappa}<-m_ec^2\)). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.