The mass of charged particles – such as protons and electrons – can be investigated using mass spectrometry whereby a beam of such particles is bent by a magnetic field and the radius of curvature is measured. For chargeless particles – like neutrons – such techniques do not work and we must be more creative. In this experiment, you will use some known facts about neutrons to design and test an experiment with the goal of determining the mass of the neutron. This lab – unlike many others in this course – allows for a significant amount of creativity and will require you to measure, adapt, and iterate in pursuit of improved measurement techniques.
Warning - Do not attempt to access the neutron source until you have been shown how to work with it safely by a member of the lab staff or a TA.
We will use a source of high energy neutrons in the lab to perform studies on the interaction of neutrons with nuclei. You will devise a series of measurements which you will use to do the following:
You will not be provided with a detailed set of instructions on exactly what measurements to take. Instead, you will be given instructions on how to use the detector – a NaI+PMT-type which you should already be familiar with from Introductory Lab: Gamma Cross Sections – and it will be up to you to decide how to address the points listed above. As neither of the above points can be directly achieved by pointing the detector at the source, you will have to instead make measurements of indirect radiation and set up a logic based on different configurations of lead, paraffin, and carbon shielding.
It is not expected that you will figure out an optimal series of measurements on your first attempt. Progressing through the experiment will be an iterative process where you try out some ideas for collecting data, do some preliminary analysis, evaluate your results with the assistance of the instructors, refine your methods, and repeat.
In order to prepare for the lab, you should read over the full theory section below, and complete the prelab exercises.
Our source of neutrons for this experiment is a “neutron howitzer”. The core of the howitzer consists of 80-grams of ${}^{239}$Pu mixed homogeneously with ${}^{9}$Be. The plutonium decays with the emission of 5.18 MeV alpha particles at a rate of ~$2 \times 10^{11}$ decays/sec (or, about 5 Curies). Some of these alphas in turn interact with the beryllium to produce neutrons by the process
| $\sideset{^4}{}\alpha +\sideset{^9}{}{\textrm{Be}} \rightarrow \sideset{^{12}}{}{\textrm{C}} + \sideset{^1}{}{\textrm{n}}$ . | (1) |
Neutrons with energy up to almost 11 MeV are emitted from the source. Most of the alpha particles lose energy by ionization in the source before interacting, but approximately 4 out of every $10^5$ produce a neutron by the above reaction, giving a flux of ~$8 \times 10^6$ neutrons/sec.
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| The four ports of the howitzer should be plugged and locked when not in use and one should never look into a port or unnecessarily spend time in front of it. |
CAUTION: One must avoid being exposed to the direct beam of the neutron howitzer. (There is no danger in handling the small 1-10 μCi button and rod gamma sources used for calibration.) The radiation dose rates for the neutron howitzer, and maximum permissible doses are given in the Tables 1 and 2 below. (See Gamma Source Dose Rates for more information.)
| Port closed | Port open, in direct beam | |||
| At surface | 1 m from center | At surface | 1 m from center | |
| Neutrons | 5.0 | 2.0 | 22.0 | 12.0 |
| Gammas | 5.0 | 0.7 | 5.0 | 0.7 |
| Totals | 10.0 | 2.7 | 27.0 | 12.7 |
Table 1: Measured neutron howitzer radiation dose rates (in mrem per hour) due to neutrons and gammas, separately
| Whole body | Extremities | |
| General public | 100 mrem/year or 2 mrem in any one hour | Not applicable |
| Radiation workers | 5000 mrem/year | 50,000 mrem/year |
Table 2: Maximum permissible doses above background (where background rate is about 360 mrem/year)
To shield against these energetic neutrons, the source is surrounded by a thick layer (~30 cm in thickness) of paraffin, a molecular chain of hydrogen and carbon, $\textrm{CH}_2$. Recall that neutrons do not interact electromagnetically (they have zero charge), so the main method for energy loss is through collisions. Since neutrons and protons (i.e. hydrogen nuclei) have nearly the same mass, the neutron loses half its energy, on the average, for each collision with a proton. The mean free path of the neutrons in paraffin (i.e. the distance between collisions) is a few centimeters, so most neutrons which escape the paraffin volume have undergone enough collisions to lose most of their energy. When these neutrons do escape, they will have been thermalized (that is, reduced in energy to $E_{avg} = k_BT = 0.025 ~\mathrm{eV}$ ) and are no longer dangerous.
We do, however, want some safe access to the high energy neutrons, and this is achieved though the four side ports where the shielding can be removed. Each port has a plug made of lucite (another hydrocarbon material) which will thermalize or block neutrons when inserted, or allow a direct beam to escape when removed. The energy spectrum of the neutrons emerging from an open port of the source is shown in Fig. 1.
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| Figure 1: Experimentally-measured neutron energy spectra for two Pu-Be sources comparable in size to the one used in this experiment. (source: [1]) |
The cross sections for thermal neutrons can be enormous: $\sigma_{thermal} \le 10^{-16}\textrm{cm}^2$. Such values mean that thermal neutrons travel very short distances before being scattered. At higher energies, cross-sections are smaller and typically measured in barns ($1~\textrm{b} = 10^{-24}~\textrm{cm}^2$) and can penetrate to greater depths.
The fact that the neutron has no electrical charge makes it difficult to measure its mass. The mass of charged particles and nuclei can be measured through the technique of mass spectrometry. So, if we assume that the masses of the proton and the deuteron (a deuteron is a bound state of a proton and a neutron) are known from mass spectrometry, we can find the mass of the neutron from the following interaction by which deuterons are produced,
| $\textrm{n + p} \rightarrow \textrm{d + }\gamma$. | (2) |
A photon (called the capture gamma) is produced because the bound deuteron has a lower total energy than the separate neutron and proton. Using conservation of energy, if the masses of the proton and deuteron are known and the energy of the capture gamma can be measured, then the mass of the neutron can then be calculated.
If our neutron howitzer is indeed producing energetic neutrons, some of them should be producing deuterons and capture gammas by the process given in Eq. (2). A NaI+PMT detector can be used to detect and measure the energy of gamma-rays coming from the howitzer.
Measuring the energy of a gamma is easy. The experimental challenge lies in demonstrating that the detected gammas were produced by the formation of deuterons, as opposed to being from some other unrelated source of radiation. This is the part of the experiment which we are challenging you to figure out.
Submit your answers to the following prelab questions. They are due before the start of lab.
The mass of a charged particle can be measured by sending the particle with known velocity through a perpendicular magnetic field and measuring the radius of the circular orbit. (This is called a cyclotron.)
If you send a charge-less particle through a magnetic field, it’s trajectory will not bend. We therefore need to think of a different method for determining the mass of the neutron. Perhaps we can infer the mass by observing the formation of a deuteron ($n + p \rightarrow d + \gamma$), where $\gamma$ represents the energy released (as a photon) due to the fact that the bound state of the deuteron has a lower rest mass than the sum of the neutron and proton separately.
In order to complete the Day 1 analysis, there are three tasks to complete. Make sure to leave yourself enough time to get through all three.
The detector is a NaI scintillator coupled to a PMT. You are already familiar with this type of detector from Introductory Lab: Gamma Cross Sections. If you need to review how this detector works, see the NaI Detector Physics and Pulse Height Spectra page.
For this experiment, you will make use of the fact that the size of the pulses from the PMT is proportional to the energy of the gamma which struck the NaI crystal. Pulses from the PMT are sent to a SpecTech UCS spectrometer which measures their total integrated charge and displays a histogram of pulse height sizes on the computer. You can use radioactive sources which produce gammas of known energy to calibrate the pulse height axis.
We will start by using the known energies emitted by ${}^{60}$Co as calibration references.
Do the following:
It is important that you make detailed notes of how you perform this calibration in your lab notebook. It is likely that you may need to refine your calibration procedure after preliminary analysis of the data. In such a case, you will need to know exactly what you did and how you set things up. (Remember, for example, to record the distance between the howitzer and your detector cart in case either object is moved between sessions.)
The in-software calibration method described above has several limitations.
Therefore, it is preferable to collect data in raw channel number and then, at home, do a more complete calibration to convert from channel to energy.
NOTE: It does not hurt to do the in-software calibration described above even if you plan to do a better calibration later. When exporting the data in the *.tsv or *.csv format, both the channel number and calibrated energy values are saved. In this way, you may use the rough calibration values from the software as a guide while in lab, but do the proper calibration when producing final plots and analysis.
We can obtain additional calibration points from Na-22 and Cs-137. With these additional points, we can fit the data to a linear function and properly incorporate all of our uncertainties.
Do the following:
Do not adjust the gain between calibration points!
Before leaving lab today, discuss both your in-software calibration and the spectra/data you have collected for your calibration fit (needed for the Day 1 analysis) with a TA. You will need to complete the calibration fit at home, but if you have time to do it in lab, you may want to discuss that with the TA as well.
In order to measure the mass of the neutron, we are making the following assumptions:
The experiment then boils down to identifying the capture gamma and measuring its energy.
You will spend considerable time on Days 2 and 3 verifying that the gamma you are investigating is really coming from the deuteron reaction, but for this first day we will simply try to observe the direct spectrum of the radiation coming from the howitzer and make plausible identification of the features.
Once the full energy peak of the capture gamma has been identified, measuring its energy is straight-forward, assuming the detector has been calibrated correctly. The tricky part is demonstrating that the full energy peak is from the capture gamma which requires a bit of detective work.
You will spend the rest of Day 1 attempting to interpret the direct spectrum from the howitzer. You will spend the remainder of the experiment (Days 2 and 3) building up the logic (and evidence) to support your identification of the capture gamma full energy peak and making the best measurement of the neutron's mass as possible.
Do the following:
Save each spectrum that you collect as an *.spu file (so that you can look at your spectra within the lab) and as a either a *.tsv or *.csv text file (so that you can replot the data at home).
Take time to try to understand as much of the spectrum as you can, and note which features are strongly attenuated by lead and which features are less attenuated (or not attenuated at all) by lead.
Discuss your spectrum and interpretation with a TA before continuing to make sure you understand the important features and have identified/measured everything you need to.
The calibration is very sensitive to changes in the high voltage to the PMT; small drifts in the AC line voltage or changes in the responses of electronic components within the power supply (for example, as they heat up) can change the multiplication factor (and therefore amplitude) of the pulses created.
In order to look for evidence of this, you will want to re-collect the three spectra (Co-60, Cs-137, and Na-22) required for the at-home calibration, and perform the calibration fit again. You may find that the calibration has drifted, or you may not… but we suggest you perform multiple calibration measurements like this each day you are in lab.
For your Day 1 analysis, you will present your energy calibration and your initial interpretation of the direct howitzer spectrum. These tasks serve as the foundation upon which the rest of the experiment (establishing the origin of the capture gamma and making a precise measurement of the neutron mass) will build.
Do the following:
Describe how you performed the calibration. (8 points)
Show a plot and fit of the calibration data. (7 points)
Show the direct howitzer spectrum and identify the relevant features. (5 points)
Your Day 1 analysis is due by 11:59 pm the day before your next day in lab.
NOTE: If you plan to make any energy measurements today, you will need to calibrate again (and monitor the calibration for drift.)
On Day 1, you made a plausible identification of the gamma capture peak, but you will spend the remainder of the experiment establishing the logic needed to support this identification. (Put another way… how do we know that peak is from the deuteron reaction? Could is just be a button source taped to the bottom of the howitzer? Is it a gamma from the plutonium decay? Is it a strong background source in the room?)
As a first step, we need to learn how to isolate (and control) neutron flux and gamma flux (and to identify and verify where on the spectrum to identify features from these two sources).
Consider the following:
We provide lead bricks which can be used as shielding for the detector. We assume that lead is more effective at attenuating gammas than neutrons, but we can test this hypothesis (and quantify the rate of attenuation for both particles, i.e. the linear attenuation coefficient (just as defined in the Gamma Cross Section experiment)).
If we can establish that we have blocked “enough” gammas while still allowing “enough” neutrons through, then we can do some interesting experiments on Day 3.
From your exploratory studies, you have likely observed that the lead shielding causes different parts of the spectrum to be attenuated by different amounts. Your detector is sensitive to energy deposited by both gammas and by neutrons, and therefore it is possible to isolate parts of the spectrum that are due to neutrons only and parts of the spectrum that are due to gammas only.
Given the above, we should be able to determine how much different thicknesses of lead attenuate gammas versus how much they attenuate neutrons.
Do the following:
NOTE: If you plan to make any energy measurements today, you will need to calibrate again (and monitor the calibration for drift.)
Now that you have determined the appropriate thickness of lead to use as shielding (so that you eliminate the majority of the gammas produced from the howitzer without eliminating all the high energy neutrons), we can do some interesting experiments.
In addition to blocks of lead, you have at your disposal the following:
Can you design an experiment which lends evidence to the hypothesis that the peak you previously identified is the capture gamma peak?
You will be expected to make measurements which not only demonstrate that capture gammas are being produced, but but to quantify the result in terms of a statistical significance as well. As you work through this experiment do not forget to consult with the lab instructors who will challenge your results. Keep in mind that this is intended to be an iterative process where your analysis of initial measurements leads to new ideas and a better measurement. This experiment is more about learning the process of thinking through how to approach and improve a measurement than it is about obtaining the mass of the neutron.
Think about experiments you can do to bolster your claim. In addition to what you have used so far, you also have blocks of paraffin and blocks of graphite (pure carbon) available, if necessary.
Do the following:
When you have a concrete idea, write down the logic of your experiment(s) clearly (and be prepared to discuss and defend them).
When you think you have a reasonable experimental plan, speak with a TA or instructor. They will approve your idea (or ask you to revise and refine it).
Use your remaining time to collect a full set of data according to the logic proposed above. Remember that you need to establish not just that features qualitatively appear or disappear under different configurations, but that the count rates change in a statistically significant way.
When you have your full data set, consider how to incorporate all the data you have collected to make the best estimate of the neutron mass (and the uncertainty associated with that estimate).
Establish the origin of the peak which you plan to claim as the capture gamma peak. You will need to address the following questions (and possibly others):
Be quantitative and precise! (Do not just say that a feature “appears” or “disappears”, but instead talk about statistically significant rate changes.) It is critical that your descriptions of the logic are clear and well-motivated and that the data you present support your claims.
Do the following:
Present logic and data in support of the argument that the peak you have identified is the capture gamma peak produced in the formation of the deuteron. (35 points)
With the origin of the peak established, show how you use this peak (along with your calibration(s)) to determine the mass of the neutron. If possible, incorporate more than one measurement of the final gamma energy (from more than one spectrum) into the determination.
Do the following:
Provide the calibration plot(s) and fit function(s) used to determine energies for data included in your final plot. (5 points)
Discuss and show how you determine the capture gamma energy from your spectrum (or spectra), and convert that to neutron mass. (20 points)
You will need to write a complete and persuasive conclusion that includes a comparison of your results to expectations/literature and puts the results in proper context.
Do the following:
Quantitatively discuss the agreement between your measurement of the neutron mass and the literature value. (5 points)
Justify your results and discuss the context surrounding your measurements. (10 points)
[1] M. E. Anderson and R. A. Neff, "Neutron energy spectra of different size 239Pu-Be(α, n) sources", Nucl. Instr. and Meth. 99, 231 (1972). This work measures the neutron energy spectra of Pu-Be sources of various sizes.
[2] An exploration of lower energy gammas from iodine excitation that appear in the spectrum.