Inserting p = γm0cβ and gives
The maximum energy transfer depends on the ratio of the rest masses of the electron and the incoming particle , as well as on the ratio of the initial particle velocity and the speed of light , which is contained in γ. We distinguish four cases:
|nonrelativistic case||extreme relativistic case|
|β ≪ 1, γ ≈ 1||β → 1, γ ≫ 1|
|incoming proton = m0 mp||ΔEmax ≈ 2meυ2||ΔEmax = E|
|incoming electron m0 = me||ΔEmax = E||ΔEmax = E|
In the case of nonrelativistic protons, the relative energy loss in a single interaction with a resting electron is limited by
Since collisions are usually ...