Electronic Structure of Superheavy Atoms. Revisited

TL;DR

This paper revisits the electronic structure of superheavy atoms with Z > 137, clarifying the mathematical and physical issues and providing new numerical insights into their spectra.

Contribution

It offers a rigorous mathematical framework for the Dirac equation in superheavy atoms and presents new numerical calculations of their electronic spectra.

Findings

Correct definition of the Dirac Hamiltonian avoids imaginary eigenvalues for Z > 137

Physical spectra can be obtained for superheavy atoms with proper mathematical treatment

Numerical results illustrate the electronic structure beyond the Z=137 limit

Abstract

The electronic structure of an atom with Z <= 137 can be described by the Dirac equation with the Coulomb field of a point charge Ze. It was believed that the Dirac equation with Z > 137 is inconsistent and physically meaningless because the formula for the lower energy level of the Dirac Hamiltonian formally gives imaginary eigenvalues. But a strict mathematical consideration shows that difficulties with the electronic spectrum for Z > 137 do not arise if the Dirac Hamiltonian is correctly defined as a self-adjoint operator, see [1]. In this article, we brie y summarize the main physical results of that consideration in a form suitable for physicists with some additional new details and numerical calculations of the electronic spectra. [1] B.L. Voronov, D.M. Gitman, and I.V. Tyutin, Theor. Math. Phys. 150(1) (2007) 34