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arXiv:physics/9805033 · Physical Review A

Antiproton-hydrogen annihilation at subkelvin temperatures

Alexei Yu. Voronin, Jaume Carbonell

Published Jun 1, 1998• 26 citations
arXivHTMLPDF

Abstract

The main properties of the interaction of ultralow-energy antiprotons $(E<~{10}^{\ensuremath{-}6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and protonium (Pn) formation spectrum. The inverse Auger process $(\mathrm{Pn}+\stackrel{\ensuremath{\rightarrow}}{e}\mathrm{H}+\overline{p})$ is taken into account in the framework of a unitary coupled-channel model. The annihilation cross section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of $\overline{p}\mathrm{H}$ near-threshold metastable states is predicted. The dependence of protonium formation probability on the position of such near-threshold $S$-matrix singularities is analyzed. An estimation for the $\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}$ annihilation cross section is obtained.

DOI
10.1103/physreva.57.4335

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The main properties of the interaction of ultralow-energy antiprotons (E< 10\ensuremath−6(E<~{10}^{\ensuremath{-}6}(E< 10\ensuremath−6 a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and protonium (Pn) formation spectrum. The inverse Auger process (Pn+e\ensuremath→H+p‾)(\mathrm{Pn}+\stackrel{\ensuremath{\rightarrow}}{e}\mathrm{H}+\overline{p})(Pn+e\ensuremath→H+p​) is taken into account in the framework of a unitary coupled-channel model. The annihilation cross section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of p‾H\overline{p}\mathrm{H}p​H near-threshold metastable states is predicted. The dependence of protonium formation probability on the position of such near-threshold SSS-matrix singularities is analyzed. An estimation for the HH\ifmmode\elseˉ\textasciimacron\fi\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}HH\ifmmode\elseˉ​\textasciimacron\fi annihilation cross section is obtained.
The collision of an antiproton and a hydrogen atom at ultralow energies is described in hyperspherical coordinates. An adiabatic approximation leads to potential-energy curves that can be used to describe the dynamics of capture in the $\overline{p}\ensuremath{-}\mathrm{H}(1s)$ collision. A unified formulation of the collision and capture processes leading to formation of pp‾p\overline{p}pp​ bound states emerges. Both $\mathrm{Pn}{(\mathrm{nl})\ensuremath{-}e}^{\ensuremath{-}}$ ``atomic-type'' and $\overline{p}\ensuremath{-}\mathrm{H}{(n}^{\ensuremath{'}}{l}^{\ensuremath{'}})$ ``molecular-type'' states are represented. These potential curves are calculated to more than 10 000 protonium Bohr radii, where low-energy antiprotons are stopped in collisions with hydrogen atoms. Elastic and inelastic partial and total protonium formation cross sections in the mass-scaled p‾\overline{p}p​-H system are calculated. The existence of protonium negative (or positive) ion in its ground and excited states is discussed.
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.
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)].
Stark transitions and induced annihilation of antiproton in the collisions of antiprotonic helium ions (\bar{p}He^{+2})_{nl} with He atoms at very low energy (~ 10 K) are considered in the framework of quantum coupled-channels method taking into account all the states with different l at given n~30, including the annihilating ns and np-states. Elastic scattering, Stark transitions and induced annihilation during collisions are produced by scalar and dipole terms in the interaction. It is shown that the most important contribution to the processes comes from the long-range polarization interaction. Admixtures of the ns and np-states to the states with higher l during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for the initial states nearly to circular orbits. Total rates of the Stark transitions from the circular orbits with n=28 - 32, averaged over the thermal motion, are compatible with the recent ASACUSA data. Isotope effect as well as the dependence on n are also qualitatively agree with the experiment.
The stability of antiproton-hydrogen compound states (p‾H)(\overline{p}\mathrm{H})(p​H) is investigated theoretically. The p‾H\overline{p}\mathrm{H}p​H compound state has decay channels of atomic electron detachment $(\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+\overline{p}p)$ and hadronic pair $(\overline{p}\text{\ensuremath{-}}p)$ annihilation, and hence it cannot be permanently stable even if the dissociation channel $(\ensuremath{\rightarrow}\overline{p}+\mathrm{H})$ is energetically closed. In this paper, information on the metastable p‾H\overline{p}\mathrm{H}p​H states at energies below the dissociation limit is obtained by analyzing low-energy resonances in ${e}^{\ensuremath{-}}+\overline{p}p$ scattering. The scattering calculation is carried out by using an R-matrix method, which also allows for the annihilation channel simultaneously. The metastable states are found to be identified as vibrational levels supported by a Born-Oppenheimer (BO) potential. The energy-level widths attributed to the electron detachment and the annihilation are also calculated using a model based on the BO picture.
Matter-antimatter interactions are investigated using hydrogen-antihydrogen collisions as an example. Cross sections for elastic scattering and for the antihydrogen loss (either through the rearrangement reaction, resulting in formation of protonium and positronium according to $\mathrm{H}+\overline{\mathrm{H}}\ensuremath{\rightarrow}p\overline{p}{+e}^{+}{e}^{\ensuremath{-}}$, or via annihilation in flight) are calculated for the first time in a fully quantum mechanical approach. Implications for experiments intending to trap and cool antihydrogen are discussed.