  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.
