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Journal of Physics B Atomic Molecular and Optical Physics

Calculation of cross sections for very low-energy hydrogen antihydrogen scattering using the Kohn variational method

Edward A. G. Armour, C. W. Chamberlain

Published Nov 5, 2002• 46 citations
Publisher

Abstract

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 .

DOI
10.1088/0953-4075/35/22/103

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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 .
We calculate cross sections for helium–antihydrogen scattering for energies up to 0.01 atomic unit. Our calculation includes elastic scattering, direct antiproton–alpha particle annihilation and rearrangement into and ground-state positronium. Elastic scattering is calculated within the Born–Oppenheimer approximation using the potential calculated by Strasburger et al (2005 J. Phys. B: At. Mol. Opt. Phys. 38 3091). Matrix elements for rearrangement are calculated using the T -matrix in the distorted wave approximation, with the initial state represented by Hylleraas-type functions. The strong force, leading to direct annihilation, was included as a short-range boundary condition in terms of the strong-force scattering length.
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.
In view of the recent interest in the trapping of antihydrogen atom $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{},$ at very low temperatures, $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}$ scattering has been investigated at low incident energies using a close-coupling model with the basis set $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}(1s,2s,2\overline{p})+\mathrm{H}(1s,2s,2\overline{p}).$ The predicted s-wave elastic phase shifts, scattering length, and effective range are in a good agreement with the other recent predictions of Jonsell et al. and of Armour and Chamberlain. The results indicate that the atomic orbital expansion model is suitable to study the $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}$ scattering at ultracold temperatures.
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.
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.