cTo observe the Compton Effect we need a source of high-energy photons and a suitable spectrometer to observe the frequency shift in photons as they recoil. The source of short-wavelength photons is not much of a problem—a 137Cs source produces photons at a wavelength λ = 1.88 × 10−12 m.
Actually, the more common unit for expressing the energy of high-frequency photons is in electronvolts. By definition, one electronvolt (eV) equals the amount of kinetic energy gained by a single electron when it accelerates through an electric potential difference of one volt. Thus, one electronvolt is equal to 1.602 × 10−19 J.
Since the energy of a photon using Planck’s formula is E = hf = hc/λ, the energy of a photon in eV is: E[eV] ≈ 1,240[eV · nm]/λ[nm]. 137Cs thus emits photons with 660 keV of energy, which is the common way in which you will see radioactive emission lines specified.
Spectrum analysis at these wavelengths is also relatively easy to do using a scintillation crystal coupled to a photomultiplier. Unlike the scintillation probe of Figure 61 however, we will need to couple the crystal to the PMT probe we built in (Figure 29). This is because the amplitude of the pulse output by a scintillator/PMT probe is proportional to the energy of the photon that causes the scintillation. Thus, as shown in Figure 86, spectral analysis with a scintillator/PMT is simply a matter of collecting a histogram of pulse heights. This histogram is essentially a representation of the number of photons detected by the scintillator that have been counted as a function of their energy.
Figure 86 A PMT coupled to a scintillation crystal produces pulses of amplitude proportional to the energy of the gamma photons that interact with the crystal. These small, narrow pulses must be amplified and shaped so they can be processed by a multichannel pulse-height analyzer (commonly known as an MCA), which produces a histogram of pulse heights that represents the energy spectrum of incoming gamma photons.
The instrument used to histogram pulse heights is called a multichannel analyzer (MCA). It measures the energy spectrum and each channel, or bin, corresponds to a narrow energy range. The histogram then represents the number of events within each bin, which is the energy spectrum.
Multichannel analyzers used to be expensive laboratory instruments. However, a very ingenious program was recently released for free by Marek Dolleiser of the University of Sydney in Australia, which allows a PC to act as an MCA. Pulse Recorder and Analyser (PRA)* analyzes scintillator signals input through the PC’s sound card. It is easy to use, and performs amazingly well, considering that it performs real-time pulse recognition and display of spectral data. The program can also be used to count pulses from Geiger counters and other radiation detectors. Although it can’t compete with the speed or performance of a commercial MCA as an analytical laboratory tool, this program is perfect for conducting our experiments!
PRA requires a PC running the 32-bit or 64-bit Windows® operating system. PRA can also run under Linux using Wine. The PC needs a sound card and very few other resources. We run it on an old Centrino® 1-GHz laptop with 256K RAM. We have found that older laptops and PCs with Windows XP (SP3) run best for this application, since some of the more recent machines micromanage the sound card to the point that PRA is rendered useless. If you have a commercial PMT pulse amplifier, you will probably have to stretch the output pulses so that they can be acquired through the sound card. We have an amplifier that outputs 2-μs pulses, and we stretch the pulses with a simple low-pass filter consisting of a 100-μ resistor in series between the amplifier’s output and the sound card input, and a 0.56-μF capacitor between the sound card’s input and ground pins. PRA includes a good help file that you should read to get your system to work.
The choice of detector for gamma-ray spectrometry is important, because not all detectors are able to equally discriminate between photons that have only slight differences in energy. This quality is characterized by the so-called energy resolution, which is defined as the width (commonly specified as the “full width at half-maximum” or FWHM) of the spectrum for a spectral line at a certain energy. In other words, the energy resolution measures how much a single spectral line is smeared out by the detector (Figure 86, bottom graph).
A typical energy resolution for 662 keV gamma rays from 137Cs of a small NaI(Tl) scintillator is around 8% FWHM. Unfortunately, for the same gamma photons, the resolution of a plastic scintillator is closer to 200% FWHM, so it would smear the spectrum so much we wouldn’t be able to distinguish the 662-keV line from the Compton Shift. You will need a small (e.g., 1-in.-diameter × 1-in.-tall) NaI(Tl) scintillation crystal to perform this experiment.
Setting up the system to observe the Compton Effect is straightforward. Couple the NaI(Tl) scintillation crystal to the PMT’s photosensitive face. Remember to use coupling grease to reduce losses, and make sure that no stray light enters the PMT. Then, simply connect the output of the PMT probe to the amplifier/discriminator that you built in (Figure 34). Power the PMT probe with a low-ripple, high-voltage power supply (e.g., Figure 31 or Figure 32), and hook up the “Analog Output” connector of the amplifier/discriminator to the PC’s microphone or line-in input (through either the right or left audio channel).
Place the scintillation probe and 137Cs source facing each other, at least 30 cm above the work surface, and away from any solid objects. You should place the source far enough away from the detector so that the MCA (e.g., the PRA software) yields a clean spectrum, as shown in Figure 87a. You should be able to see the 662-keV line produced by the 137Cs source, as well as the “Compton plateau,” which is produced by Compton scattering of gamma rays within the NaI(Tl) scintillation crystal. Note that when the scattered gamma photon escapes from the crystal, only the energy deposited on the recoiling electron is detected. The upper edge of the plateau (the “Compton Edge”) results from the most inelastic collisions—that is, those where the photon is scattered at an angle of 180°. You can use the equations that we saw before (page 122) for explaining the Compton Effect, and calculate the energy at the Compton edge from:
Figure 87 You can observe the spectrum of gamma photons being backscattered by the electrons in aluminum using this setup. (a) You should only see the 662-keV line produced by 137Cs and some Compton-scattered photons within the NaI(Tl) crystal when the source and scintillation detector are placed far away from solid materials. (b) Placing a 5-cm-think block of aluminum behind the source causes many photons to be backscattered through the Compton Effect.
where E is the energy of the original gamma photon (662 keV for 137Cs), and E’ is the energy of the backscattered photon. The Compton edge thus sits at Ee = E – E’.
Although that in itself is a demonstration of the Compton Effect, it is much more dramatic to place a thick aluminum block (at least 5-cm thick) behind the source, as shown in Figure 87b.23 This will cause a large number of photons with energy E’ to be backscattered by electrons in the aluminum. You can thus verify the Compton Effect by comparing the channel numbers at which the Compton peak (E’) and Compton edge (Ee) appear in relationship to the channel number for the 662-keV 137Cs line. If Dr. Compton was right to assume that photons are actual particles, then you should see the Compton edge Ee at around 480 keV, and the backscattered peak E’ at around 180 keV.
The correctness of the Compton Effect can also be confirmed by calculating the mass of the electron me from the measurement of the Compton edge and the Compton peak24:
Using your measurements of E, E’, and Ee for a 137Cs source and an aluminum block, estimate the rest mass of the electron. You may also want to use other gamma-ray sources (Figure 88) to obtain more data points to refine your estimate of me by measuring E, E’, and Ee for each. How well does your estimate agree with the accepted value of me = 9.11 × 10−31 kg or its equivalent of 511 keV?
Figure 88 Stylized gamma-ray spectra for disk sources that you may use to test your NaI(Tl)/PMT probe and MCA, as well as to obtain further data points for E, E’, and Ee.
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