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The size of $\pi^+\pi^-$ atom in the low lying states is considerably smallerthan the radius of atomic screening. Due to that we can neglect this screeningcalculating the contribution of multi-photon exchanges. We obtain the analyticformula for Coulomb corrections which works with a very good accuracy for theground state of $\pi^+\pi^-$ atom.Comment: 9 pages, LATEX with 1 Postscript figur

On the Coulomb corrections to the total cross section of the interaction of the π+π− atom with ordinary atoms at high energy