On the excess charge of a relativistic statistical model of molecules with an inhomogeneity correction

TL;DR

This paper establishes bounds on the maximum ionization of heavy atoms using a relativistic molecular model, showing existence of minimizers below a certain particle number and non-existence above it.

Contribution

It provides the first rigorous bounds on ionization limits in a relativistic molecular model with inhomogeneity correction.

Findings

Existence of minimizers for particle number ≤ total nuclear charge

Non-existence of minimizers for particle number > 2.56 times the total nuclear charge

Bounds on maximal ionization of heavy atoms

Abstract

We show that the molecular relativistic Thomas-Fermi-Weizs\"acker functional consisting of atoms of atomic numbers $Z_1,...,Z_k$ has a minimizer, if the particle number $N$ is constrained to a number less or equal to the total nuclear charge $Z:=Z_1+...+Z_K$. Moreover, there is no minimizer, if the particle number exceeds $2.56 Z$. This gives lower and upper bounds on the maximal ionization of heavy atoms.