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Journal of Physics B Atomic Molecular and Optical Physics

The capture of slow antiprotons in noble gases

J S Briggs, P. Thornton Greenland, Е. А. Соловьев

Published Jan 1, 1999• 29 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/32/2/005

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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.
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.
Antiproton capture by lithium atoms ($\overline{p}+\mathrm{Li}\ensuremath{\rightarrow}\overline{p}{\mathrm{Li}}^{+}+e$) 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 ($\ensuremath{\rightarrow}\overline{p}+{\mathrm{Li}}^{+}+e$) 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 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.
We investigate the state-specified capture process of antiprotons by helium. Freezing one of the two electrons, we reduce this four-body rearrangement problem into a three-body problem. The capture cross sections are calculated by solving the Chew-Goldberger-type integral equation. Differing from the capture of antiprotons by hydrogen atoms, the bumpy structures are revealed in the total angular momentum dependent capture cross sections. Further analysis shows that the bumps arise from the partial channel closing due to the removal of the energy degeneracy in the antiprotonic helium.
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.