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

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