We investigate two methods to include the strong nuclear force in hydrogenantihydrogen scattering calculations. First, we construct a model optical potential with parameters determined by the measured shift and width of the protonium ground state. Although this potential is a very crude model for the strong nuclear force, its parameters may be adjusted to reproduce both bound states and low-energy annihilation cross sections to within the experimental accuracy. It is then shown that this potential may be reduced to a short-distance boundary condition in terms of the protonantiproton strong-interaction scattering length. Elastic and annihilation cross sections for ground-state hydrogenantihydrogen scattering are calculated for s- and p-waves, and collision energies up to 1 atomic unit. The two methods are found to agree to within about 1%. The main source of discrepancy is that the scattering-length approach does not account for vacuum polarization, relativistic, and finite-size corrections. We verify that the range of the strong interaction potential does not affect the hydrogenantihydrogen s-wave scattering properties, and that the strong interaction has negligible influence on p-wave scattering. PACS Nos.: 36.10.-k, 34.90.+q
Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory