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Physical Review A

Low-energy capture of antiprotons by helium ions

Kazuhiro Sakimoto

Published Aug 4, 2006• 14 citations
Publisher

Abstract

Low-energy antiproton capture, $\overline{p}+{\mathrm{He}}^{+}\ensuremath{\rightarrow}\overline{p}{\mathrm{He}}^{2+}+e$, is investigated using a wave-packet-propagation full-quantum-mechanical method or a quantum-classical hybrid (i.e., semiclassical) approximation. If the adiabatic picture (i.e., Born-Oppenheinmer separation) is a good approximation, the antiproton capture, which is a typical nonadiabatic process, can rarely occur. It is found that the probability of the nonadiabatic transition is small (at most $\ensuremath{\sim}0.1$). However, even in the zero energy limit $(E\ensuremath{\rightarrow}0)$, the antiproton capture always occurs for the total angular momenta $J\ensuremath{\lesssim}40$. Correspondingly, the cross section for the antiproton capture diverges as $E\ensuremath{\rightarrow}0$. This happens due to the peculiarity that the Coulomb force range is longer than the centrifugal one. The importance of a Rydberg series of resonances in the capture process is emphasized. On the low-energy dynamical feature, some interesting similarities to the $e+\text{ion}$ system are also found.

DOI
10.1103/physreva.74.022709

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Low-energy antiproton capture, p‾+He+\ensuremath→p‾He2++e\overline{p}+{\mathrm{He}}^{+}\ensuremath{\rightarrow}\overline{p}{\mathrm{He}}^{2+}+ep​+He+\ensuremath→p​He2++e, is investigated using a wave-packet-propagation full-quantum-mechanical method or a quantum-classical hybrid (i.e., semiclassical) approximation. If the adiabatic picture (i.e., Born-Oppenheinmer separation) is a good approximation, the antiproton capture, which is a typical nonadiabatic process, can rarely occur. It is found that the probability of the nonadiabatic transition is small (at most \ensuremath∼0.1\ensuremath{\sim}0.1\ensuremath∼0.1). However, even in the zero energy limit (E\ensuremath→0)(E\ensuremath{\rightarrow}0)(E\ensuremath→0), the antiproton capture always occurs for the total angular momenta J\ensuremath≲40J\ensuremath{\lesssim}40J\ensuremath≲40. Correspondingly, the cross section for the antiproton capture diverges as E\ensuremath→0E\ensuremath{\rightarrow}0E\ensuremath→0. This happens due to the peculiarity that the Coulomb force range is longer than the centrifugal one. The importance of a Rydberg series of resonances in the capture process is emphasized. On the low-energy dynamical feature, some interesting similarities to the e+ione+\text{ion}e+ion system are also found.
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The capture of slow antiprotons (energies less than 1.0 au, i.e. roughly 27 eV) by the rare gas atoms helium, neon and argon is considered. Appropriate to this low velocity, the capture cross sections are calculated using the adiabatic `hidden-crossing' theory in which the collision complex is viewed as a transient diatomic molecule with the positively-charged atomic ion and antiproton as nuclei. In addition to the total capture cross section, estimates of the percentage population of long-lived `circular' states is given. Our calculations suggest that a few per cent of captured antiprotons occupy these states in helium but in the case of argon or neon the probability of primary capture into such long-lived states is negligible. These results are at variance with previous calculations of antiproton capture cross sections.
Calculations of low-energy collisions of antiprotons p‾\overline{p}p​ with helium atoms in the ground (11S)(1\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})(11S) and metastable (23S(2\phantom{\rule{4pt}{0ex}}^{3}\mathit{S}(23S and 21S)2\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})21S) states are carried out by using a semiclassical method and by further assuming that one of the two electrons is passive. Antiproton capture to form antiprotonic helium $(\ensuremath{\rightarrow}\overline{p}{\mathrm{He}}^{+}+e)$ and breakup ionization $(\ensuremath{\rightarrow}\overline{p}+{\mathrm{He}}^{+}+e)$ are investigated. The energy dependence of the capture and ionization cross sections and the distributions of the product states are presented and compared with previous theoretical calculations. For the metastable helium targets, most of the p‾He+\overline{p}{\mathrm{He}}^{+}p​He+ atoms produced in the capture have long lifetimes against subsequent Auger decays and can be observed experimentally. For the ground-state targets, however, the formation of such long-lived states is rather a rare event at low collision energies.
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 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.