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Physical Review A

Channel-coupling array theory for Coulomb three-body dynamics: Antiproton capture by hydrogen atoms

Nobuhiro Yamanaka, Atsushi Ichimura

Published Jul 11, 2006• 6 citations
Publisher

Abstract

A theory of channel coupling array is developed for rearrangement reactions in Coulomb three-body systems. Inhomogeneous coupled differential equations for the three Faddeev components are derived and directly solved with the technique of complex rotation in the exterior region. This method is applied to slow antiproton collisions with hydrogen atoms. It is found for a collision energy of $6.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ that the antiproton is captured dominantly into protonium states with the principal quantum numbers around 40 and that the electron is released with energies around $2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The electron velocity thereby obtained is much higher than the incident velocity of the antiproton. Time-dependent wave-packet propagation of the Faddeev components is also investigated to illustrate the peculiar dynamics.

DOI
10.1103/physreva.74.012503

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A theory of channel coupling array is developed for rearrangement reactions in Coulomb three-body systems. Inhomogeneous coupled differential equations for the three Faddeev components are derived and directly solved with the technique of complex rotation in the exterior region. This method is applied to slow antiproton collisions with hydrogen atoms. It is found for a collision energy of 6.8eV6.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}6.8eV that the antiproton is captured dominantly into protonium states with the principal quantum numbers around 40 and that the electron is released with energies around 2eV2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}2eV. The electron velocity thereby obtained is much higher than the incident velocity of the antiproton. Time-dependent wave-packet propagation of the Faddeev components is also investigated to illustrate the peculiar dynamics.
We presented a theoretical method to study the capture of the antiprotrons by atoms solving a Chew-Goldberger-type integral equation directly. The scattering boundary conditions are automatically satisfied by adiabatically switching on the interaction between the antiprotons and targets. Hence the outgoing wave function is obtained without the tedious procedure of adjusting the total wave function in the asymptotic region. All the dynamical information can be derived from the scattering wave function obtained on pseudo-spectral grids numerically. Using this method, we obtained the state-specified capture cross sections when antiprotons collide with helium atoms. Differing from the capture processes of antiprotons by hydrogen atoms, the anomalous bumpy structures are revealed in the angular momentum dependent capture cross sections by helium atoms. Further analysis shows that the bumps arise from the partial channel closing due to the removal of the energy degeneracy in the antiprotonic helium atoms.
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.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
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.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
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.