The ionization conjecture in Thomas-Fermi-Dirac-von Weizs\"acker theory

TL;DR

This paper proves a bound on the maximum number of electrons that can be bound by a nucleus in the Thomas-Fermi-Dirac-von Weizs"acker model, providing new bounds on potential and radius, and introducing a novel exterior region control technique.

Contribution

It establishes a universal bound on electron binding in the model and introduces a new method for controlling particles in the exterior region.

Findings

Bound of at most Z+C electrons for a nucleus of charge Z.

Derived bounds on the screened nuclear potential.

Provided estimates on the radius of the minimizer.

Abstract

We prove that in Thomas-Fermi-Dirac-von Weizs\"acker theory, a nucleus of charge $Z>0$ can bind at most $Z+C$ electrons, where $C$ is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.