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Physical Review A

Ultraslow p¯ -H collisions in hyperspherical coordinates: Hydrogen and protonium channels

Brett D. Esry, H. R. Sadeghpour

Published Jan 14, 2003• 31 citations
Publisher

Abstract

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 $p\overline{p}$ 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 $\overline{p}$-H system are calculated. The existence of protonium negative (or positive) ion in its ground and excited states is discussed.

DOI
10.1103/physreva.67.012704

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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 p‾\ensuremath−H(1s)\overline{p}\ensuremath{-}\mathrm{H}(1s)p​\ensuremath−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 Pn(nl)\ensuremath−e\ensuremath−\mathrm{Pn}{(\mathrm{nl})\ensuremath{-}e}^{\ensuremath{-}}Pn(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.
The main properties of the interaction of ultralow-energy antiprotons $(E<~{10}^{\ensuremath{-}6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and protonium (Pn) formation spectrum. The inverse Auger process $(\mathrm{Pn}+\stackrel{\ensuremath{\rightarrow}}{e}\mathrm{H}+\overline{p})$ is taken into account in the framework of a unitary coupled-channel model. The annihilation cross section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of p‾H\overline{p}\mathrm{H}p​H near-threshold metastable states is predicted. The dependence of protonium formation probability on the position of such near-threshold SSS-matrix singularities is analyzed. An estimation for the $\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}$ annihilation cross section is obtained.
Antihydrogen formation cross sections are calculated for low-energy collisions of antiproton with positronium by the hyperspherical coupled-channel method. The scattering wavefunctions are expanded in terms of a large number of sector-adiabatic states associated with the n=1-4 states of antihydrogen and n=1-3 states of positronium in the asymptotic separated-atom region. The present formation cross sections differ considerably from those of the unitarized Born approximation reported by Mitroy and Stelbovics (1994). The disagreement becomes larger with decreasing collision energy owing to the different energy dependence of the cross sections. The authors have confirmed that the formation cross sections from the 2s and 2p states are larger than that from the ground state by one order of magnitude.
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 stability of antimatter in contact with matter has been investigated. The interaction between hydrogen and antihydrogen is considered as the prototype reaction. We have focused interest on the rates for proton-antiproton and/or electron-positron annihilation during hydrogen-antihydrogen collisions at low energies. In particular, we have concentrated on the calculation of the rates for the rearrangement reaction leading to formation of protonium and positronium, ending inevitably in particle-antiparticle annihilation. The cross section for the rearrangement collision has been calculated in a fully quantum-mechanical treatment. Additionally, we have calculated cross sections for direct annihilation during the collision process, which was found to be comparable to the rearrangement cross section. The elastic cross section and its low-energy limit, given by the scattering length, have been calculated, allowing, by comparison to the inelastic processes, a prediction for the efficiency of cooling antihydrogen via collisions with ultracold hydrogen atoms.
We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single XXXH molecular state when XXX is one of the bosonic alkali atoms: 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 87Rb^{87}\mathrm{Rb}87Rb, or 133Cs^{133}\mathrm{Cs}133Cs. As a result, the only recombination process is the one that leads to formation of XXXH molecules, $\text{H}+\text{H}+X\ensuremath{\rightarrow}X\text{H}+\text{H}$, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision-induced dissociation as well as the elastic cross sections for H+XH\text{H}+X\text{H}H+XH collisions up to a temperature of 0.5 K, including the partial wave contributions from ${J}^{\ensuremath{\Pi}}={0}^{+}$ to ${5}^{\ensuremath{-}}$. We have also found that there is just one three-body bound state for such systems for ${J}^{\ensuremath{\Pi}}={0}^{+}$ and no bound states for higher angular momenta.
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.