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начиная с результата Бете-Гайтлера:

The effect of improved high-energy muon cross-sections: https://arxiv.org/abs/1910.07050

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.

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