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Physical Review A

Leptonic annihilation in hydrogen-antihydrogen collisions

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

Published Aug 20, 2004• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.70.022509

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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×\else\texttimes\fi10\ensuremath−4a.u.1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}1.4\ifmmode×\else\texttimes\fi10\ensuremath−4a.u. for the singlet state of the leptonic spins, and 1.2\ifmmode×\else\texttimes\fi10\ensuremath−7a.u.1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}1.2\ifmmode×\else\texttimes\fi10\ensuremath−7a.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.
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.
Calculations of leptonic and hadronic annihilation rates in the hydrogen-antihydrogen molecule are presented. Both the leptonic potential and leptonic wave function are evaluated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potential are also obtained. Explicitly correlated Gaussians are employed as basis functions, which describe accurately the hydrogen-antihydrogen interaction. Given the leptonic potential the hadronic part of the wave function for each molecular level of the hydrogen-antihydrogen quasimolecule is calculated by solving the corresponding Schr\"odinger equation by means of precise BBB-spline representations. The decay rates of the quasimolecule into separate positronium and protonium systems are estimated for a number of molecular levels. Utilizing the leptonic and hadronic wave functions the leptonic- and hadronic-annihilation rates for different molecular levels are computed.
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.
Ever since antiparticles were discovered their nature has been something of a mystery. They were postulated to be identical to regular particles except for having opposite charge, but this would imply that an equal amount of antiparticles and particles should have been created at the beginning of time. However, everywhere we look the Universe seems to be constituted of regular particles, giving rise to the question whether there is something else that differentiates antiparticles from regular particles, or if there is something amiss in the Standard Model of particle physics. This thesis focuses on a central system of study in this field, the hydrogen-antihydrogen system and the theory surrounding it, as well as an expansion into systems with an antiproton interacting with small molecules, bridging the fields of quantum physics and quantum chemistry. Methods expanding on the Born-Oppenheimer approximation for the interaction between the two atoms are presented. The resulting 2-body interaction potential is then used for creating a part of the basis in a non-adiabatic 4-body method in order to look for resonance states whose existence could impact cross-sections of hydrogen-antihydrogen scattering. The eigenfunctions obtained from the non-adiabatic method are used by extracting the 2-body hadronic density function and comparing it to the adiabatic wave function, for measuring the adiabaticity of the hydrogen-antihydrogen system. The antiproton-matter interaction is first investigated by a quantum dynamical approach of an antiproton scattering on molecular hydrogen, common products in high-energy collision experiments, continued by a study of the potential energy surfaces of an antiproton interacting with a range of functional groups present in the human body.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.