TITLE: The four-body system made up of hydrogen and antihydrogen at low energies AUTHORS: E.A.G. Armour, C. Chamberlain and V. Zeman AFFILIATION: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, U.K. SUMMARY: We describe calculations that we are carrying out for hydrogen and antihydrogen $\bar{H}$ interacting at low temperatures. Our calculations already go beyond the Born-Oppenheimer approximation. It is hoped to be able to present the results of a fully quantum mechanical treatment of H-$\bar{H}$ scattering at the conference.