Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Antihydrogen-formation cross sections in antiproton-positronium collisions with a time-dependent coupled-channel method

Nobuhiro Yamanaka, Yasushi Kino

Published Jun 6, 2002• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.65.062709

Related papers

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

Akinori Igarashi, Naoki Toshima, Takeshi Shirai

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.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 14, 1994•27 citations

Calculation of antihydrogen formation via antiproton scattering with excited positronium

C. M. Rawlins, Alisher S. Kadyrov, A. T. Stelbovics +2 more

The two-center convergent close-coupling method is used to calculate antihydrogen $(\overline{\mathrm{H}})$ formation via positronium (Ps) scattering on antiprotons $(\overline{p})$ at near threshold energies. For excited Ps of energy $\ensuremath{\varepsilon}$, the $1/\ensuremath{\varepsilon}$ behavior of the $\overline{\mathrm{H}}$ 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 $\overline{p}$-Ps collisions to form antihydrogen in beams, and held in traps, are discussed.

Physical Review A•Jan 19, 2016•46 citations

Antihydrogen formation in antiproton collisions with positronium: the adiabatic approach

J S Briggs, Е. А. Соловьев

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.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 23, 2001•10 citations

Formation of antihydrogen in three-body antiproton-positron collisions

Sumalay Roy, S. Ghosh Deb, Chittaranjan Sinha

A quantum-mechanical approach is proposed for the formation of antihydrogen $(\overline{H})$ in the ground and excited states $(2s,2p)$ via the mechanism of three-body recombination (TBR) inside a trapped plasma of antiprotons $(\overline{p})$ and positrons $({e}^{+})$ 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 ${e}^{+}$'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 $(\overline{H})$ 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 ${e}^{+}$'s than for equal energies, as expected physically.

arXiv:0803.3673•Physical Review A•Aug 8, 2008•5 citations

Stability of hydrogen-antihydrogen mixtures at low energies

S. Jonsell, Alejandro Sáenz, Piotr Froelich +2 more

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.

Physical Review A•Oct 12, 2001•78 citations

Quantum suppression of antihydrogen formation in positronium-antiproton scattering

Alisher S. Kadyrov, Igor Bray, M. Charlton +1 more

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.

Nature Communications•Nov 10, 2017•30 citations
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 \ensuremathπa02=0.880\ifmmode×\else\texttimes\fi10\ensuremath−16cm2\ensuremath{\pi}{a}_{0}^{2}=0.880\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16} {\mathrm{cm}}^{2}\ensuremathπa02​=0.880\ifmmode×\else\texttimes\fi10\ensuremath−16cm2 at an antiproton energy of 9.2 eV in the center-of-mass frame.
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.
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.
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.
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.
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.