Magnetic moment of the positronium ion and virial relations

TL;DR

This paper derives a hypervirial relation for the positronium ion, clarifies the magnetic moment calculation, and improves the precision of the binding correction, advancing theoretical understanding of this three-body system.

Contribution

It introduces a hypervirial relation for the positronium ion that reconciles previous formulas for its magnetic moment and enhances the accuracy of binding correction calculations.

Findings

Derived a hypervirial relation for the positronium ion

Reconciled two previously published formulas for magnetic moment

Improved the precision of the leading binding correction

Abstract

We derive a hypervirial relation for the positronium ion, a three-body bound state of two electrons and a positron. It relates expectation values of three operators and reconciles two recently published, seemingly inequivalent formulas for the magnetic moment of the ion. As a by-product, the precision of the leading binding correction is improved.