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The model of Rutherford scattering of α particles on gold nuclei was based on four assumptions: i) The gold nucleus mass (M) is much larger than the α particle mass m_{α} (M >> m_{α}); ii) Scattering of α particles on atomic electrons is negligible because m_{α} >> m_{e} (m_{e} is the electron mass); iii) The α particle does not penetrate the nucleus (meaning no nuclear reactions); iv) The classical relationship for the kinetic energy E_{K} of the α particle (E_{K} = m_{α}υ^{2}/2) is valid (υ is the velocity of the α particle).
When the α particle (positive charge ze) approaches the nucleus (positive charge Ze) the interaction between them is a repulsive Coulomb interaction, and thus, the α particle follows a hyperbolic trajectory, as shown in Figure 4417. The nucleus is in the outer focus of the hyperbola because of the repulsive interaction. The relationship between the impact parameter b and the scattering angle θ may be derived by determining two independent expressions for the change in momentum Δp of the scattered α particle. υ_{∞} is the initial velocity of the α particle and p_{∞} is the initial momentum of the α
particle. The momentum transfer is along a line that bisects the angle π − θ. The magnitude of the Coulomb force Fcoul acting on
the α particle is given by,
 [4417a]
where,
r  The distance between the α particle and the nucleus M
z  The atomic number of the α particle (for helium z = 2)
Z  The atomic number of the absorber (for gold Z = 79)
Figure 4417. Schematic diagram for scattering of an α particle on a nucleus.
The momentum transfer Δp is given by,
 [4417b]
The impact parameter b may be written as,
 [4417c]
In HAADF STEM, the "highangle" means beyond the angle at which diffraction maxima (spots) can be found. Highangle scattered electrons are few in number of elections and are mostly induced by Rutherford scattering.
Table 4417 shows that electrons interact with 1 electron, many electrons, 1 nucleus, and many nuclei in solids.
Table 4417. Effects of interactions of electrons in solids.

Interaction with electron(s) 
Interaction with nucleus/nuclei 

1 electron 
Many electrons 
1 nucleus 
Many nuclei 
Scattering type 
Inelastic 
Inelastic 
Quasielastic 
Elastic 
Inelastic 
Scattering effect 
Electron Compton effect; electron excitation (from 50 eV to a few keV: EDS and EELS) 
Plasmon excitation (< 50 eV, ~100 nm TEM specimen); Cerenkov effect 
Rutherford scattering; phonon scattering (< 1 eV, heat) 
Bragg scattering 
Bremsstrahlung 
