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Journal of Physics Conference Series

Towards prediction of the rates of antihydrogen positive ion production in collision of antihydrogen with excited positronium

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

Published Jan 1, 2020• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/1412/5/052012

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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.
Antihydrogen formation cross sections are calculated for low-energy collisions of antiproton with positronium by the hyperspherical coupled-channel method. The scattering wavefunctions are expanded in terms of a large number of sector-adiabatic states associated with the n=1-4 states of antihydrogen and n=1-3 states of positronium in the asymptotic separated-atom region. The present formation cross sections differ considerably from those of the unitarized Born approximation reported by Mitroy and Stelbovics (1994). The disagreement becomes larger with decreasing collision energy owing to the different energy dependence of the cross sections. The authors have confirmed that the formation cross sections from the 2s and 2p states are larger than that from the ground state by one order of magnitude.
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.
The two-center convergent close-coupling method is used to calculate antihydrogen (H‾)(\overline{\mathrm{H}})(H) formation via positronium (Ps) scattering on antiprotons (p‾)(\overline{p})(p​) at near threshold energies. For excited Ps of energy $\ensuremath{\varepsilon}$, the $1/\ensuremath{\varepsilon}$ behavior of the H‾\overline{\mathrm{H}}H formation cross sections is valid strictly only at the respective threshold, as is the $1/\sqrt{\ensuremath{\varepsilon}}$ behavior for Ps in the ground state. Simple equations are given for the $\overline{\mathrm{H}}(n\ensuremath{\le}4)$ formation cross sections from $\text{Ps}(n\ensuremath{\le}3)$ from zero to around 0.1 eV above threshold. Some of the implications of using p‾\overline{p}p​-Ps collisions to form antihydrogen in beams, and held in traps, are discussed.
Abstract The study of collision between metastable positronium (Ps) and antihydrogen ( H ¯ ) is crucial for precision experiments involving H ¯ . In this paper, we investigate the elastic scattering between H ¯ and Ps(2s) by combining the confined variational method with the projection method, for scattering energies from 0.0245 eV to 0.068 eV. Our calculations provide accurate phase shifts and cross sections for the 1,3 S and 1,3 P symmetries. Near the binding threshold, the rapid increase in the total cross section may be attributed to the P-wave resonance effect. Additionally, we determined the S-wave scattering lengths to be 9.34 a 0 and 5.81 a 0 for singlet and triplet elastic scattering, respectively.