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We calculate cross sections for helium-antihydrogen scattering for energies up to 0.01 atomic unit. Our calculation includes elastic scattering, direct antiproton-alpha particle annihilation and rearrangement into He +p and groundstate positronium. Elastic scattering is calculated within the Born-Oppenheimer approximation using the potential calculated by Strasburger et al (2005 J. Phys. B: At. Mol. Opt. Phys. 38 3091). Matrix elements for rearrangement are calculated using the T -matrix in the distorted wave approximation, with the initial state represented by Hylleraas-type functions. The strong force, leading to direct annihilation, was included as a short-range boundary condition in terms of the strong-force scattering length. Acknowledgment 15 References 15

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In this paper, a study is made of the interaction of atomic helium with an antiproton within the Born–Oppenheimer approximation. The electronic energy curve is calculated using the variational method with basis sets containing Hylleraas-type basis functions. The energies and nuclear wave functions for 50 s states are then obtained using this potential by solving the nuclear wave equation numerically using the Cooley–Numerov algorithm. It is possible that the state with the lowest energy is a bound state. The remaining states are all above the lowest continuum threshold for and are thus quasi-bound states.