  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.
