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Physical Review A

Moleculelike metastable states of antiprotonic and mesic helium

Isao Shimamura

Published Oct 1, 1992• 135 citations
Publisher

Abstract

The exotic helium atom, consisting of a helium nucleus ${\mathrm{He}}^{2+}$, 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 ${\mathrm{He}}^{2+}$ 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 ${\mathrm{He}}^{2+}$-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ 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 ${\mathrm{He}}^{2+}$. 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 $^{4}\mathrm{He}^{2+}$-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ and $^{3}\mathrm{He}^{2+}$-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and those for $^{4}\mathrm{He}^{2+}$-${\mathit{K}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ 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 (${\mathrm{He}}^{2+}$-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$)-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ exists for any ${\mathrm{He}}^{2+}$-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ 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.

DOI
10.1103/physreva.46.3776

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A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions (p‾H\overline{p}\mathrm{H}p​H), which in the separated atom limit correlate with p‾+H(n=2)\overline{p}+\mathrm{H}(n=2)p​+H(n=2) (nnn being the principal quantum number). The p‾H\overline{p}\mathrm{H}p​H molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\ensuremath{\rightarrow}\overline{p}p+e$). However, if the p‾H\overline{p}\mathrm{H}p​H molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the H\mathrm{H}H atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of p‾+H(n=2)\overline{p}+\mathrm{H}(n=2)p​+H(n=2) behaves as 1/R21/{R}^{2}1/R2 (RRR being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the p‾H\overline{p}\mathrm{H}p​H molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}$). The p‾H\overline{p}\mathrm{H}p​H system is dynamically similar to ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ molecules in high rotational states. This suggests that the p‾H\overline{p}\mathrm{H}p​H molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with p‾\overline{p}p​ beams.
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.
About 3% of antiprotons () stopped in helium are long-lived with microsecond lifetimes, against picoseconds in all other materials. This unusual longevity has been ascribed to the trapping of on metastable bound states in He+ helium atom-molecules thus named atomcules. Apart from their unique dual structure investigated by laser spectroscopy – a near-circular quasi-classical Rydberg atom with l ~ n – 1 ~ 37 or a special diatomic molecule with a negatively charged nucleus in high rotational state with J = l – the chemical physics aspects of their interaction with other atoms or molecules constitute an interesting topic for molecular physics. While atomcules may resist to million collisions in helium, molecular contaminants such as H2 are likely to destroy them in a single one, down to very low temperatures. In the Born-Oppenheimer framework, we interpret the molecular interaction obtained by ab initio quantum chemical calculations in terms of classical reactive channels, with activation barriers accounting for the experiments carried out in He and H2. From classical trajectory Monte Carlo simulations, we show that the thermalization stage strongly quenches initial populations, thus reduced to a recovered 3 % trapping fraction. This work illustrates the pertinence of chemical physics concepts to the study of exotic processes involving antimatter. New insights into the physico-chemistry of cold interstellar radicals are anticipated.
Exotic molecule tests fundamental symmetry Spectroscopy of exotic molecules can offer insight into fundamental physics. Hori et al. studied the transition frequencies of an unusual helium atom in which one of the two electrons was substituted by an antiproton, the negatively charged antiparticle partner of the proton (see the Perspective by Ubachs). The antiprotonic helium was cooled down to low temperatures to allow the frequencies to be measured with high precision. The extracted mass of the antiproton (relative to the electron mass) was in good agreement with previous measurements of the proton mass. This finding is in keeping with the implications of the combined charge, parity, and time-reversal symmetry of physical laws. Science , this issue p. 610 ; see also p. 546
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.
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