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Physical Review A

Calculation of antihydrogen formation via antiproton scattering with excited positronium

C. M. Rawlins, Alisher S. Kadyrov, A. T. Stelbovics, Igor Bray, M. Charlton

Published Jan 19, 2016• 46 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.93.012709

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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 \ensuremathε\ensuremath{\varepsilon}\ensuremathε, the 1/\ensuremathε1/\ensuremath{\varepsilon}1/\ensuremathε behavior of the H‾\overline{\mathrm{H}}H formation cross sections is valid strictly only at the respective threshold, as is the 1/\ensuremathε1/\sqrt{\ensuremath{\varepsilon}}1/\ensuremathε​ behavior for Ps in the ground state. Simple equations are given for the H‾(n\ensuremath≤4)\overline{\mathrm{H}}(n\ensuremath{\le}4)H(n\ensuremath≤4) formation cross sections from Ps(n\ensuremath≤3)\text{Ps}(n\ensuremath{\le}3)Ps(n\ensuremath≤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.
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)].
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.
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.