Photon scattering
Photons can be scattered through four main methods, depending on their energy. Low energy photons exhibit the photoelectric effect, medium energy photon undergo Thomson or Compton scattering, and high energy photons pair produce.
Compton scattering
Compton scattering is an inelastic scattering process where a photon scatters off a free charged particle. When it does so, some of its energy is lost. The energy is transfered to the the recoiling particle.
Compton Scattering Calculation
The Compton scattering equation was derived under the assumption that photons behave like particles and obey conservation of energy and momentum.
The change in the photon wavelength after scattering, depends on the scattering angle: $$\lambda' - \lambda = \frac{h}{m_e c}(1-\cos{\theta})$$ where \(\lambda\) is the initial wavelength, \(\lambda'\) is the wavelength after scattering, \(h\) is the Planck constant, \(m_e\) is the electron rest mass, \(c\) is the speed of light, and \(\theta\) is the scattering angle.
The maximum amount of energy transfer is when the photon is scattered at a 180° angle. The wavelength shift in that case is two times the Compton wavelength of the electron, or 0.00486 nm.
Similarly, the energy of the scattered photon can be calculated as:
$$E_{sc} = \frac{E_o}{1+(E_o/m_e c^2)(1-\cos{\theta})}$$
where \(E_{o}\) is the original photon energy, \(E_{sc}\) is the scattered photon energy, \(m_e c^2\) is the electron mass energy, and \(\theta\) is the scattering angle.
The energy of the recoil electron is \(E_e = E_{sc} - E_{o}\)
Energy transfer vs angle
Why
Compton scattering was among the initial evidence that light behaves as a particle and can be treated as a particle in calculations.
Compton scattering is the main mechanism through which radiation therapy (and poisoning) works. Compton interactions are the most prevalent, and X-rays and gamma rays scatter off the electrons of the atoms in tissue. The tissue is ionized and ejected electrons and free radicals are produced that in turn damage DNA strands, either causing cell death or reproductive death.