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Physical Review A

Ab initio calculations of scattering cross sections of the three-body system ( p¯,e+,e− ) between the e−+H¯(n=2) and e−+H¯(n=3) thresholds

Mateo Valdes, M. Dufour, Rimantas Lazauskas, Paul-Antoine Hervieux

Published Jan 31, 2018• 12 citations
Publisher

Abstract

The ab initio method based on the Faddeev-Merkuriev equations is used to calculate cross sections involving the $(\overline{p},{e}^{+},{e}^{\ensuremath{-}})$ three-body system, with an emphasis on antihydrogen formation $(\overline{\mathrm{H}})$ via antiproton $(\overline{p})$ scattering on positronium. This system is studied in the energy range between the ${e}^{\ensuremath{-}}+\overline{\mathrm{H}}(n=2)$ and the ${e}^{\ensuremath{-}}+\overline{\mathrm{H}}(n=3)$ thresholds, where precisely calculated cross sections can be useful for future experiments (GBAR, AEGIS, etc.) aiming to produce antihydrogen atoms. A special treatment is developed to take into account the long-range charge-dipole interaction effect on the wave function. Emphasis is placed on the impact of Feshbach resonances and Gailitis-Damburg oscillations appearing in the vicinity of the $\overline{p}+\mathrm{Ps}(n=2)$ threshold.

DOI
10.1103/physreva.97.012709

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Nature Communications•Nov 10, 2017•30 citations
The ab initio method based on the Faddeev-Merkuriev equations is used to calculate cross sections involving the (p‾,e+,e\ensuremath−)(\overline{p},{e}^{+},{e}^{\ensuremath{-}})(p​,e+,e\ensuremath−) three-body system, with an emphasis on antihydrogen formation (H‾)(\overline{\mathrm{H}})(H) via antiproton (p‾)(\overline{p})(p​) scattering on positronium. This system is studied in the energy range between the e\ensuremath−+H‾(n=2){e}^{\ensuremath{-}}+\overline{\mathrm{H}}(n=2)e\ensuremath−+H(n=2) and the e\ensuremath−+H‾(n=3){e}^{\ensuremath{-}}+\overline{\mathrm{H}}(n=3)e\ensuremath−+H(n=3) thresholds, where precisely calculated cross sections can be useful for future experiments (GBAR, AEGIS, etc.) aiming to produce antihydrogen atoms. A special treatment is developed to take into account the long-range charge-dipole interaction effect on the wave function. Emphasis is placed on the impact of Feshbach resonances and Gailitis-Damburg oscillations appearing in the vicinity of the p‾+Ps(n=2)\overline{p}+\mathrm{Ps}(n=2)p​+Ps(n=2) threshold.
Cette thèse est consacrée au calcul de sections efficaces de réactions impliquant le système à trois corps (e − , e + , p̄) à des énergies représentatives de l’expérience GBAR. Deux approches théoriques ont été utilisées. La première, appelée méthode des canaux couplés, permet de traiter le système dans un cadre théorique plus simple. La deuxième, basée sur le formalisme rigoureux des équations de Faddeev-Merkuriev, a permis le calcul explicite des sections efficaces. Une des difficultés majeures provient de la dégénérescence accidentelle du premier état excité des atomes d’antihydrogène et de positronium. Le traitement de cette dégénérescence a été réalisé dans un premier temps dans le formalisme de canaux couplés avant d’être adapté au code des équations de Faddeev-Merkuriev. Dans ce document, nous discutons les sections efficaces dans le contexte de l’expérience GBAR et interprétons les phénomènes résonnants mis en évidence, les résonances de Feshbach et les oscillations de Gailitis-Damburg.
Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy EEE scattering on antiprotons. In the case of Ps(1s\mathrm{Ps}(1sPs(1s) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as 1/E1/21/{E}^{1/2}1/E1/2. For Ps(2s\mathrm{Ps}(2sPs(2s), oscillations spanning orders of magnitude on top of the 1/E1/E1/E behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as 1/E1/E1/E at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailitis [J. Phys. B: At. Mol. Phys. 15, 3423 (1982)].
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 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.
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.