Compton Shift

This relation gives the change in wavelength of a photon after it scatters from a free or weakly bound electron, with the shift depending only on the scattering angle. It comes from conserving both energy and momentum in a photon-electron collision, which shows that the photon must give up some momentum to the electron, reducing its energy and increasing its wavelength. The factor h/(m_ec) is the electron's Compton wavelength, setting the natural scale of the effect, while the (1 - cosb8) term makes the shift zero for forward scattering and largest for backscattering.

Use this when analyzing X-ray or gamma-ray scattering from electrons, especially in Compton scattering experiments or radiation interactions with matter. It is appropriate when the electron can be treated as approximately free and the photon energy is high enough that wavelength change is measurable.

• Using the photon's initial wavelength in the formula instead of the fixed electron Compton wavelength h/(m_e c)
• Forgetting that the result is a wavelength increase, so scattered photons have larger wavelength and lower energy
• Using degrees or radians inconsistently when evaluating cos(b8); the angle must match the calculator setting