Coherent production of the long-lived pionium nP states in relativistic nucleus-nucleus collisions

The coherent production of the nP states of the ${\pi }^{+}{\pi }^{-}$ atoms ($A_{2\pi }$) in relativistic nucleus-nucleus collisions is considered as a possible source of the $A_{2\pi }(nP)$ beam for the pionium Lamb-shift measurement. A general expression for estimation of the $A_{2\pi }(nP)$ yield is derived in the framework of the equivalent photon approximation.