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i am trying to calculate the energy deposited by high energy electrons traveling through Silicon. I am dealing with energies in the range of 10^6 - 10^12 eV. I have read that radiative losses will dominate at higher energies and the critical energy where ionization loss = radiative loss is ~ 40 MeV for silicon. Can someone please direct me to the equations i can use to calculate both ionization and radiative losses for high energy electrons? Thanks.

Rich.