Sharp upper bounds for the density of relativistic atoms: Noninteracting case

TL;DR

This paper establishes the best possible upper bounds on electron density in relativistic atomic models without electron-electron interactions, considering angular momentum channels separately.

Contribution

It provides the first sharp upper bounds for electron densities in relativistic atoms in the noninteracting case, including angular momentum decomposition.

Findings

Derived optimal upper bounds for electron density in relativistic models.

Extended bounds to densities in individual angular momentum channels.

Abstract

We prove an optimal upper bound for the density of electrons of an infinite Bohr atom (no electron-electron interactions) described by the relativistic operators of Chandrasekhar and Dirac. We also consider densities in each angular momentum channel separately.