A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization

TL;DR

This paper introduces a one-dimensional model for many-electron atoms in extremely strong magnetic fields, establishing an upper bound on the maximum number of electrons based on nuclear charge and magnetic field strength, and analyzing electron binding thresholds.

Contribution

It presents a novel one-dimensional model incorporating magnetic field effects and derives bounds on electron number and binding conditions, extending Lieb's approach to this context.

Findings

Maximum electron number bounded by 2Z+1 + c sqrt{B}

Identifies critical nuclear charge for two-electron binding

Uses convexity to analyze electron interactions in strong fields

Abstract

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.