Calculation of cross sections for very low-energy hydrogen–antihydrogen scattering using the Kohn variational method

In view of current interest in the trapping of antihydrogen () atoms at very low temperatures, we have carried out a calculation of s-wave hydrogen–antihydrogen scattering at very low energies, using the Kohn variational method, taking into account rearrangement scattering into the three channels that contain positronium in its ground state and lie closest to threshold. We find that our values for the elastic cross section are in good agreement with the values obtained by Jonsell et al (Jonsell et al 2001 Phys. Rev. A 64 052712) using a distorted wave approximation. However, our values for the total rearrangement cross section are much larger than their values. In particular, the largest such cross section is for the N = 23 s-state of protonium and positronium in its ground state, a channel that was estimated to make a negligible contribution by Jonsell et al. As a consequence of our much larger values for the total rearrangement cross section, we predict that cooling of by cold H would be considerably less efficient than was found to be the case by Jonsell et al.