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Physical Review A

Metastable compound states of an antiproton and a hydrogen atom

Kazuhiro Sakimoto

Published Sep 29, 2014• 4 citations
Publisher

Abstract

The stability of antiproton-hydrogen compound states $(\overline{p}\mathrm{H})$ is investigated theoretically. The $\overline{p}\mathrm{H}$ 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 $\overline{p}\mathrm{H}$ 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.

DOI
10.1103/physreva.90.032514

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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→e\ensuremath−+p‾p)(\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+\overline{p}p)(\ensuremath→e\ensuremath−+p​p) and hadronic pair (p‾\ensuremath-p)(\overline{p}\text{\ensuremath{-}}p)(p​\ensuremath-p) annihilation, and hence it cannot be permanently stable even if the dissociation channel (\ensuremath→p‾+H)(\ensuremath{\rightarrow}\overline{p}+\mathrm{H})(\ensuremath→p​+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−+p‾p{e}^{\ensuremath{-}}+\overline{p}pe\ensuremath−+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.
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Accurate three-body quantal calculations of the system composed of a proton, an antiproton, and an electron are performed in perimetric coordinates with the Lagrange-mesh method, an approximately variational calculation with the simplicity of a calculation on a grid. Quasibound states with respect to the p‾+H(n=2\overline{p} + \mathrm{H}(n=2p​+H(n=2) threshold are obtained for $L=60\ensuremath{-}73$ for various vibrational excitations. Their energies have accuracies up to about ${10}^{\ensuremath{-}14}$ atomic units, while less precise energies are determined for L=56−−59L=56--59L=56−−59 broader resonances. Their structure is analyzed with the help of mean distances between the particles. These mean distances indicate that the proton-electron subsystem is in excited states, mostly n=2n=2n=2, as predicted by Sakimoto [Phys. Rev. A 98, 042503 (2018)] with the Born-Oppenheimer approximation. A comparison performed with this approximation provides the accuracies of its energies and of its proton-antiproton mean distances.
The exotic helium atom, consisting of a helium nucleus He2+{\mathrm{He}}^{2+}He2+, an electron ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and a massive, negatively charged particle ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, such as an antiproton (p\ifmmode\bar\else\textasciimacron\fi{}) or a kaon (${\mathit{K}}^{\mathrm{\ensuremath{-}}}$), is studied theoretically. This exotic atom is more like a polar molecule with two nuclei He2+{\mathrm{He}}^{2+}He2+ and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, if ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ is in a low-lying orbital and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ is in a highly excited orbital. Such states are generally formed in the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ by helium. The Born-Oppenheimer (BO) separation of the ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ motion and the He2+{\mathrm{He}}^{2+}He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ motion is a good approximation for these states, and affords a transparent, unified perspective of exotic helium with different ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ and different isotopes of He2+{\mathrm{He}}^{2+}He2+. A propensity rule that favors small transition energies (except for the smallest one) is found for radiative emission by low vibrational and high rotational levels. This rule resembles the selection rule for infrared emission by the usual diatomic polar molecules, and contradicts the conventional expectation that radiative transitions in exotic atoms favor larger transition energies. The radiative lifetimes \ensuremath{\tau} of highly excited states formed immediately after the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ are of the order of \ensuremath{\mu}sec for 4He2+^{4}\mathrm{He}^{2+}4He2+-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ and 3He2+^{3}\mathrm{He}^{2+}3He2+-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and those for 4He2+^{4}\mathrm{He}^{2+}4He2+-${\mathit{K}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ are about half the values for the antiprotonic helium.The effect of the electronic charge polarization by ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ on \ensuremath{\tau} is explained quantitatively in a simple picture in terms of the molecular dipole moment. Low vibrational, high rotational states are described as circular or near-circular states in the atomic picture. They are stable against Auger decay, which the nonadiabatic perturbation on the BO states induces. An infinite series of bound \ensuremath{\Sigma} electronic states of exotic helium negative ions (He2+{\mathrm{He}}^{2+}He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$)-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ exists for any He2+{\mathrm{He}}^{2+}He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ distances R beyond 0.819 a.u. in the BO approximation. An infinite \ensuremath{\Pi} series exists for R>3.811 a.u., and an infinite \ensuremath{\Delta} series for R>9.532 a.u.
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 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 $\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}$ annihilation cross section is obtained.
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.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.