For our gamma ray source, we will be utilizing Caesium 137 for its high probability of producing gamma rays with a predictable energy of 662keV (this will be demonstrated in the following sections). Our target of choice will be a variety of cylinders. Two aluminum cylinders of different radii and one of copper. Our detector is an Sodium Iodide crystal based detector attached to a photomultiplier.
The photomultiplier will receive hits from scattered photons. When it receives a hit, a small reaction occurs accelerating an exponentially increasing amount of electrons down the tube. Eventually they strike an anode at the end which detects a current pulse. Information about this current pulse is fed into the amplifier and then into the multi channel analyzer (MCA). The end result is that we have detected a scattered photon with somecorresponding energy.
This brings us to an issue with the MCA. The MCA operates through a PCAE program on a Windows PC. The program detects scattered photon energies not by units of energy but by channels. With every increasing channel we have a linearly increasing energy. In order to analyze information about our scattered photons, we are required to calibrate the program.
If we were to consider the energy spectrums of several known elements and feed them into our program we could calibrate our program. In turn, we would understand how much energy corresponds to each channel. So to do this, we expose the photomultiplier to a variety of radioactive materials. We used Caesium 137, Sodium 22, Barium 133, and Cobalt 57. Each one of these gamma spectrums has a known energy spike. This means that for each sample, we will receive at least one channel with a known energy. With four sources we have four channel-energy relationships. Graphing these together will give us a linear relationship between channel and energy.
A gaussian curve applied to each energy spectrum gives us the ability to determine exactly where each known energy peak existed on the PCAE program.
From the four channel energy points, the slope of our linear fit tells us the energy per channel! This calibration is necessary for the second part of the experiment.
The second part of the experiment involves measuring the differential cross section. For this part of the experiment we will be using Caesium 137 as our gamma ray source. Free electrons on the surface of metal cylinders would scatter our photons. Depending on the angle at which the detector was seated, we would receive a different spectrum of photons with different energies at each angle.
From all of the gathered data, we could analyze it in such a way that we may determine the differential cross section. We then may compare our results to the Thomson and Klein-Nishina (K-N) formulas.
Measurement
For the calibration of the channel, the radioactive sources are placed in front of the detector. The detector is then left to measure the energy of the photons emitted by the radioactive sources for 10 minutes each. Aside from the sources, the background count was also measured by placing no sources in front of it. The background count is subtracted from the count of each source spectrum to "clean" the data. Using the data obtained from the detector, a Gaussian plot is drawn in order to gauge the peak which is equivalent to the most probable energy of the photons absorbed by the detector. The channel that corresponds to the peaks are plotted over a graph shown in figure 3. The graph is linear which indicates that the calibration factor is a constant.