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

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 p̄ -H(1s) collision. A unified formulation of the collision and capture processes leading to formation of pp̄ bound states emerges. Both Pn(nl)-e ‘‘atomic-type’’ and p̄-H(n8l8) ‘‘moleculartype’’ 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 p̄-H system are calculated. The existence of protonium negative ~or positive! ion in its ground and excited states is discussed.