Production of $e^+e^-$ pairs to all orders in $Zα$ for collisions of high-energy muons with heavy nuclei

The $e^+e^-$ pair production in collisions of muon with atoms is considered to all orders in the parameter $Z\alpha$. We obtain energy distribution of $e^+$ and $e^-$ as well as energy loss of muon passing through matter with heavy atoms. The found corrections to the Born contribution do not depend on the details of the target properties except of a simple factor. For the considered example of Pb target the muon energy loss corrections vary from -65 % to -10 % depending on the pair energy.