Abstract
Corrections are made to a previous computation of the binding energies of some highly excited states of the απe and αKe atoms. The corrections take into account the effects of two approximations that were made in the original calculation. These approximations are (i) the use of the Born-Oppenheimer approximation in describing the radial motion of the meson with respect to the α particle and (ii) the use of a variational wave function to describe the motion of the electron. The corrections are found to be too small to have any significant effect on existing estimates of Auger rates for circular orbits. In each instance that is considered, the total correction to the energy difference between a circular and an almost circular orbit with the same principal quantum number is found to be only a few percent at most.