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Physical Review A

Anomalies in the decay rates of antiprotonic helium-atom states

H. Yamaguchi, Takashi Ishikawa, Jun Sakaguchi, E. Widmann, J. A. Eades, R. Hayano, M. Hori, H. A. Torii, Bertalan Juhász, D. Horváth, Toshitsugu Yamazaki

Published Aug 15, 2002• 34 citations
Publisher

Abstract

Six resonance transitions of the antiprotonic helium atom in helium gas at densities of $3\ifmmode\times\else\texttimes\fi{}{10}^{20}--3\ifmmode\times\else\texttimes\fi{}{10}^{21} {\mathrm{cm}}^{\ensuremath{-}3}$ were studied at the antiproton decelerator (AD) of CERN. The decay rates of the daughter states of these transitions were determined either from the time distributions of the resonance spikes or from the widths of the resonance lines. Whereas most of the observed decay rates agree with theoretical calculations of Auger rates, two states, $(n,l)=(37,33)$ and (32,31), were found to have decay rates two orders of magnitude larger than predicted by these calculations. The effect of coupling with near-lying electron-excited states is considered to be the reason for the anomaly of the (37, 33) state, as pointed out by Kartavtsev et al. [Phys. Rev. A $61,$ 062507 (2000)].

DOI
10.1103/physreva.66.022504

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Physical Review A•Oct 1, 1992•135 citations
Six resonance transitions of the antiprotonic helium atom in helium gas at densities of 3\ifmmode×\else\texttimes\fi1020−−3\ifmmode×\else\texttimes\fi1021cm\ensuremath−33\ifmmode\times\else\texttimes\fi{}{10}^{20}--3\ifmmode\times\else\texttimes\fi{}{10}^{21} {\mathrm{cm}}^{\ensuremath{-}3}3\ifmmode×\else\texttimes\fi1020−−3\ifmmode×\else\texttimes\fi1021cm\ensuremath−3 were studied at the antiproton decelerator (AD) of CERN. The decay rates of the daughter states of these transitions were determined either from the time distributions of the resonance spikes or from the widths of the resonance lines. Whereas most of the observed decay rates agree with theoretical calculations of Auger rates, two states, (n,l)=(37,33)(n,l)=(37,33)(n,l)=(37,33) and (32,31), were found to have decay rates two orders of magnitude larger than predicted by these calculations. The effect of coupling with near-lying electron-excited states is considered to be the reason for the anomaly of the (37, 33) state, as pointed out by Kartavtsev et al. [Phys. Rev. A 61,61,61, 062507 (2000)].
A systematic study of the decay rates of antiprotonic helium (p‾4He+{\overline{p}}^{4}{\mathrm{He}}^{+}p​4He+ and p‾3He+{\overline{p}}^{3}{\mathrm{He}}^{+}p​3He+) at CERN Antiproton Decelerator has been made by a laser spectroscopic method. The decay rates of some of its short-lived states, namely those for which the Auger rates ${\ensuremath{\gamma}}_{A}$ are much larger than their radiative decay rates $({\ensuremath{\gamma}}_{\mathrm{rad}}\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{s}^{\ensuremath{-}1})$, were determined from the time distributions of the antiproton annihilation signals induced by laser beams, and the widths of the atomic resonance lines. The magnitude of the decay rates, especially their relation with the transition multipolarity, is discussed and compared with theoretical calculations.
The rates of Auger transitions of antiprotonic helium 4{}^{4}4He+p‾{}^{+}\overline{p}+p​ and 3{}^{3}3He+p‾{}^{+}\overline{p}+p​ are calculated by using a variational scattering method with an elaborate three-body trial function. The shift of the energy levels of these systems due to the coupling with the Auger-decay channels is also obtained from this calculation. Thus an improvement is made over the previously calculated nonrelativistic energies. Together with the relativistic corrections calculated elsewhere, the theoretical transition wavelength between the states (n,l)=(37,34)(n,l)=(37,34)(n,l)=(37,34) and (38,33)(38,33)(38,33) of 4{}^{4}4He+p‾{}^{+}\overline{p}+p​, for example, is significantly improved to be 713.593 nm, which compares well with the experimental value 713.578$\ifmmode\pm\else\textpm\fi{}0.006nm.ThecalculatedAugerlifetimeofthelevel(38,33)is3.2ps,ascomparedwiththevalue4.10.006 nm. The calculated Auger lifetime of the level (38,33) is 3.2 ps, as compared with the value 4.10.006nm.ThecalculatedAugerlifetimeofthelevel(38,33)is3.2ps,ascomparedwiththevalue4.1\ifmmode\pm\else\textpm\fi{}$0.2 ps deduced from the measured line broadening. Auger rates are calculated also using Fermi's golden-rule formula with a regular Coulomb function with no phase shift for the Auger electron. The results agree fairly well with the accurate variational results.
Laser studies of metastable antiprotonic helium atoms, which we recently initiated by observing a sharp increase of the antiproton annihilation rate induced by laser-stimulated resonant transitions, have been extended. With a single laser tuned to the resonance already found at 597.26 nm, we have now established the time dependence of the upper state population. With two lasers ignited at variable time separation, we also studied the feeding of the upper state from higher atomic levels. The initial populations and level lifetimes of excited exotic atoms were determined.
A laser spectroscopic method was developed to directly observe the lifetimes of individual states in metastable antiprotonic helium atoms (p‾4He+).(\overline{p}{}^{4}{\mathrm{He}}^{+}).(p​4He+). Collisional effects with surrounding helium atoms were studied in cryogenic gas targets at pressures between 0.1 and 9.0 bars and at temperatures between 5.5 and 7.0 K. The metastable state (n,l)=(39,35)(n,\mathcal{l})=(39,35)(n,l)=(39,35) showed a lifetime of 1.5 $\ensuremath{\mu}\mathrm{s}$, regardless of density, whereas the lifetime of the energetically lower-lying state (37,34)(37,34)(37,34) was found to shorten from 1.3 to 0.1 $\ensuremath{\mu}$s with increasing density. The lifetimes of the states (38,34)(38,34)(38,34) and (36,33)(36,33)(36,33) were determined to be 10 ns and 5 ns, respectively, showing the effects of the internal Auger process. When extrapolated to zero density, the measured lifetimes agreed with the results of calculations for the radiative and Auger widths. Using the fact that the state (37,34)(37,34)(37,34) becomes short lived at high density, the resonance $(38,35)\ensuremath{\rightarrow}(37,34)$ at 529.62 nm was detected.
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.