# Compton Scattering Motivation: It's a basic thing that is the basis of [[Compton Imaging]] ## What is Compton Scattering? Compton Scattering is the scattering of photons on stationary charged particles. In this process, both the photon and the target are scattered and the photon may lose some energy. This energy loss is deposited in the medium of scatter, which can be measured. This is one of those three primary radiation interactions with matter, with the other two being the [[Photoelectric Effect]] and [[Pair Production]]. Compton Scattering is [[Incoherent Scattering]] because there are degrees of freedom in each scattering event which are associated with the atomic electron. ## Common Formulas This first formula is the equation for the change in wavelength after the interaction, and is the most base formula. $\lambda' - \lambda = \frac{h}{m_e c^2}(1- \text{cos}\,\theta) $ where: - $\lambda$ is the initial wavelength - $\lambda'$ is the wavelength after scattering - $h$ is [[Planck's Constant]] - $m_e$ is the electron rest mass ($511 keV/c^2$) - $c$ is the speed of light - $\theta$ is the scattering angle If we want to find the change in energy, this is a simple manipulation of the equation, with the relationship between wavelength and energy for a photon. $E_{\gamma'} = \frac{E_\gamma}{1+ \frac{E_\gamma}{m_ec^2}(1 - \text{cos}\,\theta)} $ You might also see this equation use $h\nu$ instead of $E$, but this is just a more explicit way of using the frequency of the photon. This formular (heh) is the one that I use a lot more frequently when I measure radiation since I'm directly measuring the change in energy. This is especially useful if I know the expected starting energy and the final energy and or position, since this is how [[Compton Imaging]] works. Without the knowledge of the initial energy, however, things could get significantly more complicated. The derivation of this formula comes from the conservation of energy and general kinematics, and is assumed to be non-relativistic. ___ Read Knoll Radiation Chapter 2 for the useful info