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Inserting p = γm0 and $equation$gives

$equation$

The maximum energy transfer depends on the ratio of the rest masses of the electron and the incoming particle $equation$, as well as on the ratio of the initial particle velocity and the speed of light $equation$, 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

$equation$

Since collisions are usually ...

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