Total interaction cross sections of relativistic π+π--atoms with ordinary atoms in the eikonal approach

The total interaction cross sections of the relativistic pi(+)pi(-)-atoms with ordinary atoms are obtained in the eikonal approach which takes into consideration all multiphoton exchange processes. The contribution of these processes strongly depends on the atom nucleus charge Z and varies from 1.5% for titanium (Z = 22) to 14% for tantalum (Z = 73). The formulae derived are applicable for an arbitrary initial state of the pi(+)pi(-)-atom.