Practical Electron Microscopy and Database

It is different from Rutherford scattering that has m_α (α particle) << M (gold nucleus), the situation here is that a heavy charged particle M interacts with an orbital electron me (M >> m_e). Figure 4418 shows the Coulomb interaction between the heavy charged particle (charge ze and mass M) and the orbital electron (charge e and mass m_e).

Figure 4418. Schematic diagram of a collision between a heavy charged particle M and an orbital electron m_e.

Using the conservation of angular momentum, we can know the momentum transfer Δp can be given by,

             --------------- [4418a]

In the case of a heavy charged particle (ze) interacting with a stationary orbital electron (e) the scattering angle θ ≈ 0 and thus, Δp can be simplified by,

             -------------------- [4418b]

The energy transferred to the orbital electron from the heavy charged particle for a single interaction with an impact parameter b is given by,

             ---------------- [4418c]