New bounds on the excess charge for atomic systems

TL;DR

This paper establishes improved bounds on the excess charge in non-relativistic atomic systems using advanced mathematical techniques, providing the tightest bounds for bosonic systems and for fermionic systems up to iron.

Contribution

It introduces new bounds on excess charge for atomic systems, leveraging the Coulomb Uncertainty Principle, and improves upon previous bounds for specific particle statistics and atomic numbers.

Findings

Best bounds to date for bosonic systems across all Z

Improved bounds for fermionic systems with Z ≤ 26

Utilizes the Coulomb Uncertainty Principle for proofs

Abstract

In this manuscript, using a technique introduced by P.~T.~Nam in 2012 and the {\it Coulomb Uncertainty Principle}, we prove new bounds on the excess charge for non relativistic atomic systems, independent of the particle statistics. These new bounds are the best bounds to date for bosonic systems for all values of the atomic number $Z$ and they are also the best bounds for fermionic systems with $Z \le 26$ (i.e., up to the chemical element {\it iron})