The electron densities of pseudorelativistic eigenfunctions are smooth away from the nuclei

TL;DR

This paper proves that in a pseudorelativistic atomic and molecular model, the one-electron densities are smooth functions away from nuclei despite the eigenfunctions not being bounded.

Contribution

It establishes the smoothness of one-electron densities in a pseudorelativistic setting, a property not previously confirmed for such models.

Findings

One-electron densities are smooth away from nuclei.

Eigenfunctions may not be bounded, yet densities remain smooth.

Results apply to atoms and molecules in pseudorelativistic models.

Abstract

We consider a pseudorelativistic model of atoms and molecules, where the kinetic energy of the electrons is given by $\sqrt{p^2+m^2}-m$. In this model the eigenfunctions are generally not even bounded, however, we prove that the corresponding one-electron densities are smooth away from the nuclei.