A precise simulation of muons with energies above a TeV is crucial for
neutrino telescopes or cosmic ray experiments. To further increase the
precision of these simulations, improved cross-section calculations are
needed. At these energies, the interaction probability is dominated by
bremsstrahlung for large energy losses and electron-positron pair production
for small energy losses.

Improved analytical calculations for these processes were developed with more
precise screening functions of the target atom as well as higher order
corrections reducing the systematic uncertainties below the percent level.
The new calculations are already implemented in the new version of the lepton
propagator PROPOSAL, which was designed to be highly performant for the
propagation through large volumes of media using interpolation tables and to
do systematic studies with its multiple available cross-section calculations.
The new calculations of the differential cross section result in a maximum
deviation of 3 percent to the current standard. Their effects on the muon
simulation with the resulting flux and energy loss distribution are
presented.