NOTE: This is general for charged particles, some mechanisms specific to electrons are discussed in 1.2.3
Three Main Mechanisms by which charged particles loose energy by emitting photons - these mechanism are distinguished by the energy of the photons:
1. Cherenkov Radiation
2. Ionizations of Atoms
3. Transition Radiation
All are derived from considerations of electromagnetic interactions in material, using the diffractive index n and the dielectric constant epsilon.
1. Cherenkov Radiation (<1eV)
If the energy of the emitted photon is below the excitation energy of the traversed material, real photons are emitted, if the velocity of the particle is higher than the phase velocity of light in the material -> Cherenkov radiation with:
sqrt(epsilon) (v/c) cosTheta_c = 1
2. Ionization of Atoms / Energy loss by ionization
Also derived by full description of photoabsorption.
The *average* energy loss dE/dx per particle is described by the Bethe-Bloch-Formula.
The *differential* energy loss (dN/d(E)) is harder to describe and has large fluctuations, e.g. from the fact the electron that are knocked off their shells have an energy distribution of 1/E^2 - electrons that are freed in these ionization processes and have more than > 100 eV can ionize further atoms. This makes everything a bit messy.
Just as a comparison: For silicon, the energy of hole-electron pairs created is just around 3 eV, therefore there are less statistical fluctuations in the number of produced pairs.
The differential distribution has a high-energy tail from the delta-rays, which can be described using a Landau-Distribution.
3. Transition Radiation
This is valid for photons X-ray energies. Here, the threshold velocity, at which Cherenkov radiation would be emitted, is larger than the vacuum speed of light. Then radiation is only emitted in transition region of two materials. This is essentially the interference of Cherenkov radiation at the two boundary surfaces with different phases. Can be derived using the full photoabsorption formula.
Another small effect are delta-rays (knock-on electrons) that are electrons knocked out off their atomic shells with very high energies. (They can be seen in bubble chamber pictures as curled tracks alongside the track of the charged particle)