On the Coulomb corrections to the total cross section of the interaction   of the $\pi^+\pi^-$ atom with ordinary atoms at high energy
  The size of $\pi^+\pi^-$ atom in the low lying states is considerably smaller than the radius of atomic screening. Due to that we can neglect this screening calculating the contribution of multi-photon exchanges. We obtain the analytic formula for Coulomb corrections which works with a very good accuracy for the ground state of $\pi^+\pi^-$ atom. 
D.Yu. Ivanov and L. Szymanowski