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Physical Review A

Long-lived states of antiprotonic lithium p¯ Li + produced in p¯+ Li collisions

Kazuhiro Sakimoto

Published Sep 2, 2011• 6 citations
Publisher

Abstract

Antiproton capture by lithium atoms ($\overline{p}+\mathrm{Li}\ensuremath{\rightarrow}\overline{p}{\mathrm{Li}}^{+}+e$) is investigated at collision energies from $0.01$ to 10 eV by using a semiclassical (also know as quantum-classical hybrid) method, in which the radial distance between the antiproton and the Li${}^{+}$ ion is treated as a classical variable, and the other degrees of freedom are described by quantum mechanics. Analyzing the wave packet of the emitted electrons and making use of the energy conservation rule enable us to calculate the state distribution of the produced antiprotonic lithium $\overline{p}{\mathrm{Li}}^{+}$ atoms and also to distinguish between the capture and ionization ($\ensuremath{\rightarrow}\overline{p}+{\mathrm{Li}}^{+}+e$) channels at collisional energies above the ionization threshold. This method is tested for the capture of negative muons by hydrogen atoms, which was rigorously investigated in previous quantum mechanical studies. Most of the $\overline{p}{\mathrm{Li}}^{+}$ atoms produced in $\overline{p}+\mathrm{Li}$ are found to be sufficiently stable against Auger decays and are experimentally observable as long-lived states. The present system bears close similarities to the system of $\overline{p}+\mathrm{He}(2S)$. It is therefore expected that long-lived antiprotonic helium $\overline{p}{\mathrm{He}}^{+}$ atoms can be efficiently produced in the $\overline{p}$ capture by metastable He($2\phantom{\rule{0.16em}{0ex}}{}^{3}S$) atoms.

DOI
10.1103/physreva.84.032501

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Antiproton capture by lithium atoms (p‾+Li\ensuremath→p‾Li++e\overline{p}+\mathrm{Li}\ensuremath{\rightarrow}\overline{p}{\mathrm{Li}}^{+}+ep​+Li\ensuremath→p​Li++e) is investigated at collision energies from 0.010.010.01 to 10 eV by using a semiclassical (also know as quantum-classical hybrid) method, in which the radial distance between the antiproton and the Li+{}^{+}+ ion is treated as a classical variable, and the other degrees of freedom are described by quantum mechanics. Analyzing the wave packet of the emitted electrons and making use of the energy conservation rule enable us to calculate the state distribution of the produced antiprotonic lithium p‾Li+\overline{p}{\mathrm{Li}}^{+}p​Li+ atoms and also to distinguish between the capture and ionization (\ensuremath→p‾+Li++e\ensuremath{\rightarrow}\overline{p}+{\mathrm{Li}}^{+}+e\ensuremath→p​+Li++e) channels at collisional energies above the ionization threshold. This method is tested for the capture of negative muons by hydrogen atoms, which was rigorously investigated in previous quantum mechanical studies. Most of the p‾Li+\overline{p}{\mathrm{Li}}^{+}p​Li+ atoms produced in p‾+Li\overline{p}+\mathrm{Li}p​+Li are found to be sufficiently stable against Auger decays and are experimentally observable as long-lived states. The present system bears close similarities to the system of p‾+He(2S)\overline{p}+\mathrm{He}(2S)p​+He(2S). It is therefore expected that long-lived antiprotonic helium p‾He+\overline{p}{\mathrm{He}}^{+}p​He+ atoms can be efficiently produced in the p‾\overline{p}p​ capture by metastable He(23S2\phantom{\rule{0.16em}{0ex}}{}^{3}S23S) atoms.
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.
A semiclassical, many-body atomic model incorporating a momentum-dependent Heisenberg core to stabilize atomic electrons is used to study antiproton capture on helium. Details of the antiproton collisions leading to eventual capture are presented, including the energy and angular-momentum states of incident antiprotons which result in capture via single- or double-electron ionization, i.e., into He2+{\mathrm{He}}^{2+}He2+p\ifmmode\bar\else\textasciimacron\fi{} or He+{\mathrm{He}}^{+}He+p\ifmmode\bar\else\textasciimacron\fi{}, and the distribution of energy and angular-momentum states following the Auger cascade. These final states are discussed in light of recently reported anomalously long-lived antiproton states observed in liquid He [Iwasaki et al., Phys. Rev. Lett. 67, 1246 (1991)].
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+ione+\text{ion}e+ion system are also found.
Cold, two-body antiprotonic helium ions p‾ 4He2+\overline{p}\text{ }^{4}\mathrm{H}\mathrm{e}^{2+}p​ 4He2+ and p‾ 3He2+\overline{p}\text{ }^{3}\mathrm{H}\mathrm{e}^{2+}p​ 3He2+ with 100-ns-scale lifetimes, occupying circular states with the quantum numbers ni=28−−32{n}_{i}=28--32ni​=28−−32 and ${\ensuremath{\ell}}_{i}={n}_{i}\ensuremath{-}1$ have been observed. They were produced by cooling three-body antiprotonic helium atoms in an ultra-low-density helium target at temperature $T\ensuremath{\sim}10\text{ }\text{ }\mathrm{K}$ by atomic collisions, and then removing their electrons by inducing a laser transition to an autoionizing state. The lifetimes of p‾ 3He2+\overline{p}\text{ }^{3}\mathrm{H}\mathrm{e}^{2+}p​ 3He2+ against annihilation induced by collisions were shorter than those of p‾ 4He2+\overline{p}\text{ }^{4}\mathrm{H}\mathrm{e}^{2+}p​ 4He2+, and decreased for larger-ni{n}_{i}ni​ states.
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.
Antiproton, the antiparticle of proton, is a unique projectile in the study of atomic collision physics, which can be treated theoretically either as a `negative proton' or a `heavy electron'. Atomic capture of an antiproton will result in formation of a highly excited exotic atom. Antiprotonic helium atom has been studied intensively by means of precision laser spectroscopy, which has led to a stringent determination of antiproton mass and charge to a level of ppb. Comparison of these values with those of proton gives one of the best tests of CPT invariance, the most fundamental symmetry in physics. However, the dynamic processes of antiproton capture remain unclarified, except for some indirect information given by those optical and X-ray observations. With an aim to produce an antiproton beam at atomic-physics energies for `pure' collision experiments, we have so far developed techniques to decelerate, cool and confine antiprotons in vacuo, using a sequential combination of the Antiproton Decelerator (AD) at CERN, a Radio-Frequency Quadrupole Decelerator (RFQD), and an electromagnetic trap. Our recent success in stable extraction of monoenergetic ultra-slow antiprotons, about 3×105 in number available every 5 minutes, has opened up the possibility to study ionization and atomic capture processes between an antiproton thus provided as a beam and an atom prepared in the form of a supersonic gas-jet target, at an unprecedented low energy from 10 eV to 1 keV under the single-collision condition. Our design and strategy of the cross-beam experiments are discussed.