On the maximal ionization of atoms in strong magnetic fields

TL;DR

This paper establishes upper bounds on the maximum number of spin-1/2 particles that can be bound to a nucleus in strong magnetic fields, incorporating spin-field coupling effects.

Contribution

It extends Lieb's method to include spin-field interactions, providing new bounds for bound particles in strong magnetic fields.

Findings

Upper bounds depend on nuclear charge Z and magnetic field B.

Inclusion of spin-field coupling modifies the bounds significantly.

Results applicable to fermionic particles in homogeneous magnetic fields.

Abstract

We give upper bounds for the number of spin 1/2 particles that can be bound to a nucleus of charge Z in the presence of a magnetic field B, including the spin-field coupling. We use Lieb's strategy, which is known to yield N_c<2Z+1 for magnetic fields that go to zero at infinity, ignoring the spin-field interaction. For particles with fermionic statistics in a homogeneous magnetic field our upper bound has an additional term of order $Z\times\min{(B/Z^3)^{2/5},1+|\ln(B/Z^3)|^2}$.