COMPTON SCATTERING

Compton scattering is the scattering of photons of electromagnetic radiation from (quasi-) free electrons in matter. The energy of the scattered photon is lower than that of the incident photon because the electron (originally at rest) exits with some of the energy. The energy E’ of the scattered photon is related to the energy E of the incident photon by

1/E’ –1/E = (1/mc²) (1-cos q)

where mc² is the rest mass energy of the electron (511 keV) and q is the scattering angle of the photon. In this experiment you will measure E’ versus q for two values of E.

1) ¹³⁷Cs source: Using a ¹³⁷Cs source, which emits a 637 keV gamma ray, you will first observe the energy spectrum in a NaI detector. The Compton effect is already evident in the spectrum itself, even for a single energy photon entering the crystal. A photon entering the crystal may interact with it in two major ways:

a) Photoelectric effect: the photon is absorbed by an atom in the crystal and an electron is ejected with the excess energy (nearly the full 637 keV in this case) . This electron then slows down and stops in the crystal, leaving the atoms of the crystal in excited states. These atoms then decay, emitting visible photons, which are in turn allowed to fall onto a photosensitive surface of a vacuum tube (photocathode). Here the photoelectric effect again occurs, ejecting a large number of electrons. This number of electrons is multiplied further by striking a number of electrodes in the tube, multiplying at each step, until a charge pulse is produced which is big enough to amplify and measure. The MCA provided makes a histogram of the number of counts versus the size of this pulse. The net effect of this long chain of events is therefore a histogram of the number of counts versus the energy deposited in the NaI by the incident gamma ray.

b) Compton effect: Sometimes the incident gamma ray just Compton scatters off an electron in the NaI, and the scattered photon escapes. Then the energy deposited is decreased by the energy E’ of the scattered photon. If this scattering is head on, E’ is small, and most of the energy (but not all) is still left in the crystal. It this scattering is glancing, E’ is very large, and very little energy is left in the crystal. Because all scattering angles are possible, the spectrum from the NaI will show a very broad “Compton shoulder” ranging between these two limits. You will see this immediately in the shape of the NaI spectrum.

Experimental approach:

1) Place the ¹³⁷Cs source about 5 inches from the NaI and take a spectrum. Be sure you can identify the photopeak and the Compton shoulder in the spectrum. Print out the spectrum and identify these features on it.

2) Place a piece of Al behind the source, and take a spectrum for a preset time for a couple of minutes. Then remove the source, place the MCA on subtract, and subtract a spectrum without the Al (but with the source) for the same time. The difference is the photopeak due to Compton scattering from the Al at about 180 degrees. Print out the spectrum, and evaluate the energy of the peak, using the knowledge that the photo peak is at 637 keV. Does it agree with what you calculate from the above formula?

3) Try to do a measurement with the Al at some more glancing angle and describe what happens.

2) ²⁴¹Am source: This source emits a 59.54 keV gamma ray, much lower energy, so the dependence of E’ on angle will be less. However, the beam is very well collimated and well suited to a Compton scattering measurement. (This is a very strong source. It should be handled only by your instructor.) You will measure the energy spectrum using a proportional counter, which gives only a photopeak (no visible Compton). The spectrum is actually rather complicated, so just use the 59.54 keV peak and ignore the rest. Place the source about ten inches from the detector and measure a spectrum. Then change the geometry so that the beam from the source scatters off a block of Al at an angle p into the detector. Take a spectrum for long enough to get good statistics ( a couple of minutes at each angle at least). Measure E’ as a function of angle. Plot out a direct spectrum and one taken at 90 degrees, and indicate which peak corresponds to E and/or E’. Measure E’ versus theta for several angles (say 0,45,90,135 degrees) and plot it up. Make a graph of E’ versus angle and plot the calculated values of E’ from the above equation on the same graph. Does the equation work?