# Compton edge

In spectrophotometry, the Compton edge is a feature of the spectrograph that results from the Compton scattering in the scintillator or detector. When a gamma-ray scatters off the scintillator but escapes, only some fraction of its energy is registered by the detector. The amount of energy deposited in the detector depends on the scattering angle of the photon, leading to a spectrum of energies each corresponding to a different scattering angle. The highest energy that can be deposited, corresponding to full back-scatter, is called the Compton edge.

## Background

Gamma-spectrum of a radioactive Am-Be-source. The photopeak after the Compton edge corresponds to detection of the incident gamma rays. The significantly lower count in the region between the Compton edge and the photopeak reflects the fact that no gamma rays of this energy can be absorbed by the detector.

In a Compton scattering process, an incident photon collides with an electron in a material. The amount of energy exchanged varies with angle, and is given by the formula:

${\displaystyle {\frac {1}{E^{\prime }}}-{\frac {1}{E}}={\frac {1}{m_{\text{e}}c^{2}}}\left(1-\cos \theta \right)}$

or

${\displaystyle E^{\prime }={\frac {E}{1+{\frac {E}{m_{\text{e}}c^{2}}}(1-\cos \theta )}}}$ [1]
• E is the energy of the incident photon.
• E' is the energy of the outgoing photon, which escapes the material.
• ${\displaystyle m_{\text{e}}}$ is the mass of the electron.
• c is the speed of light.
• ${\displaystyle \theta }$ is the angle of deflection for the photon.

The amount of energy transferred to the material varies with the angle of deflection. As ${\displaystyle \theta }$ approaches zero, none of the energy is transferred. The maximum amount of energy is transferred when ${\displaystyle \theta }$ approaches 180 degrees.

${\displaystyle E_{T}=E-E^{\prime }}$
${\displaystyle E_{\text{Compton}}=E_{T}({\text{max}})=E\left(1-{\frac {1}{1+{\frac {2E}{m_{\text{e}}c^{2}}}}}\right)}$

It is impossible for the photon to transfer any more energy via this process, hence there is a sharp cutoff at this energy giving rise to the name Compton edge.

The region between the Compton edge and the energy of the 180 degree deflection is known as the Compton plateau. Referring to these two points as ${\displaystyle E_{\text{max}}}$ and ${\displaystyle E_{\text{min}}}$, respectively, the energy transfer equation above can be expressed in a form that emphasizes the fact that the plateau is located equidistant between the main photopeak and 0 energy. This visual clue is useful when analyzing experimental results from gamma spectroscopy of a radioactive source. [2] This is true as long as the incident photon has less than twice the electron rest mass (1.02 MeV), otherwise the energy of Pair production must be taken into account as well.

${\displaystyle E_{\text{min}}=E-E_{\text{max}}}$

## References

1. ^ Knoll, Glenn F. Radiation Detection and Measurement 2000. John Wiley & Sons, Inc.
2. ^ D. Prutchi and S.R. Prutchi, Exploring Quantum Physics Through Hands-On Projects 2012. John Wiley & Sons, Inc.