Stability of three-unit-charge systems

Observation of a shape resonance of the positronium negative ion

When an electron binds to its anti-matter counterpart, the positron, it forms the exotic atom positronium (Ps). Ps can further bind to another electron to form the positronium negative ion, Ps⁻ (e⁻e⁺e⁻). Since its constituents are solely point-like particles with the same mass, this system provides an excellent testing ground for the three-body problem in quantum mechanics. While theoretical works on its energy level and dynamics have been performed extensively, experimental investigations of its characteristics have been hampered by the weak ion yield and short annihilation lifetime. Here we report on the laser spectroscopy study of Ps⁻, using a source of efficiently produced ions, generated from the bombardment of slow positrons onto a Na-coated W surface. A strong shape resonance of ¹P^o symmetry has been observed near the Ps (n=2) formation threshold. The resonance energy and width measured are in good agreement with the result of three-body calculations.

The Positronium negative ion is formed by two electrons bound to a positron, and experimental investigations of its states and energy levels are difficult due to its short lifetime. Here, the authors report on laser spectroscopy of positronium using a source of efficiently produced ions.

Proof that the hydrogen-antihydrogen molecule is unstable

In the framework of nonrelativistic quantum mechanics we derive a necessary condition for four Coulomb charges (m1(+), m2(-), m3(+), m4(-)), 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 hydrogen-antihydrogen and muonium-antimuonium molecules and hydrogen-positron-muon systems are unstable. It also proves that replacing hydrogen in the hydrogen-antihydrogen molecule with its heavier isotopes does not make the molecule stable. These are the first rigorous results on the instability of these systems.