Compton Scattering of X-rays

Compton Scattering of X-rays

compton scatteringThe Compton formula was published in 1923 in the Physical Review. Compton explained that the X-ray shift is caused by particle-like momentum of photons. Compton scattering formula is the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays. In the case of Compton scattering the photon of frequency f collides with an electron at rest. Upon collision, the photon bounces off electron, giving up some of its initial energy (given by Planck’s formula E=hf). While the electron gains momentum (mass x velocity), the photon cannot lower its velocity. As a result of momentum conservation law, the photon must lower its momentum given by:

As a result of momentum conservetion law, the photon must lower its momentum given by this formula.

Compton Scattering
In Compton scattering, the incident gamma-ray photon is deflected through an angle Θ with respect to its original direction. This deflection results in a decrease in energy (decrease in photon’s frequency) of the photon and is called the Compton effect.
Source: hyperphysics.phy-astr.gsu.edu

So the decrease in photon’s momentum must be translated into decrease in frequency (increase in wavelength Δλ = λ’ – λ). The shift of the wavelength increased with scattering angle according to the Compton formula:

 

The shift of the wavelength increased with scattering angle according to the Compton formula

where λ is the initial wavelength of photon λ’ is the wavelength after scattering, is the Planck constant = 6.626 x 10-34 J.s, me is the electron rest mass (0.511 MeV)c is the speed of light Θ is the scattering angle. The minimum change in wavelength (λ′ − λ) for the photon occurs when Θ = 0° (cos(Θ)=1) and is at least zero. The maximum change in wavelength (λ′ − λ) for the photon occurs when Θ = 180° (cos(Θ)=-1). In this case the photon transfers to the electron as much momentum as possible. The maximum change in wavelength can be derived from Compton formula:

The maximum change in wavelength can be derived from Compton formula. Compton length

The quantity h/mec is known as the Compton wavelength of the electron and is equal to 2.43×10−12 m.

Interaction of X-rays with Matter

Although a large number of possible interactions are known, there are three key interaction mechanisms with matter. The strength of these interactions depends on the energy of the X-rays and the elemental composition of the material, but not much on chemical properties, since the X-ray photon energy is much higher than chemical binding energies. The photoelectric absorbtion dominates at low-energies of X-rays, while Compton scattering dominates at higher energies.

  • Photoelectric absorption
  • Compton scattering
  • Rayleigh scattering
References:

Radiation Protection:

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See above:

X-rays