The Maximal Negative Ion of the Time-Dependent Thomas-Fermi and the Vlasov Atom

TL;DR

This paper proves that atoms modeled by the time-dependent Thomas-Fermi or Vlasov equations cannot bind more than four times their atomic number of electrons, providing a fundamental limit on electron binding in these models.

Contribution

It establishes a new upper bound on the number of electrons that can be bound in time-dependent Thomas-Fermi and Vlasov atom models.

Findings

Atoms cannot bind more than 4Z electrons in these models.

Provides a theoretical limit on electron binding.

Enhances understanding of atom stability in mean-field models.

Abstract

We show an atom of atomic number $Z$ described by the time-dependent Thomas-Fermi equation or the Vlasov equation cannot bind more than $4Z$ electrons.