1. Compton scattering is being used to model the distribution of x-rays produced when a black hole disturbs a star.
2. Compton scattering based tomography can be used to map the electron density of a material
3. Compton scattering is a critical theoretical component of investigating the substructure of nucleons (e.g. protons)
4. Wooden materials can be non-destructively probed via Compton scattering, which can give insight into the density distribution of materials and possible defects present.

In the first experiment of the course last fall, you measured the interaction cross section for gamma rays in aluminum. You most likely found that the purely classical Thomson Scattering model was not always in good agreement with you data. It was postulated in that experiment that Compton Scattering is a more complete description of how photons scatter off of free electrons.

A purely classical wave model of scattering allows for no change in wavelength at a boundary (due to continuity constraints), and thus would predict that scattered gammas would have the same energy as the source. In this experiment you will test the Compton Scattering model's prediction (which was foundational in establishing modern quantum mechanics) for the relationship between the energy of the scattered gamma ray and the angle through which it scattered.

Before your Preparation meeting with your TA, you and your lab partner(s) should do some background research. The purpose of this is so that you can go into your first meeting with the TA with a picture of what you need to measure, how those measurements will be made, what complications you are likely to encounter, and how you might deal with them. Then, at your first meeting you can focus on the details of what you need to do to start getting data to work with. Remember that you are expected to come to this meeting prepared to participate and demonstrate your understanding of these concepts.

Questions that your group should answer are the following:

• What is Compton scattering?
• What quantities are you trying to measure.
• What do you expect the relationship between these quantities to look like?
• What is the apparatus at your disposal capable of measuring?

In other words, what will your raw data look like and what do you have to do to it to get real-world quantities like photon energies, does anything need to be calibrated?

• How does your detector (a NaI crystal coupled to a photomultiplier and read out by a pulse-height analyzer) work? You have worked with these detectors and you seen pulse height spectra before in the Gamma Cross Sections experiment.
• What will the pulse height spectra (PHS) from a monoenergetic gamma source look like, and how do you expect it to change as a function of scattering angle?
• What will you measure from the PHS.

• Are there likely to be statistical uncertainties in measured quantities? How can you determine what an acceptable statistical uncertainty is? (Note, you really cannot answer this question unless you understand the previous questions related to what measurement will you be making.)
• What systematic effects do you expect to be present? How will they bias your results and how might you deal with them?

If your group goes into its first meeting with the TA having thought about and done some background research on these questions, you will be in a good position to come out of the meeting with an understanding of what data you need to collect and how it should be collected.

Figure A: Schematic drawing of Compton Scattering

After your prelab meeting you should be confident that you understand:

• What the Compton Scattering model is.
• How you will use a PMT+NaI detector and PHA to test the model.
• What you need to accomplish in the lab.
• What you will do on your first day in lab.

For a more rigorous description of Compton Scattering you can turn to any modern physics or quantum mechanics textbook. Wikipedia also has a good discussion https://en.wikipedia.org/wiki/Compton_scattering. Here we just provide a brief overview.

Consider the scattering of a gamma (photon) from a free electron as shown in Fig. 1.

Figure 1: An incident gamma of energy E “collides” with an electron and scatters with energy E' at angle θ relative to the initial trajectory.

The energy of a gamma scattered by a free electron, $E'$, depends on the scattering angle, $\theta$, and the energy of the incident gamma, $E$. It can easily be derived from the conservation of energy and momentum as

where $mc^2 = 511\;\mathrm{keV}$ is the rest energy of the electron. This is the model which you will test.

Figure 2: The Compton scattering apparatus.

The experimental apparatus is shown schematically in Fig. 2.

A collimated beam of 662 keV $\gamma$ -rays produced in the decay of cesium-137 is incident on a cylindrical aluminum rod. A PMT+NaI detector which has been magnetically shielded and housed in a Lead Pig is attached to a goniometer allowing it to be rotated about the scattering rod. Pulses from the PMT+NaI detector are sent to a UCS-30 pulse height analyzer (PHA) Spectrum Techniques UCS-30.

A pair of ${}^{137}\textrm{Cs}$ sources produce 662 keV gammas. These sources sit at the center of a lead pig to shield you from the radiation. The radiation emerges from the pig in a collimated beam aimed at the scatterer in the middle of the table.

The “source” is actually two sources having strengths as follows:

• 32.5 millicuries (mCi), produced 5/19/69
• 30.0 mCi, produced 7/11/69

These activities are nominal values only, as the activity will decay with time. (Cesium-137 has a half-life of 30.17 years.) When not in use, the pig is “closed” by a tungsten rod inserted into the exit aperture of the pig. A locking brass door holds the plug in place.

• The source is “opened” by swinging the door away from the face of the pig and removing the plug using the long handled tongs so that your hands are not exposed to the beam.  
• When you are finished taking data, the tongs should be used to reinsert the plug and the door should be closed.

To calibrate the pulse height axis of the PHA, a set of small radioactive sources is provided. Sources include ${}^{241}$Am, ${}^{133}$Ba, ${}^{57}$Co, ${}^{137}$Cs, and ${}^{22}$Na, and should yield discernible gamma peaks with energies between 59.5 keV and 661.6 keV.  

You need not consider energies above 662 keV when doing your calibration.

Energies and relative intensities of the calibration sources are available from the nuclear decay schemes. Note that these sources all have low activity so as to not overwhelm the detector with counts and cause charge pileup (also known as voltage sag.)

• The PMT you are using requires positive HV which should not exceed +1500V.
• When the HV is first turned on it takes some time for the performance of the PMT to come to equilibrium. During this time the noise and gain characteristics of the PMT may change by a small amount.
  • Note you do not have to guess when the PMT has come to equilibrium. You can make measurements which will tell you what you need to know.
  • Also note that you have four hours in the lab period to work with the apparatus so you cannot wait hours before beginning data collection. You need to balance the need to collect a minimum set of data in a finite amount of time vs. optimizing the detector performance.

• To minimize interference, when not in use the calibration sources should be kept behind the lead bricks at the far end of the bench from the detector.
• There is a trade off between how many data points you can take and how long you can spend collecting each data point. As an experimentalist it is up to you to evaluate the tradeoffs and decide on an appropriate data collection strategy. Don't guess (note that picking 10 data points because 10 seems like a good number is guessing), use you knowledge of the model you are testing to plan an effective and efficient data collection strategy.
• Don't ask the lab staff or TA if your data look good, or if you have taken enough data. Plot your data as you take it. There is simply no other way to know if you are getting the data which you need. You have to decide the answers to these questions and the best insight you have comes from looking at the data itself. For this purpose you can make plots anyway you want, plotting by hand in your lab notebook is perfectly acceptable. You don't need calculated uncertainties or even calibrated data for this, you can absolutely make plots of PHA channel vs scattering angle to see how your data collection is going!
• While you are sitting in lab waiting for data to collect work on analyzing the data you have. Does your calibration look good? Do you think you need more calibration data? Do Not wait until later when you are not in lab to do these things because if you run into problems there is nothing you can do about it.

Since there will be other groups working on the apparatus it is your responsibility to ensure that everything in the lab is in order with the next group arrives. The room should be tidy and everything should be either put away or reset to it's default. If the lab room was in disarray when you arrived you are still responsible for leaving it in the appropriate state for the next group. Here are some general tips on things to check before you leave.

1. The main source should be properly closed.
2. Calibration sources should be in their appropriate container behind the lead shielding at the end of the bench.
3. The PMT HV should be turned off. Leave the HV cable connected to the PHA.
4. All other cables and connections you may have made should be undone and cables properly stowed.
5. All applications on the lab computer should be closed. Don't forget to log out of any accounts you may have logged into.
6. The PHA should be turned off.
7. Sign out of the logbook.
8. The room lights should be off and the door closed when the last person leaves the lab.

Your analysis is due 4 days after your second day in lab. The analysis is not a lab report, rather it is all of the data reduction, number crunching, calculations, curve fitting, error propagation etc. which is necessary for you to establish your final conclusions. Think of it as being more like an extended homework set where you have to show how you got your final results.

Three days after your analysis submission your group will have a meeting with the TA to go over your analysis and make sure you are prepared to write your final report.

The final report is due three days after the analysis meeting.

Your graded analysis will be returned along with your graded final report.

Three days after your analysis is due your group will meet with the TA to discuss the overall analysis and make clear what needs to go into your final report. Note that this meeting is not for the purpose of discussing your grade on the analysis, you will receive the grade on the analysis along with the graded final report. Instead this is an opportunity for the TA to have reviewed your analysis to identify where you may have short comings or misconceptions in your understanding of the experiment with the goal of improving what goes into your final report. It is also an opportunity for you to make sure that you understand what your TA is looking for in your report.

You are expected to bring a detailed outline for your final report to this meeting. The outline should consist of section and sub-section headings which make clear what information you will put into the report as well as the order in which that information will appear. This should literally be a single page document. Having a meaningfully thought out outline will count towards your participation grade for the meeting.

The expectation is that between feedback on your analysis and your outline you should leave this meeting with a clear idea of how you will write up your final report.

Your final report will be evaluated based on the following rubric. The rubric is not a format for your analysis, you are not expected to have a specific section on Data Handling or Presentation of Data. Elements of the different rubric categories will appear at different points through out your analysis writeup. For example you will be presenting data in your discussion of the calibration, your discussion of determining peak locations, and likely in your final results. Your writeup of your analysis should be structured in a way that is clear and readable, there should be a logic to the flow of it.

Each item below is graded on a 0-4 point scale:

• 4 – Good (A): completes all listed tasks and provides appropriate context; thinks carefully about data and analysis; addresses all concerns raised by the results (where appropriate).
• 3 – Adequate (B): misses one or more minor element or lacks appropriate context; leaves a problem or ambiguity unaddressed; does not present analysis clearly enough.
• 2 – Needs improvement (C): omits or mishandles one or more item which renders the analysis fundamentally incorrect or incomplete; presents results in an incorrect or unclear way.
• 1 – Inadequate (D): omits or mishandles multiple items or treats them at an insufficient level; presentation is overall muddled or inaccurate; flaws in logic or process.
• 0 – Missing (F): omits all elements or makes no meaningful attempt.

All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items.

A. A. Bartlett, Am J. Phys. 32, 120 (1964) This paper is a historical review of the experiments that were later explained by Compton's discovery of the Compton effect.

A. H. Compton, Am. J. Phys. 29, 817 (1961) Compton reviews the experimental evidence and the theoretical considerations that led to the discovery and interpretation of x-rays acting as particles.