Proof that the Hydrogen-antihydrogen Molecule is Unstable

TL;DR

This paper proves rigorously that the hydrogen-antihydrogen molecule cannot be stable within nonrelativistic quantum mechanics, based on a derived necessary condition involving mass ratios of the constituent particles.

Contribution

It introduces the first rigorous stability criterion for a four-particle Coulomb system and applies it to demonstrate the instability of hydrogen-antihydrogen molecules.

Findings

Hydrogen-antihydrogen molecule is proven unstable.

Derived a necessary stability condition based on mass ratios.

First such proof for a four-particle Coulomb system.

Abstract

In the framework of nonrelativistic quantum mechanics we derive a necessary condition for four Coulomb charges $(m_{1}^+, m_{2}^-, m_{3}^+, m_{4}^-)$, where all masses are assumed finite, to form the stable system. The obtained stability condition is physical and is expressed through the required minimal ratio of Jacobi masses. In particular this provides the rigorous proof that the hydrogen-antihydrogen molecule is unstable. This is the first result of this sort for four particles.