The Four-Body System Made up of Hydrogen and Antihydrogen

Proof that the Hydrogen-Antihydrogen Molecule Is Unstable

“…It has long been conjectured that with pure Coulomb forces no bound state of hydrogen-antihydrogen exists. The numerical evidence supports this conjecture [2], yet there is a lack of rigorous proof as remarked by some authors [3], [4]. Our aim in this Letter is: (i) to supply such proof under assumption that only Coulomb forces act between the constituents, (ii) to provide insight into the screening effect within the system of four charged particles.…”

“…The ground state wave function of h 12 is φ 0 = 8/π exp(−2x) so that h 12 φ 0 = −φ 0 . By the particle ordering the energy threshold corresponding to dissociation into two neutral pairs is E th = −1−µ y /2, which is the sum of the binding energies of the pairs (1,2) and (3,4). Following [5] we shall cut off the positive part of W by introducing W − ≡ (|W | − W )/2 and W + ≡ (|W | + W )/2 which results in the decomposition W = W + − W − , where W ± ≥ 0.…”

Stability of few-charge systems in quantum mechanics

“…However, the work on the preparation of H described above has generated greater theoretical interest in this system, Armour et al [169,211,212,213,214,215] Jonsell, Froelich et al [216,217,218,219,220,221,222], Sinha and Ghosh [223], Voronin and Carbonell [224].…”

“…As Richard points out, in this situation the existence or otherwise of four-body bound states depends on whether the three very much heavier particles have a bound state that can form a charged 'nucleus' that can bind the very much lighter particle, which is of opposite charge. It follows that the form of the stability domain on the above surface is the same as for three particles, two of which have the same positive charge and the other has the opposite negative charge [168,169], with upper vertex on AB or CD, the sides of the tetrahedron that are considered to correspond to bound states. See Fig.…”

“…There has been interest in calculations on the interaction of H with H, since the 1970s, Junker and Bardsley [206], Morgan and Hughes [207], Ko los et al [208], Campeanu and Beu [209], Shylapnikov et al [210]. However, the work on the preparation of H described above has generated greater theoretical interest in this system, Armour et al [169,211,212,213,214,215] Jonsell, Froelich et al [216,217,218,219,220,221,222], Sinha and Ghosh [223], Voronin and Carbonell [224].…”