As the incident photon energy increases, the likelihood that it will undergo Photoelectric Effect decreases and the Compton Effect also referred to as Compton scattering becomes the dominant mode of interaction.
In Compton scattering, the incident photon with energy hv0 interacts with a loosely bound (or free) electron from an outer shell and transfers some of its energy to it. The photon is scattered at a lower energy (hv’) and scattering angle ϴ, and the Compton (recoil) electron is ejected with an energy E at an angle Φ relative to the incident photon’s direction.
From the conservation of energy and momentum, the following relations can be obtained:
Where α = hv0/m0c2 and m0c2 = 0.511 MeV is the rest mass energy of the electron.
After undergoing a Compton scattering, the scattered photon has a longer wavelength λ’ than that of the incident photon λ. The change in wavelength or Compton shift is independent of the incident photon energy and depends only on the scattering angle ϴ.
Therefore:
Δλ = λ’ – λ = h/m0c(1-cos ϴ) = λc(1-cos ϴ)
Where λc = h/m0c = 0.02426 Ȧ = 2.426 x 10-10 m is the Compton wavelength, or the wavelength of a photon whose energy is just equal to the rest mass energy of the electron.
The scattered photon’s energy and consequently, how much energy is imparted to Compton electron, depends on the scattering angle and the incident photon energy. It is important to note that, when a photon is scattered at small angles (ϴ → 0), very little of its energy is transferred to the electron. On the other hand, as the photon scattering angle increases (ϴ = 0 → 180), a greater fraction of the incident energy is imparted to the electron.
Since the Compton interaction involves a free electron, it is independent of the atomic number Z of the medium and depends only on the number of electrons per gram, which is constant for almost all materials. Therefore, the Compton mass attenuation coefficient ơ/ρ is the same for all materials. That is, gram for gram all materials will undergo the same Compton interaction. However, the linear attenuation coefficient ơ will be larger for denser materials.
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