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Physical Review A

Near-threshold behavior of positronium-antihydrogen scattering cross sections

Takuma Yamashita, Yasushi Kino, Emiko Hiyama, S. Jonsell, Piotr Froelich

Published May 31, 2022• 7 citations
Publisher

Abstract

The authors numerically study the scattering of antihydrogen and positronium atoms, at collision energies just above the threshold for the rearrangement reaction resulting in antihydrogen positive ions. The formation of such ions is of interest for ongoing or planned experiments involving antimatter with antihydrogen at CERN.
DOI
10.1103/physreva.105.052812

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Formation of the Positronium Antihydride Molecules (HˉPs\bar{\textrm{H}}\textrm{Ps}HˉPs) in Low Energy, 5-Body Collisions of Antihydrogen Ion Hˉ+\bar{\textrm{H}}^+Hˉ+ with Positronium Atoms Ps
Abstract In this paper we present the first pilot calculation of the elastic and inelastic cross sections for the 5-body scattering of antihydrogen ions with positronium atoms. These cross sections have not been calculated before and are not known experimentally. In particular, we focus on the collisional rearrangement reactions Hˉ++Ps→HˉPs+e+\bar{{ \mathrm H}}^+ + \textrm{Ps} \rightarrow {\bar{\textrm{H}}}\textrm{Ps} +{\mathrm{e^+}}Hˉ++Ps→HˉPs+e+ H ¯ + + Ps → H ¯ Ps + e + which deplete the Hˉ+\bar{\textrm{H}}^+Hˉ+ H ¯ + ions and result in stable atomcules HˉPs\bar{\textrm{H}}\textrm{Ps}HˉPs H ¯ Ps . To better understand the mechanism of this rearrangement, we study the 3-dimensional, angle resolved positron densities of the 3- and 4-body fragments in the initial and final states of the rearrangement collision.
Abstract We present a 4-body calculation of scattering between an antihydrogen atom ( H ¯ ) and a positronium (Ps) aiming at the prediction of cross sections for the production of antihydrogen positive ions H ¯ + . The antihydrogen positive ions are expected to be a useful source of ultra-cold anti-atoms for the test of matter-antimatter gravity. We convert the Schrödinger equation to a set of coupled integro-differential equations that involve intermediate states which facilitate the internal region description of the scattering wavefunction. They are solved using a compact finite difference method. Our framework is extended to scattering between an excited Ps and H. Cross sections of the reactions, Ps (1s/2s/3s) H ¯ → e − + H ¯ + , in s-wave collisions, are calculated. It is found that the reactions originating from Ps (1s/2s) + H ¯ produce H ¯ + with a constant cross section within 0.05 eV above the threshold while the reaction cross section from Ps (3s) decreases as the collision energy increases in the same energy interval. Just above the threshold, the cross section of H ¯ + production from Ps (3s) + H ¯ in s-wave collision is 7.8 times larger than that from Ps (1s) + H ¯ in s-wave and 2.3 times larger than that from Ps (2s) + H ¯ in s-wave. The near-threshold de-excitation reaction from Ps (3s) + H ¯ occurs more rapidly than the H ¯ + production.
Synopsis We present the 4-body calculation of the antihydrogen-positronium scattering aiming at the prediction of cross sections for the production of antihydrogen positive ions. The latter are expected to be a useful source of ultra-cold atoms for the test of matter-antimatter gravity. We convert the Schrödinger equation to a set of coupled integro-differential equations that involve intermediate states and are solved using the compact finite difference method. We will present the investigation of the rearrangement reaction between the ground-state antihydrogen atom and the excited positronium.
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.