Compton Scattering

Compton scattering is the elastic scattering of a photon by a quasi-free charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron.

A photon of wavelength λ  comes in from the left, collides with a target at rest, and a new photon of wavelength λ’  emerges at an angle θ. Because the mass-energy and momentum of a system must both be conserved, it is not generally possible for the electron simply to move in the direction of the incident photon. The interaction between electrons and high energy photons (comparable to the rest energy of the electron, 511 keV) results in the electron being given part of the energy (making it recoil), and a photon containing the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is conserved.

The Compton effect could be seen in the gamma spectrum of cesium-137. Where it can be seen a Compton edge at about 490 keV, a plateau and a Compton backscatter peak at about 170 keV. The latter is due to the backscatter photons which are Compton scattered at an angle of 180°.

Experimental Setup

In order to highlight the Compton effect the experimental setup shown in the following image has been used :

Putting a metal background behind the radioactive source it is as if it has been put a source of electrons which can act as Compton scattering centers. So we expect an increase in the height of the backscatter peak when we put the metal background behind the cesium radioactive source.   

In the gamma spectra reported below you see how the backscatter peak is evident when the measurement is taken with the metallic background present behind the source.

Electron Mass Determination

The electron mass can be determined experimentally by measuring the spectrum of the Compton scattering of a gamma source and using the equations of the theory to calculate the mass of the electron that operates the scattering. In the following paragraphs we describe the measurement and the calculation in the case of cesium 137 and Sodium 22 gamma ray sources .

Cs 137 Compton Scattering

Source	Peak Ey	Compton Edge Emax	Back Scatter EBS	Me measured	Me
Cs 137	662 keV	475 keV	192 keV	541 keV	511 keV

Electron Mass Determination from Cs 137

Calculation E_MAX = E_ϒ – E_BS = 662 – 192 = 470 keV  ̴ 475 keV (measured)

From compton scattering theory :  1/Ey’ – 1/Ey = (1 – cosθ)/M_ec²

For the back scatter gamma photon θ = 180° : 1/E_BS – 1/Ey = 2/M_ec²

With the measured values we obtain : M_ec² = 541 keV

Na 22 Compton Scattering

Source	Peak Ey	Compton Edge Emax	Back Scatter EBS	Me measured	Me
Na 22	511 keV	330 keV	180 keV	556 keV	511 keV

Electron Mass Determination from Na 22

Calculation E_MAX = E_ϒ – E_BS = 511 – 180 = 331 keV  ̴ 330 keV (measured)

From compton scattering theory : 1/Ey’ – 1/Ey = (1 – cosθ)/M_ec²

For back scatter gamma photon θ = 180° : 1/E_BS – 1/Ey = 2/M_ec²

With measured values we obtain : M_ec² = 556 keV

The values ​​obtained in the two cases, 541 keV and 556 keV agree quite well with the exact value of 511 keV.

References

Some ideas about this experiment are taken from the website : www.diyphysics.com

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