Is there a convenient parameterization for muon radiative losses in matter?

[stakhanov]

The muon energy loss equation (at high energies) is:

-dE/dx = a(E) + b(E)E

where a(E) represents the ionization losses (Bethe equation), and b(E) represents radiative losses (bremsstrahlung, pair production, photo-nuclear).

From what I have read, at high energies for high-Z materials, radiative losses dominate ionization losses (beyond the muon critical energy). I am ok with the ionization part but is there a simple way to represent the radiative losses (b(E)E) for a certain Z or density?

I can't seem to find anything, even though on the graphs you see of energy loss v. energy, the radiative losses seem to pretty much follow a straight line.

 

[stakhanov]

I take it that's a 'no' then!

 

[Astronuc]

Perhaps these are of interest

http://geant4.cern.ch/G4UsersDocuments/UsersGuides/PhysicsReferenceManual/html/node48.html

http://geant4.cern.ch/G4UsersDocuments/UsersGuides/PhysicsReferenceManual/html/node46.html

from a CERN Physics Reference Manual (from Geant4 Users' Documents)

This might also be of use:

Muon Bremsstrahlung and Muonic Pair Production in Air Showers.
http://arxiv.org/PS_cache/astro-ph/pdf/0006/0006108v1.pdf
Some good references.

Or use seach Google with "muon","bremsstrahlung","cross section"