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Physical Review A

Stability of hydrogen-antihydrogen mixtures at low energies

S. Jonsell, Alejandro Sáenz, Piotr Froelich, Bernard Zygelman, A. Dalgarno

Published Oct 12, 2001• 78 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.64.052712

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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.
An overview of the antiatom interactions with matter is given in the context of the ongoing efforts to trap and cool antihydrogen at CERN. We show how the atom‐antiatom scattering can, in addition to annihilation, result in a number of collisional reactions such as elastic scattering, rearrangement to protonium and positronium, and even radiative association leading to formation of unusual short‐lived atom‐antiatom molecules. We also show that sufficiently cold antiatoms can be reflected from material walls. The rates for these reactions are of interest for the experiments with antihydrogen atoms at CERN, they probe the feasibility of collisional cooling of antihydrogen and they contribute to the understanding of stability of matter in contact with antimatter in general.
We consider the question of competition between leptonic and hadronic annihilation in matter-antimatter interaction. The rate of direct positron-electron annihilation in cold hydrogen-antihydrogen collisions has been calculated. The presence of leptonic annihilation introduces an absorptive, imaginary component to the hydrogen-antihydrogen scattering length; this component is $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ for the singlet state of the leptonic spins, and $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ for the triplet state. Leptonic annihilation is shown to be about 3 orders of magnitude slower than proton-antiproton annihilation.
In view of current interest in the trapping of antihydrogen ( ) atoms at very low temperatures, we have carried out a calculation of s-wave hydrogen–antihydrogen scattering at very low energies, using the Kohn variational method, taking into account rearrangement scattering into the three channels that contain positronium in its ground state and lie closest to threshold. We find that our values for the elastic cross section are in good agreement with the values obtained by Jonsell et al (Jonsell et al 2001 Phys. Rev. A 64 052712) using a distorted wave approximation. However, our values for the total rearrangement cross section are much larger than their values. In particular, the largest such cross section is for the N = 23 s-state of protonium and positronium in its ground state, a channel that was estimated to make a negligible contribution by Jonsell et al . As a consequence of our much larger values for the total rearrangement cross section, we predict that cooling of by cold H would be considerably less efficient than was found to be the case by Jonsell et al .