Compton edge

Background

In a Compton scattering process, an incident photon collides with a weakly bound electron, leading to its release from the atomic shell. The energy of the outgoing photon, *E' *, is given by the formula:

: E^\prime = \frac{E}{1 + \frac{E}{m_{\text{e}} c^2}(1-\cos\theta)}

• E is the energy of the incident photon.
• m_{\text{e}} is the mass of the electron.
• c is the speed of light.
• \theta is the angle of deflection of the photon.

(note that the above formula does not account for the electron binding energy, which can play a non-negligible role for low-energy gamma rays).

The energy transferred to the electron, E_T, varies with the photon's scattering angle. For \theta equal to zero there is no energy transfer, while the maximum energy transfer occurs for \theta equal to 180 degrees (backscattering).

: E_T = E - E^\prime

: E_{\text{ComptonEdge}} = E_T (\text{max}) = E \left(1-\frac{1}{1 + \frac{2E}{m_{\text{e}} c^2}} \right)

In a single scattering act, it is impossible for the photon to transfer any more energy via this process. Thus, there is a sharp cutoff at this energy, leading to the name Compton edge. If multiple photopeaks are present in the spectrum, each of them will have its own Compton edge. The part of the spectrum between the Compton edge and the photopeak is due to multiple subsequent Compton-scattering processes.

The continuum of energies corresponding to Compton scattered electrons is known as the Compton continuum.

References

References

1. Knoll, Glenn F. ''Radiation Detection and Measurement'' 2000. John Wiley & Sons, Inc.
2. (2010). "Nuclear medicine instrumentation". Jones and Bartlett Publishers.