Low Temperature Hydrogen Antihydrogen Interactions

Abstract

In view of current interest in the trapping of antihydrogen ($\bar {\mathcal{H}}$) atoms at low temperatures [1–3], we have carried out a full four-body variational calculation to determine s-wave elastic phase shifts for hydrogen antihydrogen scattering, using the Kohn Variational Principle. Terms outside the Born–Oppenheimer approximation have been taken into account using the formalism of Kołos and Wolniewicz [4]. As far as we are aware, this is the first time that these terms have been included in an H $\bar {\mathcal{H}}$ scattering calculation. This is a continuation of earlier work on H–$\bar {\mathcal{H}}$ interactions [5–7]. Preliminary results differ substantially from those calculated using the Born–Oppenheimer approximation [8–10]. A method is outlined for reducing this discrepancy and taking the rearrangement channel into account.