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Physical Review A

Collisions of antiprotons with excited positronium atoms

M. Charlton, Harindranath B. Ambalampitiya, I. I. Fabrikant, Dmitry V. Fursa, Alisher S. Kadyrov, Igor Bray

Published Dec 6, 2021• 9 citations
Publisher

Abstract

A detailed theoretical investigation of the fundamental three-body antiproton-positronium system is presented, utilizing both quantum convergent close coupling and classical trajectory methods. We evaluate scattering cross sections for all major processes, including charge transfer and breakup, over a wide range of positronium kinetic energies and states with principal quantum number ${n}_{\mathrm{Ps}}\ensuremath{\le}6$. The study has significantly extended previous work, and the direct quantum-classical comparison has revealed a systematic approach to obtaining cross sections for arbitrarily high ${n}_{\mathrm{Ps}}$. This is of major significance for prospective applications of collisions of excited positronium atoms in cold (anti-)atomic physics.

DOI
10.1103/physreva.104.l060803

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A detailed theoretical investigation of the fundamental three-body antiproton-positronium system is presented, utilizing both quantum convergent close coupling and classical trajectory methods. We evaluate scattering cross sections for all major processes, including charge transfer and breakup, over a wide range of positronium kinetic energies and states with principal quantum number nPs\ensuremath≤6{n}_{\mathrm{Ps}}\ensuremath{\le}6nPs​\ensuremath≤6. The study has significantly extended previous work, and the direct quantum-classical comparison has revealed a systematic approach to obtaining cross sections for arbitrarily high nPs{n}_{\mathrm{Ps}}nPs​. This is of major significance for prospective applications of collisions of excited positronium atoms in cold (anti-)atomic physics.
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.
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.
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 (H‾)(\overline{\mathrm{H}})(H) via antiproton (p‾)(\overline{p})(p​) scattering on positronium. This system is studied in the energy range between the ${e}^{\ensuremath{-}}+\overline{\mathrm{H}}(n=2)$ 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 p‾+Ps(n=2)\overline{p}+\mathrm{Ps}(n=2)p​+Ps(n=2) threshold.
Predicted 20 years ago, positron binding to neutral atoms has not yet been observed experimentally. A scheme is proposed to detect positron-atom bound states by colliding Rydberg positronium (Ps) with neutral atoms. Estimates of the charge-transfer reaction cross section are obtained using the first Born approximation for a selection of neutral atom targets and a wide range of incident Ps energies and principal quantum numbers. We also estimate the corresponding Ps ionization cross section. The accuracy of the calculations is tested by comparison with earlier predictions for charge transfer in Ps collisions with hydrogen and antihydrogen. We describe an existing Rydberg Ps beam suitable for producing positron-atom bound states and estimate signal rates based on the calculated cross sections and realistic experimental parameters. We conclude that the proposed methodology is capable of producing such states and of testing theoretical predictions of their binding energies.
Abstract We compare classical and quantum predictions of the cross section for anti-hydrogen formation by charge exchange between Rydberg positronium and antiprotons as a function of the positronium energy. We show that these two highly different approaches furnish the same scaling law with the principal quantum number of positronium n Ps and numerical values in agreement within some tens of percent for n Ps ≥ 3 and down to very low collision energy of tens of μ eV. We discuss these results in the context of a recently claimed hypothesis of quantum suppression of the reaction driven by supposedly different scaling law of classical and quantum predictions. Finally we underline how the basic agreement between classical and quantum results enforces the reliability of the classical calculations that, presently, are the only ones able to obtain the cross section for positronium initially in high Rydberg states and in the presence of external electric and magnetic fields.
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.