  It is shown that the corrections of $\alpha^2$ order to the total cross
sections for interaction of elementary hydrogen-like atoms with target atoms,
reported in the previously published paper [S.Mrowczynski, Phys.Rev. D36, 1520
(1987)], do not include some terms of the same order of magnitude. That results
in a significant contribution of these corrections in particular cases. The
full $\alpha^2$-corrections have been derived and it is shown that they are
really small and could be omitted for most practical applications.
