The maximal excess charge in M\"uller density-matrix-functional theory

TL;DR

This paper proves that in M"uller density-matrix-functional theory, an atom cannot bind more than a fixed number of electrons beyond its nuclear charge, using comparison with Thomas-Fermi theory and a new bound on electron distribution.

Contribution

It establishes a universal upper bound on the excess electrons an atom can bind in M"uller theory, extending understanding of atomic stability in this model.

Findings

Maximum excess electrons is bounded by a universal constant.

Comparison with Thomas-Fermi theory is used for the proof.

Introduces a novel bound on electrons far from the nucleus.

Abstract

We consider an atom described by M\"uller theory, which is similar to Hartree-Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most Z+C electrons, where C is a universal constant. Our proof proceeds by comparison with Thomas-Fermi theory and a key ingredient is a novel bound on the number of electrons far from the nucleus.