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It is shown that the corrections of $\alpha^2$ order to the total crosssections 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 resultsin a significant contribution of these corrections in particular cases. Thefull $\alpha^2$-corrections have been derived and it is shown that they arereally small and could be omitted for most practical applications.Comment: 5 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Contribution of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>terms to the total interaction cross sections of relativistic elementary atoms with atoms of matter

Contribution ofα2terms to the total interaction cross sections of relativistic elementary atoms with atoms of matter