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Physical Review A

Metastable states of antiprotonic helium in the energy range of the 2S and 2P states of helium: Hyperspherical analysis of the system

Oleg I. Tolstikhin, Shinichi Watanabe, Michio Matsuzawa

Published Nov 1, 1996• 18 citations
Publisher

Abstract

Metastable states of antiprotonic helium $\overline{p}{\mathrm{He}}^{+}$ whose energies lie in the range of the $2S$ and $2P$ excited states of He are discussed and their energies are calculated using the hyperspherical method within the "symmetric top" approximation. These states can be populated via collisions of antiprotons with excited He atoms. They represent another group of the potentially observable metastable states of $\overline{p}{\mathrm{He}}^{+}$, which are characterized by the total angular momentum $L\ensuremath{\sim}70$, in contrast to the recently discovered metastable states having $L\ensuremath{\sim}35$.

DOI
10.1103/physreva.54.r3705

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Metastable states of antiprotonic helium p‾He+\overline{p}{\mathrm{He}}^{+}p​He+ whose energies lie in the range of the 2S2S2S and 2P2P2P excited states of He are discussed and their energies are calculated using the hyperspherical method within the "symmetric top" approximation. These states can be populated via collisions of antiprotons with excited He atoms. They represent another group of the potentially observable metastable states of p‾He+\overline{p}{\mathrm{He}}^{+}p​He+, which are characterized by the total angular momentum L\ensuremath∼70L\ensuremath{\sim}70L\ensuremath∼70, in contrast to the recently discovered metastable states having L\ensuremath∼35L\ensuremath{\sim}35L\ensuremath∼35.
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 recent paper by T. Yamazaki and K. Ohtsuki [Phys. Rev. A 45, 7782 (1992)] discusses properties of antiprotonic helium (He2+{\mathrm{He}}^{2+}He2+p\ifmmode\bar\else\textasciimacron\fi{}${\mathit{e}}^{\mathrm{\ensuremath{-}}}$) formed in collisions of antiprotons (p\ifmmode\bar\else\textasciimacron\fi{}) with helium. Here we point out problems with approximations and assumptions used in deriving the results of that paper.
The cross sections and rates for quenching of thermalized antiprotonic helium atoms in binary collisions with ordinary helium atoms are calculated in perturbation theory and in the coupled-channel formalism at the temperature and the number density of the helium gas, T=6KT=6\phantom{\rule{0.3em}{0ex}}\mathrm{K}T=6K and $N={10}^{21}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}3}$, respectively. It is shown that quenching is unlikely to be relevant for the metastable states of the antiprotonic helium atom with $32\ensuremath{\leqslant}n\ensuremath{\leqslant}40$. Comparison with experiment shows a good quantitative agreement for the (n,l)=(39,35)(n,l)=(39,35)(n,l)=(39,35) state of antiprotonic helium and a large disagreement for the (37,34)(37,34)(37,34) state. As a byproduct of this work, the existence of a series of bound states of the He−−p‾4He+\mathrm{He}--\overline{p}\phantom{\rule{0.2em}{0ex}}^{4}\mathrm{He}^{+}He−−p​4He+ dimer is demonstrated numerically for $n\ensuremath{\geqslant}38$.
Potential energy curves for excited leptonic states of the helium-antihydrogen system are calculated within the Ritz variational approach. An explicitly correlated ansatz for the leptonic wave function is employed describing accurately the motion of the leptons (two electrons and positron) in the field of the helium nucleus and of the antiproton with an arbitrary orbital angular momentum projection Lambda onto the internuclear axis. Results for Lambda=0, 1, and 30 are presented. For quasibound states with large values of Lambda and rotational quantum numbers J>Lambda no annihilation and rearrangement decay channels occur; i.e., they are metastable.
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.
Initial distributions of metastable antiprotonic 4He^{\mathrm{4}}\mathrm{H}\mathrm{e}4He and 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms over principal (nnn) and angular momentum ($\ensuremath{\ell}$) quantum numbers have been deduced using laser spectroscopy experiments. The regions n=37−−40n=37--40n=37−−40 and n=35−−38n=35--38n=35−−38 in the two atoms account for almost all of the observed fractions [$(3.0\ifmmode\pm\else\textpm\fi{}0.1)%$ and $(2.4\ifmmode\pm\else\textpm\fi{}0.1)%$] of antiprotons captured into metastable states.