Coulomb corrections to the bremsstrahlung and electron pair production cross section of high-energy muons on extended nuclei

The energy reconstruction of high-energy muons depends on the energy loss characteristics. Accurate knowledge of the cross sections of the energy loss processes is necessary for precise measurements of the energy spectrum of muons and muon-induced neutrinos. The cross sections of the two most dominant processes, electron pair production and bremsstrahlung are calculated exact in the coupling parameter $Z\alpha$ to the electromagnetic field of a nucleus for realistic extended screened nuclei. An analytical parametrization of the mass and nuclear-charge dependence of the cross section is given.