Corrections to the Born-Oppenheimer approximation as applied to a system made up of hydrogen and antihydrogen

Interest in antihydrogen (AH) is increasing as it seems likely that it will soon be possible to observe lit in its rest frame. The simplest atom with which antihydrogen atoms can interact is atomic hydrogen. We recently obtai ned an upper bound of 0.8 a(0) for the critical value of the distance betwe en the proton and the antiproton below which the electron and positron ceas e to be bound to the nuclei. In this calculation, the nuclei were assumed t o be fixed. In this article, we examine the effect on the energy of the ele ctron and the positron of taking into account the motion of the nuclei. The corrections are found to be small. (C) 1999 John Wiley & Sons, Inc.