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Physical Review Letters

Hydrogen-Antihydrogen Interactions

B. R. Junker, J. N. Bardsley

Published May 8, 1972• 49 citations
Publisher

Abstract

The interaction potential between hydrogen and antihydrogen is obtained by a variational calculation. A potential maximum is found, but its peak is below the dissociation limit. A classical calculation shows that the cross section for total annihilation decreases monotonically from $31{{a}_{0}}^{2}$ at 0.01 eV to $4{{a}_{0}}^{2}$ at 20 eV.

DOI
10.1103/physrevlett.28.1227

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The interaction potential between hydrogen and antihydrogen is obtained by a variational calculation. A potential maximum is found, but its peak is below the dissociation limit. A classical calculation shows that the cross section for total annihilation decreases monotonically from 31a0231{{a}_{0}}^{2}31a0​2 at 0.01 eV to 4a024{{a}_{0}}^{2}4a0​2 at 20 eV.
Accurate quantum-mechanical calculations on the system hydrogen-antihydrogen (HH‾\mathrm{H}\overline{\mathrm{H}}HH) are presented. The energy is calculated using the Ritz variational principle, and is obtained as a function of the proton-antiproton distance in the Born-Oppenheimer approximation. It is everywhere lower and therefore more accurate than that recently calculated by Junker and Bardsley. In particular, the maximum in the interatomic interaction reported by these authors is not seen in this calculation. The cross section for rearrangement annihilation is calculated and found to be uniformly larger than that reported by Junker and Bardsley.
The stability of antimatter in contact with matter has been investigated. The interaction between hydrogen and antihydrogen is considered as the prototype reaction. We have focused interest on the rates for proton-antiproton and/or electron-positron annihilation during hydrogen-antihydrogen collisions at low energies. In particular, we have concentrated on the calculation of the rates for the rearrangement reaction leading to formation of protonium and positronium, ending inevitably in particle-antiparticle annihilation. The cross section for the rearrangement collision has been calculated in a fully quantum-mechanical treatment. Additionally, we have calculated cross sections for direct annihilation during the collision process, which was found to be comparable to the rearrangement cross section. The elastic cross section and its low-energy limit, given by the scattering length, have been calculated, allowing, by comparison to the inelastic processes, a prediction for the efficiency of cooling antihydrogen via collisions with ultracold hydrogen atoms.
Matter-antimatter interactions are investigated using hydrogen-antihydrogen collisions as an example. Cross sections for elastic scattering and for the antihydrogen loss (either through the rearrangement reaction, resulting in formation of protonium and positronium according to H+&Hmacr;-->p&pmacr;+e(+)e(-), or via annihilation in flight) are calculated for the first time in a fully quantum mechanical approach. Implications for experiments intending to trap and cool antihydrogen are discussed.
Matter-antimatter interactions are investigated using hydrogen-antihydrogen collisions as an example. Cross sections for elastic scattering and for the antihydrogen loss (either through the rearrangement reaction, resulting in formation of protonium and positronium according to $\mathrm{H}+\overline{\mathrm{H}}\ensuremath{\rightarrow}p\overline{p}{+e}^{+}{e}^{\ensuremath{-}}$, or via annihilation in flight) are calculated for the first time in a fully quantum mechanical approach. Implications for experiments intending to trap and cool antihydrogen are discussed.
We investigate two methods to include the strong nuclear force in hydrogen–antihydrogen scattering calculations. First, we construct a model optical potential with parameters determined by the measured shift and width of the protonium ground state. Although this potential is a very crude model for the strong nuclear force, its parameters may be adjusted to reproduce both bound states and low-energy annihilation cross sections to within the experimental accuracy. It is then shown that this potential may be reduced to a short-distance boundary condition in terms of the proton–antiproton strong-interaction scattering length. Elastic and annihilation cross sections for ground-state hydrogen–antihydrogen scattering are calculated for s- and p-waves, and collision energies up to 1 atomic unit. The two methods are found to agree to within about 1%. The main source of discrepancy is that the scattering-length approach does not account for vacuum polarization, relativistic, and finite-size corrections. We verify that the range of the strong interaction potential does not affect the hydrogen–antihydrogen s-wave scattering properties, and that the strong interaction has negligible influence on p-wave scattering. PACS Nos.: 36.10.-k, 34.90.+q