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Advances in quantum chemistry

Positron–Electron Annihilation in Hydrogen–Antihydrogen Collisions

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

Published Jan 1, 2004• 0 citations
Publisher
DOI
10.1016/s0065-3276(04)47024-5

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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.
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.