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Journal of Physics Conference Series

A new time-dependent scattering theory and its application to the capture of antiprotons by atoms

Xiao‐Min Tong, K. Hino, Naoki Toshima

Published Sep 1, 2009• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/185/1/012047

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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.
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 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.
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.
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.
A semiclassical, many-body atomic model incorporating a momentum-dependent Heisenberg core to stabilize atomic electrons is used to study antiproton capture on helium. Details of the antiproton collisions leading to eventual capture are presented, including the energy and angular-momentum states of incident antiprotons which result in capture via single- or double-electron ionization, i.e., into He2+{\mathrm{He}}^{2+}He2+p\ifmmode\bar\else\textasciimacron\fi{} or He+{\mathrm{He}}^{+}He+p\ifmmode\bar\else\textasciimacron\fi{}, and the distribution of energy and angular-momentum states following the Auger cascade. These final states are discussed in light of recently reported anomalously long-lived antiproton states observed in liquid He [Iwasaki et al., Phys. Rev. Lett. 67, 1246 (1991)].