Inaccuracies of high-energetic Bremsstrahlung and MuPairProduction losses

[Jean1995]

There is already a very similar issue specially for Electron bremsstrahlung losses when LPM is enabled (#123 ).

Bremsstrahlung losses

However, inaccuracies can also be seen for other particles (even when LPM is disabled).
The following shows the sampled stochastic losses, corresponding to a sampled random number (between 0 and 1), for Muons in ice at an energy of 1e10 MeV (LPM disabled):

This is probably again due to the node distribution in v which favors an accurate description of low-v:

with the ratio plot

Although the difference in the cumulative cross section is not higher than 1e-3, this appears to be enough to cause inaccuracies in the stochastic losses.

MuPairProduction losses

The same behavior can be seen for MuPairProduction. This plot shows MuPairProduction for 1e12 MeV muons in ice, with an energy cut of 500 MeV / 0.05:

The same plot for the whole kinematic range:

[Jean1995]

For bremsstrahlung, I already tried to slightly adjust the node distribution, in a similar fashion as it has been done for interpolation in PR #240, trying to shift the nodes a bit towards higher v.

While this solves the problem with high-v at high energies, this directly starts to introduce issues at low-v for low energies. I was unable to find any satisfactory "trade-off".