Table of Contents
Prelab = 5 points
When you took PHYS131/141 one of the first labs focused on experimental uncertainties in measured quantities and how to propagate them through calculations. Such calculations will be an important part of many of the experiments you will do in PHYS211. As a brief review complete the following exercises to be handed in at the start of the first day of lab. For a review of the methods of propagation of uncertainties this wiki page will be helpful .
- Create a problem involving calculating a rate with uncertainties on the number of counts and time.
- Create a problem involving subtracting a background from a gross count.
- Create a problem involving an exponential.
In order to prepare for the lab, it will be helpful for you to read over the full theory section below (Sec. 2) and in particular pay attention to the following concepts:
- What is an interaction cross section? You do not need to know how to derive it, but you need to know what it is conceptually and understand the relationship between a cross section and a linear attenuation coefficient. We give a brief description in this wiki in Section 2.2, but you can also use Google or Wikipedia to look for definitions.
- What is Thomson scattering? This will form the model against which we will test data in this lab. What does Thomson scattering predict for the cross section of gammas interacting with electrons? What are the limits of this model?
- How does a NaI+PMT detector work? What are the different features in a pulse height spectrum? You can read about photomultiplier tubes (PMTs), sodium iodide (NaI) crystals, and pulse height spectra here.
Goals
For your first lab of this course, you will conduct a high energy particle counting experiment to test the limits of a model describing the interaction of gammas with electrons within a material.
Counting experiments are a common type of experiment in the fields of high energy particle and nuclear physics, and comparing between predicted values (given by models) and measured values (given by precision experiments) helps scientists determine which models remain plausible explanations for the real world and which have to be abandoned. For example, the experiment which detected and measured the mass of the Higgs Boson was a test of the Standard Model of particle physics. That model predicted a particle that had certain known characteristics (e.g. the interactions that could produce it) and certain unknown characteristics (e.g. its exact mass), and scientists “discovered” the particle when they were able to show that experimental data was consistent with the predictions. Now, scientists continue to investigate the particle and measure its mass to ever increasing degrees of precision because even a small deviation from the predictions of the Standard Model could be evidence of new physics.
In this experiment, you will use a PMT+NaI detector to make measurements of the total interaction cross section, $\sigma$, of gamma particles (high energy photons) in an energy range from ~100 keV to ~1.5 MeV as they pass through different elements. You will use these measurements to test how well the Thomson scattering model predicts the cross section, and to look for evidence of different or additional processes that may also be present in addition to Thompson scattering.
Thomson scattering is a classical (i.e. non-quantum mechanical) model for photons scattering from electrons. We now consider Compton scattering to be a more complete and more accurate model than Thomson scattering, and we also know that – as described below in Section 2.1 – in certain energy ranges processes like the photoelectric effect and pair production also contribute to the cross section. For the purposes of this lab, we have chosen to test the Thomson model because (despite its incompleteness) the model makes reasonably accurate predictions over a range of energies. We want you to take data precisely and with care so as to probe exactly how far we can push this model: where does it hold, where does it break, and what can we learn from how the data deviate when it does break.
The purpose of this lab is not just to show that the Thomson model is incomplete; that is something which we already know. Rather, the goal is to learn how to perform an experiment to test a model to a high degree of precision and to gain insight into the considerations and complications which go into making such a measurement.
Theory and Apparatus
Interactions of photons with matter
Click here to see details on how photons interact with matter.
Photons interact with matter in the following three ways:
- photoelectric effect: a photon is fully absorbed by an atom, liberating an electron from the shell in the process; probable only at low energies where the incident photon energy is comparable to electron binding energies.
- Compton scattering: a photon electromagnetically “collides” with an electron, giving up some energy which the electron takes as kinetic energy; possible at all photon energies.
- pair production: a photon spontaneously splits into an electron-positron pair; possible only when the photon possesses more energy that twice the rest mass of the electron, $E \ge 2m_e c^2$ .
In Fig. 1, the linear attenuation coefficient is plotted for aluminum, as are the various components which contribute to the total. (A higher resolution PDF version – as well as PDFs for other materials – is available on the Linear Attenuation Coefficient Plots page.) Notice that this quantity is highest at low energies, but decreases by about four orders of magnitude as the energy changes from 10 keV to 10 MeV.
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| Figure 1: The linear attenuation coefficient for aluminum is plotted with individual contributions to the total shown. To read the logarithmic axes, you must interpret the values of the grid lines between numbered tick marks appropriately. Each grid line represents one tenth of the value of the numbered tick mark preceding it – and all gridlines between numbered marks represent the same numerical change even though they gradually become more closely spaced. For example, starting at the 0.2 mark on the y-axis, the next grid lines correspond to 0.22, 0.24, 0.26, … , 0.48, and finally 0.50 where there is a new numbered mark. The next set of gridlines will then be worth 0.05 (one tenth of 0.5) and the values continue as 0.50, 0.55, 0.60, … [Source: Harshaw Radiation Detectors Catalog] |
Cross section
Click here for a description of what a cross section is.
As a photon passes through a material, there is a probability of interacting with an electron (through one of the above interactions) which increases with thickness. After such an interaction, the photon either disappears (e.g. it is absorbed in the photoelectric effect or is converted to mass in pair production) or is scattered into a different direction (as in Compton scattering). Either way, we don't observe the actual process, but instead see only the consequence: for a steady number of photons incident on a material, the number of photons which pass through it without interaction decreases as the thickness of the material increases.
To see why this is the case, consider the following model, illustrated in Fig. 2.
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| Figure 2: A slab of material with a face of area A and thickness dx has an average number of electrons $NAdx$, each with “effective area” (or cross section) $\sigma$ |
Suppose we have a a small volume of material with a face of area $A$ and thickness $dx$. If this material has an electron density (that is, a number of electrons per unit volume) of $N$, and each electron has an “effective area” $\sigma$, then the fraction of the area which is covered in electrons is $(NAdx)\sigma /A = N\sigma dx$. (We know that electrons are point-like, but they can interact at a distance through the Coulomb interaction… hence the “effective” area.)
If a beam of photons with rate of intensity $R$ (number of photons per unit time) is incident on our slab, then the intensity will be reduced by an amount
| $dR = -N\sigma dxR$. | (1) |
Rearranging and integrating, we find
| $R = R_0e^{-N\sigma x}$. | (2) |
The rate of photons decreases exponentially as the thickness of the material increases. In this context, we call $\sigma$ the total interaction cross section. The standard unit for the cross section is the barn, where 1 barn = $10^{-24}\textrm{cm}^2$. As mentioned above, the cross section is energy-dependent.
The electron density can be computed from the material's mass density by
| $N = \rho Z/A$. | (3) |
where $\rho$ is the mass density (mass per unit volume), $Z$ is the atomic number (number of electrons per atom) and $A$ is the atomic mass (average mass of one atom). It is common to rewrite this equation not in terms of the cross section, but in terms of the linear attenuation coefficient, $\lambda = N\sigma$ such that
| $R = R_0e^{-\lambda x}$. | (4) |
The standard unit for the linear attenuation coefficient is the inverse centimeter, cm${}^{-1}$.
Inverting the linear attenuation coefficient gives us the radiation length, $X_0 = 1/\lambda$. The intensity of a beam of photons through a material will decrease by a factor of $1/e$ in one radiation length. Therefore, a material will make an effective “shield” against gamma radiation of a particular energy if it is at least several radiation lengths thick.
Sodium iodide detector and photomultiplier tube
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Think back to Sec. 2.1. There, we spoke of how photons interact with a material; in each possible process, the photon gives up some or all of its energy to the material as it passed through. If we had a way to measure the energy which was deposited in the material, we could tell when a photon was scattered or absorbed and how much energy it left in the process.
For this lab, we use a crystal of sodium iodide doped with thallium – NaI(Tl) – as our detector. Iodine is a high Z material (i.e. it has lots of electrons), so there is a large cross section for interaction. When a high-energy photon scatters in the crystal, electrons carry away the deposited energy and zip through the solid. These high energy electrons knock into other electrons and create many smaller energy events. In turn, the thallium dopant is excited, and when it quickly de-excites, new photons are emitted. Though the whole process is complicated, it is relatively fast (a few hundred nanoseconds) and the amount of light given off by the thallium dopant is proportional to the energy left by the initial higher-energy photon. This process is called scintillation.
In order to make use of this new scintillation light, the crystal is optically coupled to a photomultiplier tube (PMT). This tube is a series of plates (called dynodes), each held at a successively higher voltage potential. The scintillation photons released by the thallium are absorbed in the first dynode of the PMT and kick out electrons via the photoelectric effect. These electrons are accelerated toward the next dynode where they produce more electrons. At each stage the number of electrons kicked out exceeds the number of electrons coming in, so a small input signal gets “multiplied” into a larger output signal at the final plate. The multiplication factor of the PMT (and therefore the size of the final signal) is determined by the number of dynodes and the applied high voltage.
Summarizing, the Na(Tl) crystal coupled to the PMT reliably produces an output voltage which is proportional to the amount of energy deposited in the crystal by the incoming photon.
For more information, see NaI Detector Physics and Pulse Height Spectra.
Spectrum features
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The output signal from the PMT can be examined on an oscilloscope, but the main way we will study this signal is by processing it with a pulse-height analyzer (PHA). Such a device measures the voltage (or current) of the PMT output signal and places those pulses into channel bins in a histogram according to their amplitude (or total integrated charge). Since the pulse voltage and current are proportional to the amount of energy deposited in the crystal, we can interpret channel number as a proxy for photon energy.
If we collect these pulses over a period of time, we build up an energy spectrum. A typical gamma spectrum has several features, as illustrated in Fig. 3:
- If a photon manages to deposit all of its energy in the detector, the PMT signal will be proportional to the full photon energy and we will find a Gaussian peak centered on the true photon energy. This is called the full energy peak or photopeak.
- If the photon Compton scatters once before escaping from the detector, it will deposit only some of its energy in the detector. There is a range of possible energies which the photon can give up, and such events form a continuous region called the Compton plateau or Compton shelf. This plateau, however, does not extend all the way to the full energy peak; there is, instead, a maximum energy transfer which occurs when the photon is scattered through an angle of $180^\circ$. This maximum defines the Compton edge.
- Some photons initially travel away from the detector before scattering and changing direction back toward the detector. Such photons are called backscatter photons. In principle, backscatters can occur at many different angles leaving photons with many different energies. However, some geometries are such that scatters through particular angles are more likely to scatter back into the detector than others. For the vertical geometry used here, we are susceptible to 180-degree backscatters – photons which initially travel away from the detector, scatter off the table top, then pass back through the source into the detector.
- There is a nice relationship between the energies of the full energy peak $E_\gamma$, the Compton edge $E_{CE}$ and the 180-degree backscatter peak $E_{BS}$ : $E_\gamma = E_{CE} + E_{BS}$.
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| Figure 3: A pulse-height spectrum produced by Cs-137 with the prominent features labeled. The energy of the main photopeak is 662 keV. |
For more information, see NaI Detector Physics and Pulse Height Spectra.
Using the PHA Software
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PHA setup
For more information, see SpecTech Spectrometers and Software
Starting the software The software we will use for this experiment is called USX. It is designed to control and communicate with the SpecTech UCS-30 pulse-height analyzers. A link to the program can be found on the computer desktop. Before starting the software, makes sure the PHA is on and that the USB cable is connectedto the computer. If the program initializes correctly, a box saying “Loading hex files” should briefly appear and the device name should appear along the title bar. If you see the warning “No device connected” or if some buttons on the software appear greyed out or unresponsive, the program may not have loaded properly. Try turning the PHA off then on again and restarting the program. If that does not work, restart both the PHA and the computer. Sometimes, usually after a system update, Windows will need to reload the drivers for the UCS PHA. If the loading drivers message comes up when the PHA is first turned on, allow the process to finish. There are two drivers which need to be loaded and it typically takes a minute or so.
Setting the high voltage
The PMT high voltage (HV) for this experiment will be supplied by the PHA and the value is controlled in software. Make sure the high voltage cable from the PMT (the cable coming from the red output port labeled “HV”, not the BNC signal cable from the output labeled “sig”) is plugged into the positive voltage output on the PHA and turn the voltage on by clicking the “OFF” button in the upper left corner. It should now read “ON” and be red. (Yes… this is confusing notation. We can't change it.) The light on the front of the PHA indicating HV should change from green (off) to red (on).
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| High voltage when turned off | High voltage when turned on |
Set the high voltage to +1000 V. (Note that the voltage setting box does not display units… only numbers. The hidden units are in fact “volts”.) You may adjust the voltage down if needed later, but do not exceed +1000 V.
Good Geometry
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In order to perform an accurate count measurement, it is necessary to choose appropriate geometry. If we assume a point source of gammas and a detector with a circular face toward the source, then the gammas from the source which arrive at the detector all fall within the cone shown in Fig. 4.
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| Figure 4: An illustration of “good geometry”. Note that the absorber is of a slightly larger diameter than the cone formed by the gammas emitted by the source and that the material is placed approximately equidistant between source and detector face. |
Clearly, placing a scatterer between the source and the detector will reduce the number of gammas reaching the detector. However, if the scatter is smaller than the cone, some gammas will miss the scatterer and still be detected. On the other hand, if the scatterer is larger than the cone, some gammas which would have missed the detector will nonetheless scatter into it, artificially increasing the number of detections. A good compromise is to place the scatterer halfway between the source and the detector, with its diameter just slightly larger than the cone size at that position. We will call this setup good geometry.
As you change absorber thickness during the experiment, you may need to adjust the absorber holder position to maintain the absorber bulk at approximately the midpoint. Do not, however, change the overall source to detector distance once you have begun collecting data on a particular source.
Lab notebook
You are expected to keep a record of your work in a permanent lab notebook. There is no exact formula for what should go into a lab notebook. A good rule of thumb is to record everything which you would need to refer back to if you wanted to exactly reproduce your experiment at a later time, or that you might need to know when writing a paper on your results or explaining to a colleague what you did and how you did it.
Exercises
The experimental task is to measure the absorption cross section for gamma-ray's over a range of energies from 31keV to 1.27MeV for Al. An outline of the different tasks which need to be performed would look like this.
- For a given gamma-ray energy, measure the rate of gamma-rays reaching your detector as a function of absorber thickness.
- Plot these rates vs absorber thickness. The data should be well fit by an exponential function where the time constant of the exponent is related to the linear attenuation coefficient as described in the theory section.
- For each energy gamma-ray compare your measured linear attenuation coefficients with the values predicted by both the Thomson and Compton models.
Before you begin to collect data however you will complete a number of specific tasks, each of which is focused on a skill or technique which you need to understand in order to complete the experiment. Successfully completing these tasks, as determined by the instructors during the lab, will count for 40% of the grade of this lab.
Verify PMT Operation = 5pts
No scientist does an experiment by hooking everything up and taking the data. A significant amount of effort goes into making sure that you understand how your apparatus works and ensuring that everything is operating correctly. You will also spend plenty of time tracking down why your experiment is not working as you expect, and this is part of doing science. Oscilloscopes are one of the most common tools used in physics laboratories, they are especially useful when doing particle physics experiments and you will make use of them in most of your labs in this course. You already have experience working with digital scopes from your PHYS132/142 labs. For this exercise you will use a digital scope to verify that your PMT+NaI detector is operating properly. Do the following:
- Connect the output of your PMT to the digital scope. PMT's produce fast pulses so make sure to use the 50Ω terminator provided. Be careful not to connect the HV supply of the USX30 to the input of the scope. If you are unsure of which connections to make get assistance from an instructor or one of your fellow students.
- Apply positive 900V to the PMT and place a Cs137 source up against the NaI scintillator.
- Find the PMT pulses on the scope. Our PMT's output pulses which are negative polarity, have a fast risetime (order 10ns) and a longer decay time (order 100's of ns). The amplitude of the pulses will vary based on the HV (higher HV results in larger PMT pulses) and the enrgy of the gammas entering the NaI crystal as described in the theory section, but they should be somewhere in the range of 10's to 100's of mV.
- Obtain a stable trigger on the PMT pulses and use the cursor function of the scope to measure the amplitude, rise time and decay time of the pulses.
In your lab notebook we will want to see a sketch of what the PMT pulses looked like including notations of the measurementes you made. There is no need for estimating uncertainties for this task. We will also want to see the signal on the scope for you to receive credit for this task.
Collect and Evaluate a Pulse Height Spectrum for a Single Energy Gamma-Ray = 5pts
In this experiment you will need to collect pulse height spectra (PHS) for different radioactive sources as you vary the thickness of the absorber material. You will need to understand the features of a PMT+NaI PHS in order to properly select regions to be analyzed. In the theory section we describe the features of such a PHS and explain why they occur. For this exercise you will collect a PHS for Na22, which has two different energy gamma-rays, and identify all of the features which you find in the spectra.
Based on our description of the PHS for a monoenergetic source like Cs137, you should have a pretty good idea of what to expect for a source with two different energy gamma-rays. Replace your Cs137 source with a Na22 source and collect a PHS which shows both gamma-rays.
- Sketch the PHS you see in your lab notebook and identify and annotate the features which you observe including full energy peaks, Compton shelves and edges, back scatter peaks, etc.
- Use the cursor function in the USX software to measure the pulse height channel in which the different features occur, then use your knowledge of how the different features are formed and the known energies of the two gamma-rays to verify the features you have identified. Hint, the pulse height channel on the x-axis of the PHS correlates with the energy deposited in the NaI crystal. So if you know the channel of a gamma-rays full energy peak you should be able to calculate in which channel its corresponding compton edge should appear. Similarly you can verify that the two full energy peaks you identify are consistent with being produced by the known energy gamma-rays.
- All of the calculations should appear in your lab notebook to receive credit for the task. We will also want to see the PHS spectra on the computer.
- Save the PHS as a .csv file. You can use the python script provided to read and plot the spectra from the saved file. You can do this part out of the lab. Each partner must produce their own plot and we need to see it before the last day in lab.
Identify and assess uncertainties in measured quantities (except for total counts) = 10pts
When doing an experiment one of the most difficult but important things you need to understand is how well you know your measured quantities. If you are trying to show agreement or disagreement with a theoretical prediction or a model, or trying to measure a fundamental property of a particle like the mass of the Higgs Boson to a higher degree of precision, you must know how to assess the uncertainties in your measurements, both statistical and systematic.
For this exercise do the following:
- Identify what your measured quantities are going to be. Hint, there are three measured quantities in this experiment, one of which is the total number of counts in the PHA that correspond to a particular energy gamma-ray. We will deal with the uncertainty in this quantity in the next exercise. For now figure out what the other two measured quantities are.
- For each of the quantities determine what will limit how well you can know it.
To receive credit for this exercise you will need to articulate the answers to these two questions to one of the instructors. You do not need to write them out unless you wish to. You simply need to convince us that you understand what your measured quantitied are going to be and what limits how well you know the measured values.
Estimating the number of counts in a photo-peak = 10pts
The total number of counts in a photo-peak (N) is primary measurement you will be making in this experiment. Unlike measuring the time or thickness, estimating N involves a lot of subtle questions and you have to make decisions about how best to accomplish this. It would be easy if all of the pulses in the PHS represented a detection of the gamma-ray of interest. However this is not the case. Some of the pulses are due to random noise fluctuations in the PMT, or back ground radiation in the room not related to the source you are measuring. Some sources emit more than one gamma-ray energy, resulting in multiple overlapping PHS for each one.
As the experimenter it is up to you to make decisions about how to analyze the data. The purpose of this course is NOT to tell you some so called “right” way to make this particular measurement so that you get the “right” results. The purpose is to teach you how to identify the important considerations and how to deal with them yourself, because in research there is no one to tell you the “right” way of doing it. We will tell you that for the sake of simplicity in this lab you should focus on estimating the number of counts in the photo-peak corresponding to the gamma-ray of interest.
There are two obvious ways one can go about estimating the number of counts corresponding to a feature in a PHS in this lab. The first way is to use the functionality built into the USX software to define a region of interest. The second way, which may or may not be better depending on a multitude of factors, is to save the data from the PHS and fit the photo-peak to a functional form which accurately represents both the signal of interest and the background component.
For this task do the following. Collect a PHS of Cs137 without any absorbers, and use it for both of the following methods.
Using the USX software. (5 of the 10 points for this exercise)
The USX software allows you to use the cursor to read off the values of individual data points. You can also click and drak the cursor to hilight a region of the data (ROI) and the software will then calculate the gross and net counts in the ROI as well as the centroid and FWHM of the distribution in the ROI. You can use the help function in the software to get more details on what the software is doing.
If you understand what the software is doing, and you understand the features in the PHS you can use this simple method of defining an appropriate ROI and using the net counts as your estimate of N with good results. Doing so does however require making well informed decisions about where to place the boundaries of the ROI.
Use the USX software to estimate the number of counts in the 662keV photo-peak including the uncertainty in that estimate. Note that the software is calculating the gross counts which have a statistical uncertainty. It then estimates the number of counts in that region which are due to “background”, a number which also has an associated statistical uncertainty. Finally it subtracts the background counts from the gross counts to arrive at the estimate of for the Net counts, which means you have to propagate the uncertainties through that calculation!.
Do this several times, erasing and reselecting the ROI each time to get a sense of how sensitive the resulting net count is to the ROI boundaries you choose. This has important ramifications for how you use this feature in the experiment.
To receive credit for this part of the task we will want to see how you choose your ROI, either an accurate sketch in your lab notebook or a saved plot or screen shot. You need to record all of the measured values, with uncertainties in your lab notebook and show the calculations and propagation of uncertainties.
Fitting the Data (5 of the 10 points for this exercise)
Fitting your data can, if done properly, provide a better estimate for the number of counts in the photo-peak after accounting for background. Fitting the data is more time intensive however and the results can be more challenging to assess. For this exercise do the following, which can be done out of lab using the python scripts we provide.
Save your Cs137 PHS as a .CSV file and use the provided python scripts to perform a fit to the data. You will have to select a region of the data to fit, just as you did with defining the ROI in the USX software. You might have to try running the fit with different region selections in order to obtain the “best” fit you can. The script gives you a simple model of the data to fit to, a gaussian representing the photo-peak and a linear term for the background. You can always try to fit a more complicated functional form to the data, but for the purposes of this exercise just stick with the gaussian plus linear background and try to obtain the best fit that you can. For this part of the exercise we will want to see the final plot of your data with the best fit, the goodness of fit parameters, best estimates for the functional parameters and their estimated uncertainties. Be prepared to discuss what these parameters tell you about your fit and why you think that the fit is good or bad.
Evaluate possible source of systematic bias due to source-absorber-detector geometry = 10pts
Not all uncertainties in measurements are due to statistical fluctuations. In fact the most important and challenging uncertainties are those which are related to the details of how you conduct your measurements, how your instruments perform, etc. These uncertainties are referred to collectively as systematic effects. In this experiment one possible systematic effect which could in principle introduce a bias to your measured rates is the relationship between the positions of radioactive source, the absorber and the detector. We will use this particular systematic effect to illustrate the process for assessing whether or not how you setup the source-absorber-detector impacts the data you collect. We choose this particular potential systematic effect simply because it is one which is easy to understand and relatively straight forward to investigate at least roughly.
Read the section below on Good Geometry. In principle the geometry you use could bias your measurements. But how do you know if it is a meaningful effect? The answer is you identify how the geometry might impact your measurements and devise a mini-experiment to collect data that will reveal whether or not this is going to be a problem. For this task we want you to do the following:
- Explore the extreme cases of placing the absorber directly on top of the source, vs placing the absorber directly underneath the detector. Based on your understanding of what you are attempting to measure, i.e. a total interaction cross section, what undesirable effect might these two cases introduce in terms of the measurements you will be making? We will want you to articulate how you expect a potential bias to manafest itself in the data.
- Once you have a clear idea of what you are testing for, conduct a simple experiment which would reveal such a bias if it is in fact present. This experiment can be as simple as three measurements, or as complicated as you wish to make it.
- From the data you collect do you observe any impact on the data. If so what will you do to minimize or compensate for this potential bias.
To receive credit for this task we expect to see a description, including clear diagrams, of the experiment you devise in your lab notebook along with the data you collect and calculations you perform. We will expect you to articulate what you are testing for, how your experiment will work and what your results are.
Obtain linear attenuation coefficient for 662keV gamma-rays = 10pts
One of the biggest mistakes you can make as an experimental physicist is to sit down to an experiment with the expectation that you will collect all of your data and then analyze it later and expect things to work out. That never happens, regardless of how smart you are, how much experience you have in the lab, or how good your equipment is. !!Full stop period!!.
Doing experiments is hard. Doing them well is even harder. You save yourself a lot of time, and frustration by learning how to break an experiment down in to smaller chunks and make sure you understand each chunk as you build up to a complete experiment. For your final task, before going on to “do” the experiment, we want you to go through the whole process of data collection and analysis for one single energy gamma-ray. Doing this will reveal how well you understand what you are doing, it will reveal things which do not work as you expect and give you an opportunity to figure out what you are missing. For this task do the following:
- For the 662 keV gamma-ray of Cs137, collect a full set of rate vs absorber thickness data.
- Calculate your rates as a function of absorber thickness, including propagating all uncertainties.
- Plot your rates vs thickness and fit the data to an exponential.
- Extract the linear attenuation coefficient from the fit, with uncertainties.
- Compare your measured value to the literature value.
- Assess how well your measurement agrees with the literature value.
To receive credit for this task we will want to see the parameters of your experiment like PMT HV, distances between sources and absorbers and detectors in your lab notebook. Your also needs to include your raw data with uncertainties, tabulations of your calculated rates with uncertainties, calculations related to extracting your linear attenuation coefficient from the fit to the data, and the final comparison of the data to the literature value.
We provide jupyter notebook python scripts for you to use when plotting and fitting the data. Some of this work will likely be done outside of lab, but we want to see the results before you move on to collecting the rest of your data for the full experiment.
Note, the data you collect for this exercise will form part of your full data set for the experiment as a whole. There will be no need to retake this data, so it pays to take the time to do it right and understand what you are doing.
Full Experiment
Once you are finished with the skill building tasks you should be prepared to take a complete set of data for the remaining gamma-ray energies, 31keV, 511keV and 1.27MeV. So just do it, do not forget to continue recording relevant information in your lab notebook as you did for the exercises.
Final Results to be handed in one week from the third day in lab worth 60 points
You have one week to perform a full and complete analysis of the data you collect in lab. You will write up a full assessment of the results of your experiment. You will also submit your analysis which includes:
- A tabulation of your measured quantities along with uncertainties.
- Your plots of rate vs thickness for each energy gamma-ray including fits.
- Your calculations of the linear attenuation coefficients and propagation of uncertainties.
- A plot comparing your measured values to the predictions of the Thomson and Compton models.
Your assessment and conclusions should address blah, blah, blah…
Note, you are encouraged to collaborate with your lab partner on how to do the analysis, the plotting and fitting, the calculations, and what your conclusions are. But everything you hand in must be your own work! You have to make all of your own plots, perform all of the fits to the data, do all of the calculations yourself. You are not permitted to divide the work up with your partner doing one set of plots while you do the other set. Also, you are free to use and modify the python scripts which we provide. But you are not allowed to use your partner's code, you must do your own coding.
A good rule of thumb is that when you sign your name to your work you are attesting that everything in that body of work was done by you. Including work done by your lab partner without attribution is plagiarism which we something we take very seriously. Including work done by your lab partner with attribution is not plagiarism, but you will not receive credit for work not done by you.