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# 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 a fraction of its energy is registered by the detector. This leads to a spectrum of gamma-rays in the data that is not really there. The highest energy that occurs from this process is the Compton edge.

## Background

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

$\frac{1}{E^\prime} - \frac{1}{E} = \frac{1}{m_e c^2}\left(1-\cos \theta \right)$

or $E^\prime = \frac{E}{1 + \frac{(1 - \cos \theta)E}{m_e c^2}}$

• E is the energy of the incident photon.
• E' is the energy of the outgoing photon, which escapes the detector.
• me is the mass of the electron.
• c is the speed of light.
• θ is the angle of deflection for the photon.

The amount of energy transferred to the scintillator varies with the angle of deflection. As θ approaches zero, none of the energy is transferred. The maximum amount of energy is transferred when θ approaches 180 degrees.

$E_T = E - E^\prime$

$E_{Compton} = E_T (max) = E \frac{2E}{m_e c^2 + 2E}$

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.