Possible additional Gamma sources:

https://doi.org/10.1016/S0969-8043(02)00083-0

  • 912 keV from ${}^{228}$Ac
  • 1.12 MeV from ${}^{214}$Bi
  • 1.46 MeV from ${}^{40}$K
  • 1.76 MeV from ${}^{214}$Bi
  • 2.12 & 2.2 MeV from ${}^{214}$Bi
  • 2.6 MeV from ${}^{208}$Tl
  • 4.4, 3.9, 3.4 MeV from ${}^{12}$C${}^*$ metastable state & escape peaks
  • .2 and .5 MeV from ??? (.5 is likely betas)

https://doi.org/10.1016/j.nimb.2006.06.004

  • 59.6 keV from ${}^{241}$Am
  • 129.3, 203.5, 345, 375, and 314.7 keV from ${}^{239}$Pu

https://doi.org/10.1016/j.apradiso.2020.109175

Due to neutron capture from elements in stainless steel, might see:

  • 465 keV from Ni
  • 778 keV from Mo
  • 834 keV from Cr
  • 871 MeV from O

https://doi.org/10.1016/j.nima.2016.12.022

Due to neutron capture by iodine in NaI detector

  • 137 keV

https://doi.org/10.1016/j.apradiso.2015.05.011 Example gamma spectrum:

1-s2.0-s0969804315300300-gr9_lrg.jpg

Mass of the Neutron

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.

An overhead view of the neutron howitzer and NaI+PMT detector

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:

  • Confirm that deuterons are produced by the interaction of neutrons with protons.
  • Measure the mass of the neutron.

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.

A 30 second exposure of a 5“ diameter NaI crystal adjacent to a 250 $\mu \textrm{Ci}$ Na-22 source. You can see the faint blue light produced by the scintillation process as gammas from the source lose energy to electrons in the crystal. If you were to sit in a completely dark room for 15 to 20 minutes to allow your eyes to dark-adapt, you would be able to see this soft glow from the crystal with your own eyes.

Before you come to lab...


In order to prepare for the lab, you should read over the full theory section below, and – in particular – pay attention to the following questions. Some of these can be answered based on what you find in the theory section, but others may require outside research online. Make sure you can answer the following before you arrive for Day 1:

  • 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.) Look up the mass of the proton and the mass of the deuteron* and report the value (to as many digits as you can find). Provide a reference for your values.
    • *Note that the deuteron is a bound nucleus with one proton and one neutron, while deuterium is the bound state of a deuteron nucleus with an electron. The two have slightly different energies since there is some binding energy associated with the electron.
  • 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.
    • To make an order of magnitude estimate, approximate the mass of the neutron to be equal to the mass of the proton. Determine the gamma energy as the difference in rest energies between the deuteron and two times the rest energy of the proton. We know from other evidence (e.g. the beta decay of a free neutron into a proton, an electron and an antineutrino) that that the neutron is actually slightly heavier than the proton. Does this mean the expected gamma energy is larger or smaller than your estimate?

Theory

The neutron howitzer

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.

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.

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 mass of the neutron

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.

Exercises


Before you begin to collect the bulk of the data, 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 a total of 25% of the grade of this lab.

Completing these exercises will likely take most of the first one or two days of lab. Go slowly, and make sure you understand each step!

Energy calibration of the detector

The detector is a NaI scintillator coupled to a PMT. You are already familiar with this type of detector from the 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.

1. In-software calibration (5 points)

We will start by using the known energies emitted by ${}^{60}$Co as calibration references.

Do the following:

  • Make sure that the port from the neutron howitzer is closed.
  • Use lead to shield the detector from radiation produced by the howitzer.
  • Place the Co-60 rod source in the chamber in front of the NaI detector and photomultiplier tube (PMT). 
  • Verify that the high voltage and anode output cables are appropriately connected to the NaI detector. These cables should be routed through the wall into the next room. With the high voltage cable plugged into the power supply, turn on the voltage and set it to -1000 V.
  • Collect a spectrum. It may be necessary to adjust the coarse and/or fine gain to move all features on-screen.

  • If the “Dead Time” meter reads more than ~15%, move the source further away from the detector face to lower the count rate.

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.)

Figure 2: Neutron howitzer and the detector inside the lead “chamber”.

Continuing, do the following:

  • Collect a spectrum.
    • From the Nuclear Decay Schemes, identify the energies corresponding to the two emitted gammas and identify the corresponding features on the spectrum.

  • Remember that you ultimately will want to measure the centroid of a peak corresponding to a gamma of greater than 1 MeV (as determined in the Preparation Question). In order to make sure that such a peak will appear be on screen, adjust the gain so that energies of at least 3 MeV will be on screen. (You can assume that the relationship between channel and energy is linear.) Note the gain settings in your notebook.
  • In addition to the two peaks, you should find a third peak at higher energy (> 2 MeV). Can you explain the origin of this peak?
    • HINT: Consider both the typical time scale of a sodium iodide crystal pulse (look back to the notes from your first lab or plug the detector output into a scope) and the lifetime of the intermediate state in the relaxation of Ni-60 to the ground state as shown on the decay scheme.
    • Once you determine the origin of this peak and know its energy, this point can be used as a third calibration point.
  • In the drop-down menus, select “Three-Point Calibration” and use the values of the energy and channel to calibrate the x-axis.
    • Verify that the peaks now appear with the correct energies.

2. Calibration with additional sources (5 points)

The in-software calibration method described above has several limitations.

  • It does not incorporate the uncertainties on the measured peak channel positions.
  • It does not explicitly provide the fit function and does not provide uncertainties on the fit parameters determined.

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:

  • Collect additional spectra using the Na-22 and Cs-137 sources.
  • For each spectrum, record the full energy peak centroid values and identify the known energies that these peaks correspond to.

    • You may later fit the peaks to Gaussians, or you may identify the peaks “by-eye”; either is OK so long as you properly estimate uncertainties.
  • From the peak centers for all three samples, perform a fit to extract a function converting channel to energy, $E(ch)$.

    • However, since your dominant uncertainties are in the channel (peak centroid), it will be better to first fit $ch(E)$ and then invert the function (and the associated uncertainties).

Do not adjust the gain between calibration points!

Building evidence

In order to measure the mass of the neutron we are making the following assumptions:

  1. That energetic neutrons from the source are interacting with protons in the paraffin shielding material, producing capture gammas as described in the theory section above.
  2. That the rest masses of the proton and deuteron are already known from mass spectrometry. (You can look these values up in the literature.)

The experiment then boils down to identifying the capture gamma and measuring its energy. 

The detector can be used to measure the spectrum of the radiation coming from the howitzer with various shielding configurations. Once the full energy peak of the capture gamma has been identified, measuring its energy is straight-forward, assuming the detector has been calibrated as described in Sec. 3. The tricky part is demonstrating that the full energy peak is from the capture gamma which requires a bit of detective work. This task can be accomplished using the following:

  • Given assumption #1 above, the howitzer should be a source of capture gammas, regardless of whether or not the ports are open or closed. So, with the ports closed, the howitzer should be a strong gamma source with very little neutron radiation escaping.
  • When a port is open, it will emit a collimated beam of energetic neutrons in addition to the capture gammas.
  • We use three different materials that interact with particles and gammas in this experiment:
    • Lead bricks are provided for use in shielding the detector. Lead is more effective at attenuating gammas than neutrons. (Measure the ratio of gamma attenuation to neutron attenuation for the thickness of lead shielding that you choose to use.)
    • Paraffin (a material containing both protons in the form of hydrogen atoms, and carbon nuclei) blocks are provided.
    • Blocks of graphite (a form of pure carbon) are provided.

You will be expected to make measurements which not only demonstrate that capture gammas are being produced in the howitzer, 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.

3. Direct howitzer spectrum (5 points)

Now that you have a calibrated channel axis, you can measure the absolute energy of features that you observe in spectra.

Do the following:

  • Remove the lead shielding in front of the detector and collect a spectrum directly from the howitzer.
  • Take additional exploratory spectra as you see fit (e.g. with and without shielding, and with port open or with port closed).
  • Interpret what you see.

4. Establishing the logic (5 points)

Have you identified the gamma capture peak on your spectra?

While you may be tempted to measure the energy of that peak and call the experiment complete, we want to first build up evidence to support the hypothesis that the peak you see is in fact the peak produced by the gamma released during deuteron formation. (For example, how do we distinguish a gamma capture peak from a peak produced by a button source taped to the bottom of the howitzer or a peak produced by a strong background source in the room?)

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:

  • Take additional spectra and/or make additional measurements as needed to generate ideas for how you could show that the peak in question is in fact the capture gamma peak.
  • 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).

5. Attenuation studies (5 points)

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:

  • Identify suitable regions of the neutron howitzer spectrum to monitor. Where are you counting gammas? Where are you counting neutrons?

  • Determine how much different thicknesses of lead attenuate neutrons and gammas (separately).

    • It is possible to determine the attenuation coefficient like you did in the gamma cross sections (i.e. by plotting rate versus thickness and fitting to an exponential), but you do not need to do this. It is sufficient just just tabulate how much the rate changes at each thickness of lead that you choose.
  • From your above studies, determine the “optimal” thickness(es) of lead to use in your experiment(s).

Completing the data taking

Armed with a plan, you are now ready to build up your evidence and to make the most precise measurement of the capture gamma energy that you can.

It is expected in this experiment that you will take data, analyze it, revise technique and repeat – possibly multiple times – until you achieve statistically significant results.

As you progress, do not forget to continue recording relevant information in your lab notebook as you did for the exercises.

Final data analysis


You have one week to perform a full and complete analysis of the data you collect in lab and submit the following assignments. You can score up to a maximum of 75 points total on these assignments.

Establishing the origin of the capture gamma peak (25 points)

As a first step, establish the origin of the peak which you plan to claim as the capture gamma peak. Be quantitative and precise!

Do the following:

  • Present your full data in support of the argument that the peak you have identified is the capture gamma peak produced in the formation of the deuteron.
  • Outline the logic, and provide tables of values and/or plots where relevant.
    • What data or studies you include are up to you, but may include attenuation calculations, spectra (and/or tables of count rates) under different shielding configurations, fits, uncertainty calculations, background studies, etc.

Measure the mass of the neutron (25 points)

With the origin of the peak established, show how you use this peak (along with your calibration) to determine the mass of the neutron.

Do the following:

  • Discuss and/or show how you extract the capture gamma energy from your spectrum (or spectra).
  • Discuss your calibration methods and present data and fits related to your calibration.
    • Discuss (and if possible address) difficulties or ambiguities with the calibration.
  • Discuss how you determine the overall uncertainty in the capture gamma energy.
    • Provide data, plots, calculations, etc. in support of your uncertainty estimate.
  • Use your gamma energy to determine the mass of the neutron (with uncertainty).

Conclusions and comparison with literature (25 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:

  • Provide whatever table(s) of results and/or plot(s) that you think are relevant.
    • Even if you have included this material above, please summarize and conclude for the reader. Highlight the most important take-away quantities and make sure there is a clear, final message.
  • Discuss the agreement between the data and the literature (for individual points and/or overall, as appropriate).
  • Justify your results and discuss the context surrounding your measurements. This may include asking yourself the following non-exhaustive list of questions:
    • What do your results mean?
      • E.g., for someone who is hearing about this experiment for the first time, why are your results important and why is this experiment the right way to make these measurements?
    • Why should the reader believe your results and your estimates of uncertainties on those values?
      • E.g., what about your technique and data collection or analysis strategy gives the reader confidence in your work?
    • If you disagree with expectations, do you disagree in some systematic way or is it random?
      • E.g., consider your results in the larger physics context, and address anything which isn't consistent with what you (and other experts) know. Separate statistical uncertainty from systematic bias.
    • Is your experiment complete, or are there holes in the picture?
      • E.g., are there results that you cannot explain or disagreements that you cannot give plausible explanations for? Do you need more (or different data) to investigate the problem fully, or are there measurements that need to be retaken or rethought?
  • Consider shortcomings in your work or things that you would improve if you were to continue this experiment (e.g. changes apparatus or technique, alternate analysis methods, or different models). Point towards future directions of study.

References