New bounds on the maximum ionization of atoms

TL;DR

This paper establishes new upper bounds on the maximum number of electrons an atom can bind, improving previous bounds for large atomic numbers and extending the results to atoms in magnetic and pseudo-relativistic regimes.

Contribution

The paper introduces tighter bounds on atomic ionization limits and extends the analysis to magnetic and pseudo-relativistic atoms.

Findings

Maximum ionization bound is less than 1.22Z+3Z^{1/3}

Improves Lieb's bound for Z ≥ 6

Limit superior of N_c/Z is at most 1.22 in extended cases

Abstract

We prove that the maximum number $N_c$ of non-relativistic electrons that a nucleus of charge $Z$ can bind is less than $1.22Z+3Z^{1/3}$. This improves Lieb's upper bound $N_c<2Z+1$ [{\it Phys. Rev. A} {\bf 29}, 3018-3028 (1984)] when $Z\ge 6$. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, $\limsup_{Z\to \infty}N_c/Z \le 1.22$.