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Nature Communications

Quantum suppression of antihydrogen formation in positronium-antiproton scattering

Alisher S. Kadyrov, Igor Bray, M. Charlton, I. I. Fabrikant

Published Nov 10, 2017• 30 citations
Publisher

Abstract

Abstract The interaction of antiprotons with low-energy positronium atoms is a fundamental three-body problem whose significance is its utility for formation of antihydrogen. Particular importance resides in understanding processes involving excited positronium states. Until recently such studies were performed using classical techniques. However, they become inapplicable in the low-energy domain. Here we report the results of comprehensive quantum calculations, which include initial excited positronium states with principal quantum numbers up to ni = 5. Contrary to expectation from earlier work, there are only muted increases in the cross-sections for antihydrogen formation for ni > 3. We interpret this in terms of quantum suppression of the reaction at higher angular momenta. Furthermore, the cross-sections for elastic scattering are around two orders of magnitude higher, which we attribute to the degeneracy of the positronium states. We outline some experimental consequences of our results.

DOI
10.1038/s41467-017-01721-y

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arXiv:0803.3673•Physical Review A•Aug 8, 2008•5 citations
Abstract The interaction of antiprotons with low-energy positronium atoms is a fundamental three-body problem whose significance is its utility for formation of antihydrogen. Particular importance resides in understanding processes involving excited positronium states. Until recently such studies were performed using classical techniques. However, they become inapplicable in the low-energy domain. Here we report the results of comprehensive quantum calculations, which include initial excited positronium states with principal quantum numbers up to ni = 5. Contrary to expectation from earlier work, there are only muted increases in the cross-sections for antihydrogen formation for ni > 3. We interpret this in terms of quantum suppression of the reaction at higher angular momenta. Furthermore, the cross-sections for elastic scattering are around two orders of magnitude higher, which we attribute to the degeneracy of the positronium states. We outline some experimental consequences of our results.
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.
We investigate the consequences of unexpectedly large elastic cross sections for the scattering of low-energy antiprotons from $n\ensuremath{\le}3$ positronium (Ps) on the experimental implementation of antihydrogen formation via Ps-antiproton collisions. The integrated elastic cross sections, obtained using the two-center convergent close-coupling theory, can be up to three orders of magnitude greater than their counterparts for antihydrogen formation. The differential momentum transfer cross sections, which suppress the large cross sections at forward scattering angles, show remarkably rich behavior across all scattering angles. We discuss the implications of these findings for the heating, via momentum transfer, of clouds of trapped antiprotons that are typically used for the creation of antihydrogen.
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.
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.
A quantum-mechanical approach is proposed for the formation of antihydrogen (H‾)(\overline{H})(H) in the ground and excited states (2s,2p)(2s,2p)(2s,2p) via the mechanism of three-body recombination (TBR) inside a trapped plasma of antiprotons (p‾)(\overline{p})(p​) and positrons (e+)({e}^{+})(e+) or in the collision between the two beams of them. Variations of the differential as well as the total formation cross sections are studied as a function of the incident energies of both the active and the spectator e+{e}^{+}e+'s. Significantly large cross sections are found at very low incident energies in the TBR process as compared to other processes leading to antihydrogen. The present (H‾)(\overline{H})(H) formation cross section decreases with increasing positron energy (temperature) but no simple power law could be predicted for it covering the entire energy range $(\ensuremath{\sim}5--50\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$, corroborating the experimental findings qualitatively, the latter being at a much lower energy regime $(\ensuremath{\sim}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$. The formation cross sections are found to be much higher for unequal energies of the two e+{e}^{+}e+'s than for equal energies, as expected physically.