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Journal of Physics B Atomic Molecular and Optical Physics

Hyperspherical coupled-channel calculation for antihydrogen formation in antiproton-positronium collisions

Akinori Igarashi, Naoki Toshima, Takeshi Shirai

Published Aug 14, 1994• 27 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/27/15/010

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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.
Antihydrogen-formation cross sections in antiproton-positronium collisions are calculated by using a time-dependent coupled-channel (TDCC) method. Nonuniform grid points are taken in the two-dimensional radial space to obtain accurate wave functions. High numerical accuracy of the TDCC method is demonstrated in a calculation of positronium-formation cross sections in positron-hydrogen collisions. The result is somewhat discrepant with previous results; in the present calculation, the cross section has a maximum of 16.19 in units of $\ensuremath{\pi}{a}_{0}^{2}=0.880\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16} {\mathrm{cm}}^{2}$ at an antiproton energy of 9.2 eV in the center-of-mass frame.
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 cross section for antihydrogen formation in collision of an antiproton with ground-state positronium has been calculated using the adiabatic hidden-crossing method. At collision velocities below the cross section maximum (3 keV) it is shown that the adiabatic approach provides a very simple description of the positron transfer process, in that capture occurs by a two-state mechanism involving coupling between the 1sσ and 2pσ potential curves only. Good numerical agreement with previous estimates is obtained. 1.
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.
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.
The differential cross sections for antihydrogen formation, in ground and excited states, from energetic antiproton–positronium collisions are computed analytically, using the Faddeev formalism in a second-order approximation. At the considered range of the impact energy, the second-order terms corresponding to the classical Thomas double-scattering processes are dominant. It is also shown that there exists a dynamical interference between two of the second-order partial amplitudes. Both amplitudes correspond to classical double-collision mechanisms in which the laboratory critical angle is 0.54 mrad. The interference between these amplitudes is approximately destructive for the capture into s-states with even parity.